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Archive for November, 2006

Benford’s Law in the NFL

Posted by Doug on November 30, 2006

Benford's Law is a fascinating bit of mathematical trivia that has nothing to do with football. Yesterday's post was superficially related to it, so I'm using that as an excuse to introduce it to those of you who haven't seen it before.

Yesterday's post was about the yards that get rounded out of a players' fantasy point total in a lot of leagues. The amount of yards a player loses to rounding depends on the last digit of his rushing yardage total for each game. In the comments, someone asked whether the distribution of final digits on rushing totals is uniform leaguewide. Well, it doesn't appear to be exactly uniform, but it's pretty close.

digit Freq PCT
0 1521 0.077
1 2334 0.118
2 2472 0.125
3 2223 0.113
4 2123 0.108
5 1994 0.101
6 1883 0.095
7 1838 0.093
8 1703 0.086
9 1644 0.083

Now, a very different thing happens if you take a look at the first digits of rushing totals:

digit Freq PCT
1 5982 0.303
2 3146 0.159
3 2229 0.113
4 1923 0.097
5 1712 0.087
6 1439 0.073
7 1218 0.062
8 1133 0.057
9 953 0.048

Now that's clearly not uniform and far from it. And that's just what you'd be expecting if you know about as Benford's Law. Here is the wikipedia description:

Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one-third of the time, and further, larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is the leading digit less than one time in twenty.

That's almost exactly what we see with the NFL rushing data. Now you may be thinking at this point that the distribution of NFL rushing yardage leading digits is an artifact of the game itself. People rush for between 100 and 199 yards all the time, but hardly ever between 200 and 299. Maybe that's the explanation. But maybe not. Benford's Law is pretty pervasive. It applies to populations of cities and countries, to lengths of rivers, to stock prices, and even to the collection of numbers --- from whatever source --- that appear on the front page of the newspaper over a long period of time. In a whole lot of real life data sets, you'll find numbers with a leading digit of 1 much, much more often than numbers with a leading digits of 9.

You won't find the same pattern in all sets of data. If we did this with yards per rush instead of yardage totals, we would not get a similar distribution. If we looked at the heights of NFL players, the distribution of first digits would not follow Benford's Law. But it is remarkable that it applies to so many data sets including, at least roughly, rushing yardage totals.

Now let's investigate whether the Benford phenomenon, as observed in this case, is merely an artifact of the structure of NFL football games.

What if we measured rushing totals in feet instead of yards? LaDainian Tomlinson gained 327 feet rushing last week, Rudi Johnson notched 192 feet, and so on. Here are what the leading digits look like:

digit Freq PCT
1 5600 0.284
2 3539 0.179
3 3603 0.183
4 1366 0.069
5 1013 0.051
6 2012 0.102
7 587 0.030
8 547 0.028
9 1468 0.074

Not exactly the same pattern. But still far from uniform and still skewed in essentially the same way. Did you know that Rudi Johnson rushed for 5852 centimeters last week? Here is the distribution of leading digits of rushing yardage totals measured in cm:

digit Freq PCT
1 5780 0.293
2 2901 0.147
3 2193 0.111
4 1886 0.096
5 1602 0.081
6 1348 0.068
7 1211 0.061
8 1012 0.051
9 1802 0.091

Rudi also rushed for .0364 miles last week (that counts as a leading digit of 3, not zero). Here is the distribution of leading digits for the "rushing miles" totals of all games played in the NFL since 1995:

digit Freq PCT
1 5537 0.281
2 3442 0.174
3 2778 0.141
4 1591 0.081
5 2664 0.135
6 1398 0.071
7 1053 0.053
8 534 0.027
9 738 0.037

So it really doesn't have much to do with the fact that 100--199 yards is a more common total than 200--299, or anything like that. If that were the cause of the distribution of leading digits, then the pattern would likely disappear if we measured in some other units.

And that's actually the key to why Benford's Law works. For sets of data that have units, the distribution has to be (subject to a few caveats) one that is invariant to changes of units. It just so happens that the Benford distribution has that property.

If you find this interesting, the previously-cited wikipedia writeup has more information. If you want something more hardcore, check out the Mathworld entry.

11 Comments | Posted in Statgeekery


Posted by Doug on November 29, 2006

Back in the old days of fantasy football, people computed their teams' score by opening up the Monday morning paper and scouring the box scores. In those days, it made sense to have rules like "one point for every ten yards rushing" instead of the more sensible "one tenth of a point for every yard rushing." The norm back then was that 40 yards was worth the same as 46 yards or 49 yards: 4 points. That made it much quicker to compute scores.

Now everyone who plays fantasy football utilizes some web-based service that will automatically compute scores for you, subject to whatever rules you specify. So there's no need for the cludgy round-down rules.

But a lot of leagues --- inlcuding two of the three that I'm in --- have kept the old system anyway. As far as I know, no real thought was given to the scoring system when we transitioned to a web-based league management system. We just kept the rules the same. I'm sure a lot of leagues (most?) did likewise.

Take a look at poor Charlie Frye.

Charlie Frye
1 132 44 0
2 244 10 0
3 298 6 0
4 192 -2 0
5 173 12 0
7 149 1 0
8 141 19 0
9 236 27 0
10 165 28 0
11 224 27 0
12 186 5 0

Assuming a rule of "one point per 25 yards" passing and "one point per ten yards" rushing, Charlie has lost 12.5 points because of needless rounding rules. He is the most unfortunate player of 2006 in this regard. He's got a 98, a 49, and a 24 in the passing column, plus a handful of 7s, 8s, and 9s rushing. According to my calculations, more than 12% of the yardage-based points he should have gotten leaked away to nowhere.

There are several burning questions that need to be answered here: what are the all-time greatest leakage totals in a season? Are certain kinds of players more prone to leakage than others? Or is it just dumb luck? Do I have any personal leakage-related anecdotes to share?

According to my records, the biggest leakage total of the last ten or so years belongs to Shaun Alexander from 2002:

Shaun Alexander 2002
1 0 36 36
2 0 37 46
3 0 37 8
4 0 139 92
5 0 0 0
6 0 96 25
7 0 30 16
8 0 58 38
9 0 67 48
10 0 42 2
11 0 18 23
12 0 145 6
13 0 74 77
14 0 123 8
15 0 127 15
16 0 79 6
17 0 67 14

He lost 18.5 points that season.

Now, is it just dumb luck, or can leakage be predicted to some extent? Well, luck does play a role as it appears that, leaguewide, the digits 0 through 9 are all equally likely to be the last digit of a rushing yardage total. However, it's no coincidence that the wide receiver hit hardest by leakage in 2006 is Chris Chambers. Why? Take a look:

Chris Chambers
1 0 0 59
2 0 3 55
3 0 39 39
4 0 14 28
5 0 18 29
6 0 1 60
7 0 0 29
8 0 0 0
9 0 0 58
10 0 2 66
11 0 0 44
12 0 0 23

Chambers has been unlucky for sure. But since he runs the ball more than just about any wide out, he loses points due to rounding on both his rushing total and his receiving total whereas most receivers only lose it on the receiving side. Chambers has 77 rushing yards this year, but only 50 of them "count" in most fantasy leagues. Running quarterbacks (like Charlie Frye) suffer the same fate. If you want to avoid leakage, stick with one-dimensional players. Also, of course, stick with players that get the bulk of their points from touchdowns. Touchdowns don't leak.

My colleague Jeff Pasquino says that fantasy football teams are like vacations. Everyone is glad to hear that you had one, but nobody wants to hear about the details. Nonetheless, I can't help but share the story that prompted me to do this important work.

Before Monday Night Football, I had a 28-point lead on my opponent, who had Donald Driver and Ahman Green playing for him. I went to bed at halftime and woke up to a boxscore indicating that Driver and Green had combined for exactly 28 points. So it's a tie.

But then I got word that a 7-yard completion to Driver was incorrectly credited to Green. This is not terribly uncommon and the people in charge of these things generally issue a correction on Wednesday or so. If this change gets made (which it will), then the receving yardage will change from this:

Green 46
Driver 82

to this:

Green 39
Driver 89

Seven yards going from one player to another on the same fantasy team will cause a point to evaporate and thereby change a tie into a win for me. I must be living right.

So now let me tell you about this vacation my family and I just took....

6 Comments | Posted in Totally Useless

Rule change proposal: all-intradivision weeks

Posted by Doug on November 28, 2006

Normally I save this sort of thing for Fridays, but since I've been travelling and haven't had much time to blog, I'll trot out this rule change proposal post today. This is actually more of a scheduling change proposal. I would like to see all intra-division games played during weeks 12 through 17. No divisional games for the first eleven weeks of the season, followed by two consecutive round-robins within each division.

To some extent, this is a solution in search of a problem --- there's really nothing wrong with the current scheduling system --- but I think this could add some excitement to the season. In particular, if every team's last six games are within the division, then fans of almost every team could convince themselves that they're still in the race for at least the first 10 weeks of the season. If we can just get hot for those division games...

For the first few weeks of the season, I'm happy just to be watching football. For the next few, I'm watching as teams jockey for position going into the divisional games. Then the division games hit, and we'd be sure to have several crucial games every weekend. The season would be constantly building toward something. It'd be like a miniature set of playoffs before the actual playoffs.

For me, I guess this is also partially motivated by the fact that every year there are a few weekends where some garbage game is the featured simply because it's a rivalry game. I just don't give a rip about the pageantry that is Cowboys-Redskins or Jets-Dolphins or Raiders-Chiefs or, worst of all, Packers-Anybody. Nobody does (do they?), except for fans of those teams. Now, if the Cowboys and the Redskins are playing for a division title, that's good stuff. But Cowboys-Redskins for the sake of Cowboys-Redskins? I'm not into it. Under my plan, the networks can feature the rivalry games that have the most meaning.

Not that this is necessarily an argument in favor of my plan, but it's essentially how the college football season is structured: warm-up games at the beginning, with a few key matchups sprinkled in, then the intraconference games, with the biggest rivalries generally being played at the very end of the season.

I'm not sure I've made a compelling case here. What it boils down to is I think it'd be neat. The floor is open for comments on this or anything else pertaining to the structure of the NFL schedule.

26 Comments | Posted in Rule Change Proposals

The 49ers were pretty good in the 80s and 90s

Posted by Doug on November 22, 2006

A few days ago I told you about the 49ers' run of 285 straight games without a three-game losing streak. It lasted from week 1 of 1981 until week 7 of 1999.

During that time, San Francisco went 210-74-1, for a winning percentage of .739. Suppose you had a coin that came up heads 73.9 percent of the time. If you flipped it 285 times, what are the chances that you'd see a run of three straight tails in there at some point? About 98.4%, it turns out.

Football teams are not coins, of course. I'm not sure if the things that make football teams different from coins would generally make streaks more likely or less likely. On the one hand, there is some artificial balancing created by the schedule. Teams rarely play more than two consecutive games on the road or at home, for instance. On the other hand, if you believe in teams getting hot or going through slumps, then that would make football teams more prone to streaks than coins are. Even if you don't believe in those things, injuries probably make teams streakier than coins. In any event, I'm convinced that 1.6% is a decent estimate of a team's chances of putting together a run like that, given that they're as good as the 1981--1999 Niners.

So, while unlikely, it's not that crazy that the 49ers, as good as they were during that stretch, never lost three straight. No, the crazy part is that they were that good for that long. Take a look at the records of the other NFL franchises during that same period of time.

TM Record PCT
sfo 210- 74-1 0.739
mia 175-108-1 0.618
den 174-110-1 0.612
was 164-119-1 0.579
jax 40- 30-0 0.571
dal 162-122-0 0.570
pit 158-127-0 0.554
nyg 156-127-2 0.551
chi 155-130-0 0.544
oak 155-130-0 0.544
min 155-130-0 0.544
kan 153-129-2 0.542
buf 153-132-0 0.537
gnb 147-135-2 0.521
phi 140-142-3 0.496
sea 138-146-0 0.486
nor 135-149-0 0.475
cle 111-125-1 0.470
car 32- 37-0 0.464
nwe 132-153-0 0.463
sdg 130-154-0 0.458
ten 130-155-0 0.456
nyj 127-156-2 0.449
det 125-158-1 0.442
stl 125-159-0 0.440
cin 123-162-0 0.432
atl 112-172-1 0.395
ari 111-172-2 0.393
ind 102-181-1 0.361
bal 18- 34-1 0.349
tam 97-187-0 0.342

The difference betwen San Francisco and #2 is bigger than the difference between #2 and #15. They were nearly two wins per year better than anybody else for an 18-year period.

6 Comments | Posted in General, History

More on 13 vs. 14

Posted by Doug on November 21, 2006

Last week, following up on a comment from Bill M, Chase posted this fascinating data on how often teams win when they score a given number of points. The general pattern in the data is that teams that kick a lot of field goals tend to win more often than teams that score a similar number of points, but with more touchdowns. That sparked a number of interesting comments.

Many of those comments addressed the issue of correlation and causation. Just as rushing the ball 30 times is often an effect of --- rather than a cause of --- winning, so might be kicking field goals. On the other hand, there might be something "real" here. It might be that the ability to put together scoring drives is more important than the ability to score points. This would be related to various bits of conventional wisdom, such as that it's beneficial to control the clock and keep your defense off the field.

If the latter hypothesis is true, and if the ability to complete scoring drives is a persistent skill that teams have, then scoring 13 instead of 14 should signal success not just in the given game but also in future games.

To check this out, I looked at all teams that scored a given number of points and I checked their rest-of-season record. If 13 really is a better marker of team quality than 14 is, then teams that score 13 points instead of 14 in a given week ought to win more games not just in that week (that's what Chase showed) but for the rest of the season as well. To make sure I'm comparing apples to apples, I only looked at teams that were at home in the given week (so they'd have the same number of home and road games for the rest of the season).


Home teams that scored 13 points won 46.8% of the rest of their games (N=389).
Home teams that scored 14 points won 44.8% of the rest of their games (N=422).

Here is the full chart:

Score N WinPct
0 150 0.371
1 0 0.000
2 3 0.359
3 154 0.417
4 0 0.000
5 6 0.333
6 154 0.434
7 307 0.408
8 11 0.506
9 99 0.480
10 433 0.458
11 8 0.505
12 70 0.457
13 389 0.468
14 422 0.448
15 61 0.474
16 271 0.475
17 606 0.479
18 31 0.498
19 149 0.484
20 572 0.481
21 366 0.494
22 93 0.507
23 300 0.507
24 543 0.516
25 44 0.474
26 161 0.507
27 450 0.509
28 311 0.532
29 61 0.543
30 216 0.512
31 358 0.547
32 28 0.451
33 87 0.536
34 230 0.564
35 152 0.544
36 40 0.531
37 106 0.571
38 160 0.565
39 15 0.523
40 37 0.522
41 91 0.568
42 69 0.576
43 16 0.580
44 44 0.588
45 61 0.575

As you can see, the strange spikes are not as clear here. Thirteen is still "better" than 14, but 17 is better than 16, 21 is better than 20, 24 is better than 23, and 28 is better than 27.

Further, a breakdown of this table into winners and losers fails to point toward any kind of "ability to win by scoring 13 points instead of 14." Among just teams that won in the given week, teams that won with 14 points did better in the rest of the season than teams that won with 13. And this result held true basically straight down the line.

Score N R-o-S W% N R-o-S W%
0 152 0.373 0 0.000
1 0 0.000 0 0.000
2 3 0.359 0 0.000
3 150 0.415 4 0.506
4 0 0.000 0 0.000
5 5 0.347 1 0.267
6 137 0.427 15 0.508
7 291 0.399 14 0.554
8 11 0.506 0 0.000
9 73 0.452 26 0.558
10 347 0.441 77 0.533
11 6 0.417 2 0.769
12 46 0.412 24 0.542
13 252 0.453 134 0.499
14 319 0.430 101 0.507
15 28 0.415 34 0.523
16 117 0.454 153 0.493
17 332 0.460 269 0.500
18 12 0.467 19 0.515
19 57 0.446 92 0.509
20 208 0.439 360 0.504
21 168 0.443 198 0.537
22 34 0.484 59 0.517
23 67 0.465 230 0.522
24 176 0.462 369 0.542
25 18 0.459 26 0.484
26 28 0.422 134 0.525
27 92 0.408 358 0.536
28 77 0.425 233 0.566
29 8 0.411 53 0.563
30 14 0.468 202 0.516
31 58 0.488 299 0.558
32 3 0.200 25 0.480
33 10 0.502 77 0.541
34 26 0.565 203 0.565
35 16 0.533 135 0.546
36 4 0.367 36 0.545
37 6 0.464 100 0.578
38 9 0.406 151 0.575
39 3 0.533 12 0.520
40 2 0.359 35 0.532
41 4 0.531 87 0.570
42 1 0.400 68 0.577
43 0 0.000 16 0.573
44 0 0.000 44 0.588
45 0 0.000 61 0.577
46 0 0.000 4 0.574
47 0 0.000 11 0.592
48 0 0.000 27 0.566
49 0 0.000 14 0.532

[Table corrected at 10:30 a.m. central time]

This table is interesting both horizontally and vertically. Take a look at this chunk, for example:

Score N R-o-S W% N R-o-S W%
13 251 0.453 134 0.499
14 319 0.429 101 0.508

Losers who scored 13 did better than losers who scored 14, but winners who scored 14 did (very slightly) better than winners who scored 13. For each point value, the winners did better than the losers. The fact that the 14-point-scoring losers were the worst teams in the bunch lends some credence to the philosophy that a lot of those teams were probably overmatched, scored their second TD against a prevent defense, and lost by 10 or more.

The pattern is not exactly the same for the analagous slices of the table, like 16-17 or 20-21. But it is true that, in either column, the data is more smoothly increasing than it was in Chase's post. This says, I think (but I'm eager to hear comments), that the 13/14 disctinction is more about the particular game than it is about the team. Whether it's related to time of possession, number of scoring drives, or whatever, it's more effect than cause.

10 Comments | Posted in General

Chad Johnson / Consecutive losses

Posted by Doug on November 20, 2006

Chad Johnson's two-week stretch is the best since (at least) 1995.

Player Yr Weeks REC YD TD
Chad Johnson 2006 10-11 17 450 5
Drew Bennett 2004 13-14 15 357 6
Drew Bennett 2004 14-15 25 393 5
Jerry Rice 1995 16-17 26 442 4
Carl Pickens 1996 13-14 18 285 6
Marvin Harrison 2003 4- 5 17 334 5
Randy Moss 1998 13-14 11 269 6
Qadry Ismail 1999 14-15 13 373 4
Terrell Owens 2001 4- 5 17 301 5
Jerry Rice 1995 15-16 20 410 3
Patrick Jeffers 1999 16-17 12 325 4
Jimmy Smith 2000 1- 2 21 343 4
Terrell Owens 2002 11-12 20 337 4
Eddie Kennison 1996 15-16 13 328 4
Randy Moss 1998 12-13 11 316 4
Muhsin Muhammad 2004 10-11 12 241 5
Randy Moss 2003 4- 5 13 253 5
Jeff Graham 1996 12-13 16 313 4
Eric Moulds 1998 13-14 14 373 3
Qadry Ismail 1999 13-14 11 371 3
Marvin Harrison 1999 2- 3 20 301 4
Santana Moss 2003 9-10 16 267 4
Chris Chambers 2005 13-14 23 359 3
Terrell Owens 2000 15-16 26 412 2
Cris Carter 1995 11-12 24 294 4
Antonio Freeman 1998 15-16 15 289 4
Marvin Harrison 1999 1- 2 15 226 5
Isaac Bruce 1999 4- 5 11 286 4
Randy Moss 2000 5- 6 12 286 4

In other news, the Patriots lost to the Colts in week 9 and to the Jets in week 10. This was the first time they had lost consecutive games since weeks 15 and 16 of 2002 (the Jets capped off that one in New England too). That's a streak of 57 games without two straight losses.

I'm told that a graphic popped up on the screen during that game claiming that the 49ers had the record for longest such streak, 60 games. I can confirm that streak, it ended in week 6 of 1999. But I don't think it's the record. I show the Cowboys with a 67-game run that ended in week 9 of 1970. They did have a couple of instances of two non-wins in a row (loss-tie), but according to my data they have the record for the longest stretch of games without two consecutive losses.

Here is each franchise's longest run of games without losing two in a row.

== Ended ==
TM Streak YR WK
dal 67 1970 9
sfo 60 1999 6
nwe 57 2006 10
den 53 1979 16
mia 52 1975 10
min 51 1978 7
cle 48 1954 1
chi 46 1987 14
rai 45 1978 9
phi 45 2003 1
pit 44 1980 7
ram 43 1976 10
clt 40 1972 1
oti 39 1980 1
was 39 1992 1
buf 38 1992 6
gnb 37 1964 7
det 36 1955 2
nyg 32 1960 9
kan 31 1970 1
cin 30 1983 2
sdg 29 1980 6
nyj 27 1986 13
crd 26 1976 12
nor 26 1988 10
sea 26 2006 8
atl 25 1999 2
jax 23 2006 4
tam 23 2003 10
rav 17 2004 13
car 16 2006 2
htx 6 2004 10

With their win over Green Bay yesterday, the Patriots do still have a steak of 67 games without three consecutive losses. If they keep it going, they will set that record in week 6 of 2020, a few months after Tom Brady's 43rd birthday. The 49ers went nearly two full decades --- from week one of 1981 until week 7 of 1999 --- without a three-game losing streak. People like to talk about unbreakable records. 285 games without losing three straight has got to be about as close to unbreakable as they get.

Here is the longest streak for each franchise:

== Ended ==
TM Streak YR WK
sfo 285 1999 7
min 159 1979 11
clt 141 1972 2
mia 141 1986 5
cle 133 1970 9
gnb 123 1969 10
dal 122 1974 4
chi 113 1989 7
was 113 1978 14
den 111 1990 6
rai 99 1978 15
ram 97 1979 9
kan 92 1994 15
pit 87 1997 1
buf 80 1994 17
sdg 76 1983 9
nyg 76 1964 13
sea 75 1986 10
nwe 67 CURRENT
jax 65 2000 6
oti 63 1981 9
crd 56 1977 13
det 54 1955 3
phi 51 2003 2
cin 50 1991 3
tam 50 2003 11
nor 39 1991 14
rav 39 2003 1
car 37 2001 4
atl 35 2005 17
nyj 33 1970 5
htx 7 2005 2

Because I know you're going to ask, the Raiders went 327 games without four straight losses, ending in 1986. The Broncos went 339 games without losing five straight. That run ended in 1990.

Now, what about the longest streaks without consecutive wins? As you might have guessed, the Bucs hold that distinction:

== Ended ==
TM Streak YR WK
tam 63 1989 1
buf 62 1987 6
nor 49 1973 5
nwe 47 1991 16
oti 46 1984 12
nyj 45 1997 5
det 44 2003 10
dal 43 1990 12
ram 42 1994 1
atl 41 1969 13
crd 40 1960 6
cle 41 CURRENT
nyg 40 1975 14
clt 39 1983 5
sfo 38 1980 2
was 37 1963 3
rai 36 1963 1
htx 35 2004 4
kan 35 1978 14
chi 34 1976 1
mia 31 1970 3
phi 28 1977 1
min 28 1964 1
cin 28 1999 13
gnb 27 1959 2
sea 27 1977 14
den 27 1965 4
sdg 25 2004 1
pit 24 1970 5
car 22 1998 17
rav 20 2005 16
jax 18 2003 14

Each franchise's longest streak without three consecutive wins:

== Ended ==
TM Streak YR WK
tam 144 1992 2
nor 123 1978 9
den 106 1970 2
nyg 101 1979 8
det 94 1989 14
buf 90 1973 5
atl 87 1991 14
cle 86 CURRENT
ram 85 1995 3
chi 82 2001 5
nwe 82 1993 17
sdg 77 1976 3
pit 75 1972 7
gnb 75 1989 13
was 74 1964 12
htx 74 CURRENT
car 73 2002 3
phi 71 1960 4
crd 67 CURRENT
sfo 64 CURRENT
dal 64 2003 5
oti 63 1985 9
rai 61 CURRENT
sea 60 1984 1
cin 60 2003 12
mia 59 1970 4
nyj 58 1997 6
clt 57 1986 16
kan 57 1979 6
min 43 1986 4
rav 41 1999 15
jax 30 2004 3

9 Comments | Posted in General, History

More Rutgers/BCS thoughts

Posted by Doug on November 17, 2006

Sunday Morning Quarterback had a good post last week about Rutgers, the Big East, and the BCS. In the comments, someone named Solon makes this very good point:

... if no one had a problem sticking Miami and VT in the title game when they were in the Big East, it's foolish for them to take issue with Louisville making it now--because the conference is much better now than it was then.

That was before the Louisville loss to Rutgers. Ultimately, if Louisville had finished 12-0, I don't think there would have been that much controversy. Yes, some people from a certain part of the country would have gotten upset about it, and some columnists would have tried to stir the pot a little, but I really don't think it would have been any more controversial than Virginia Tech's 1999 title game appearance. It would be even less of an issue if West Virginia were the undefeated Big East team.

But now the question is: does the same thinking apply to Rutgers?

I think there will be very strong objection to an unbeaten Rutgers team playing in the championship game instead of a one-loss SEC or Pac 10 team in the apparently-very-unlikely event that that happens. I still haven't decided if I think that's justified or not, so I will instead focus on another question:

If Rutgers is undefeated and does not play in the title game, will that be because of Big East bias, or will it be because of preseason poll bias?

Every reputable ranking system I've seen (here are a few: I, II, III) say that the Big East is stronger than the Big XII and the ACC. So the question is, if Missouri or Texas A&M or Wake Forest had gone undefeated this year, would they be getting the same treatment Rutgers is now getting? If yes, then it's preseason bias (and/or reputation bias). If no, then it's Big East bias.

I don't have any evidence to back this up, but I happen to think that it's yes. The problem isn't that people are undervaluing the Big East. It's that people, even at the end of the season, haven't phased their preseason expectations out of their internal ranking algorithms.

Honestly, I haven't either, and that's why I believe Rutgers will lose to West Virginia (if not before) and make all this moot.

12 Comments | Posted in BCS, College

Two kicks are better than one

Posted by Chase Stuart on November 15, 2006

In one of the comments to Monday's post, loyal PFR reader Bill M. mentioned that teams that have scored 13 points have won a higher percentage of games than teams that have scored 14 points. This is a bit surprising; all things being equal, you'd expect that teams that score X points would always win more games than teams that have scored X-1 points. Over a long enough time, all other things should be equal. Right?

I looked at all NFL games since 1970, and calculated the winning percentage for each "Points Scored" number. Bill M. was right: teams that have scored 13 points have won 28.5% of their games, while teams that scored 14 points won just 19.9% of their games. Considering over 800 teams have scored 13 points in a game, and over 900 have scored 14 in a single game, there's no way we could quibble about the sample size.

So what's the explanation? You might think Simpson's Paradox comes into play: perhaps in the early years, when scoring was low, teams scored 13 points more often and won more games 13-10 than 14-10; in the more recent years, with scoring up, maybe teams lost more games 17-14 than 17-13. If that was the case, there wouldn't be any real advantage to having scored 13 points, because for each era, scoring 13 points should be less successful.

That's not the case though: In fact, from 1981-2005, teams that scored 13 points had a higher winning percentage in a given season (than teams that scored 14 points) in 23 of those years; in the two years that 14 "won", the difference was worth less than 2.5 percentage points in both years. In other words, this is overwhelming evidence to suggest that scoring 13 points is more highly correlated with winning than scoring 14 points.

I wasn't being sloppy with my language there: I'm describing exactly what we know, nothing more. It's easy to see evidence like this and jump to a causation solution. But I don't think you want to say "I want my team to score 13 points instead of 14, if given the choice" just yet. Remember, we are simply seeing some highly correlated numbers, and we know nothing yet about causation.

So what's the next plan? Look up the winning percentages for all points scored totals. PF stands for points for a team in a given game, N is the number of times since 1970 that a team has scored that exact number of points, and the last column shows the team's winning percentage in those games.

0 406 0.000
1 0 ----
2 6 0.000
3 466 0.011
4 0 ----
5 15 0.133
6 366 0.071
7 763 0.038
8 22 0.045
9 234 0.218
10 1056 0.140
11 23 0.261
12 153 0.307
13 869 0.285
14 954 0.199
15 126 0.429
16 572 0.495
17 1295 0.390
18 57 0.474
19 306 0.559
20 1076 0.566
21 792 0.461
22 164 0.567
23 623 0.705
24 1030 0.648
25 84 0.667
26 285 0.807
27 793 0.768
28 533 0.700
29 123 0.837
30 393 0.891
31 646 0.824
32 54 0.852
33 155 0.871
34 421 0.884
35 250 0.872
36 62 0.855
37 206 0.942
38 273 0.923
39 20 0.850
40 65 0.969
41 151 0.960
42 115 0.983
43 24 1.000
44 73 0.986
45 95 0.989
46 8 1.000
47 21 0.952
48 35 0.943
49 25 1.000
50 11 1.000
51 15 1.000
52 17 1.000
53 0 ----
54 3 1.000
55 11 1.000
56 6 1.000
57 1 1.000
58 4 1.000
59 3 1.000
60 0 ----
61 3 1.000
62 4 1.000

In general, there's what you would expect: a positive correlation between points scored and winning percentage. The R^2 of 0.861 affirms that. Here's where it gets interesting though.

I restricted the range from teams that scored 5 points to teams that scored 42 points. You might think there's a general linear trend: but a linear trend line has an R^2 of just 0.93. A binomial trend line has an R^2 of 0.96. While these numbers are very close, and show the general trend, there's a reason we won't get to 1.00: the numbers have spikes in them for a reason.

If you look a bit closer at the data, multiples of 7 (+0 and +9) reveal some interesting data.

9 0.218 14 0.199
16 0.495 21 0.461
23 0.705 28 0.700
30 0.891 35 0.872

That chart there explains most of the bumps in the data. Sure 13 has a higher winning percentage than 14 (and higher than 9), 20 higher than 21, and 27 higher than 28, but these ones are particularly interesting. I don't know anyone that would have guessed teams that score 21 points in a game have a worse winning percentage than teams that score sixteen points.

So what's the reason? Once again, I caution anyone from jumping to conclusions here. It's easy to spot the correlation, but not so easy to figure out the causation.

On one level, each pair is an example of Simpson's Paradox. Every time a team scores 20 or 21 points, and lets up fewer than 20, it wins; every time it scores 20 or 21, and allows more than 21 points, it loses. And every time a team scores 21 points and allows 20 or 21, it never loses; every time a team scores 20 points and allows 20 or 21 points, it never wins. The reason for the higher winning percentage is that more often when a team scores 20, its opponents score fewer than 20. The key question, is why.

Here's some more data. For teams that score 20 points, the most common points allowed number is 17, which also happens to be the median. For teams that score 21 points, the mode is 24, and the median 23. When teams score 20, 15.8% of the time they have allowed 17 points; when scoring 21, just 7.7% of the time have they allowed 17 points.

This chart shows how many times a team that scored 20 or 21 points, allowed X number of points or fewer in a game.

20 21
0 2.8 2.5
1 2.8 2.5
2 2.8 2.5
3 6.0 3.9
4 6.0 3.9
5 6.0 3.9
6 9.0 5.4
7 13.8 9.7
8 14.0 9.8
9 15.0 10.9
10 21.6 16.3
11 21.6 16.7
12 22.7 17.0
13 28.8 19.9
14 34.1 25.9
15 34.9 26.0
16 37.7 30.2
17 53.5 37.9
18 53.7 38.6
19 55.9 40.7
20 57.2 45.8
21 61.1 46.3
22 62.1 47.6
23 71.3 51.5
24 76.8 61.7
25 77.3 62.2
26 80.1 64.4
27 85.2 70.1
28 86.7 75.0
29 87.1 76.8
30 89.1 78.7
31 91.4 83.8
32 91.4 84.2
33 91.9 85.0
34 93.8 88.5
35 94.7 90.7
36 95.2 90.7
37 96.2 92.6
38 97.4 94.3
39 97.5 94.4
40 97.7 95.2
41 98.6 96.1
42 99.2 97.0
43 99.2 97.0
44 99.3 97.3
45 99.5 98.1
46 99.5 98.1
47 99.5 98.2
48 99.7 98.5
49 99.8 99.0
50 99.8 99.2
51 99.8 99.4
52 99.8 99.6
53 99.8 99.6
54 99.8 99.6
55 99.9 100
56 99.9 100
57 99.9 100
58 100 100

I don't really know what's driving those numbers, but they're certainly thought-provoking.

Now, onto the main topic of the post: Are two kicks (two FGs) better than one (one XP, following a TD)? Teams that score 6 points have higher winning percentages than teams that score 7, and the lower scoring pair has a higher winning percentage at 13/14, 20/21, 27/28 and 34/35. So indeed, it does look like two FGs is better than one TD, plus 0, 1, 2, 3 or 4 TDs.

So what does it mean? Surely if your team is playing and down 17-14, and then scores a TD, you won't root for them to miss the XP so your team hits 20 instead of 21. And I don't quite think you want to root for you team to get 2 FGs instead of a TD just yet, either.

My guess is that there's another factor driving all this. One plausible theory is that it's time of possession. Consider this hypothetical, but realistic, TOP breakdown. Under 20 and 21, I've listed my estimates at the winning percentages.

TOP           20       21
25:00 .400 .420
30:00 .500 .520
35:00 .600 .620

At each of those levels, the team scoring 21 points has a higher winning percentage. But what if the number of games that fits that criteria looks like this:

TOP           20     #20      21    #21
25:00 .400 100 .420 640
30:00 .500 140 .520 310
35:00 .600 760 .620 50

If that was the case, teams that scored 20 points would have won 56.6% of their games, while teams scoring 21 points would have won just 46.1% of their games. But it wouldn't be because scoring 21 is worse than scoring 20; it's just that five minutes of time of possession is worth more than a point, and teams that score 20 points generally hold the ball longer than teams that score 21 points. After all, to score 20 points you usually need four scoring drives, not three, and that *might* mean your offense is on the field less.

This is just one theory, of course. There's got to be something driving the numbers, because the sample size is significant, and the pattern is very clear. I'd hesitate to say I'd want my team to score 9 points this weekend instead of 14, but I wouldn't disagree if you said a team is more likely to win if it scores 9 points instead of two touchdowns. But keep in mind, the reason the team is more likely, is because scoring 9 somehow helps your defense a lot more than scoring fourteen.

The time of possession theory is just one; there may be others. I'm curious to hear the comments today, to see if there are any other explanations for why two kicks are better than one.

64 Comments | Posted in General

Technical Analysis in Review

Posted by Chase Stuart on November 14, 2006

On Wednesday and Friday, I took a stab at predicting the games for week ten of the 2006 season. In a perfect world, I would have empirically explained how confident I was about each game, because then it would be simple to analyze how successful the system was. I didn't do that on purpose though, because I know you can't tell much from just one week. So instead of a big table summarizing the results, you're going to have to sift through some text today.

Tennessee @ Baltimore
Prediction: Tennessee (+9) pulls the upset. History shows that 6-2 teams are 7-7 against 2-6 teams, and hosted exactly half of those games. Road 6-2 teams are just 2-5. This game’s a coin flip, so the smart money would be on the Titans.

Result: Baltimore 27, Tennessee 26. Tennessee +9 was easy money this game, so this was a very good prediction.

Buffalo @ Indianapolis
Prediction: Colts (-11) win. Home 8-0 teams are 2-0 against 3-5 teams. Yes, you won’t get this type of analysis anywhere else: 8-0 teams are good! Against the spread this one is a toss-up, and is a game I’d avoid.

Result: Colts 17, Bills 16. I'm not going to give myself any credit for the Colts winning, but I'm glad I decided to avoid taking the Colts and the points.

Cleveland @ Atlanta; Houston @ Jacksonville
Prediction: Atlanta (-9) Jacksonville (-10.5) in romps. Road 2-6 teams are just 1-8 against these opponents. Against the spread, I’d probably avoid both of these games. Of those nine previous matchups of road 2-6 teams, the margin of victory was between 8 and 11 points in four of them. (For those curious, the one team to win was the 1978 Chargers in Oakland.)

Result: In two of the biggest upsets of the weekend: Cleveland 17, Atlanta 13; Houston 13, Jacksonville 10. The history seemed to match our intuition: a road team with three fewer wins shouldn't have a very good chance of winning. Part of the problem here, I think, is that we've got the two most difficult teams in the NFL to bet on, Atlanta and Jacksonville. It's always difficult to tell if Jacksonville and Atlanta are good teams that play bad games, or bad teams that play great games. In hindsight, I'm very glad I advised avoiding these games. As an aside, Houston is now 6-4 all time against the Jaguars, and 15-48 against the rest of the NFL.

Green Bay @ Minnesota
Prediction: Green Bay +5. 3-5 teams have actually won 9 of the last 13 matchups, and seven of those were on the road. Road 3-5 teams are 5-7 overall though, so this game is really just a coin-flip. I’d take Green Bay, with the five points.

Result: Green Bay 23, Minnesota 17. Green Bay was in control for most of this game, and the only way the Packers weren't going to cover was if this one went into overtime. I think most people saw Minnesota as the team with a better record, and at home, and the line was set that way. But this is a good example of how a road team with just one fewer win isn't at much of a disadvantage.

Kansas City @ Miami
Prediction: Kansas City (-2.5) seems like a strong bet; road 5-3 teams are 4-1 all time. As is the case in this specific matchup, generally 5-3 teams are playing for the playoffs, while 2-6 teams have less at stake. History isn’t a great guide here though, so be careful basing much on the sample size of just two games since 1990.

Result: Miami 13, Kansas City 10. As a football fan, I'm very surprised with this one. The Chiefs had been red hot, and the Dolphins just aren't very good. I imagine that now lots of people will expect another second-half surge from Miami (I can't believe that's Miami's new reputation), but I'm far from convinced. I noted the small sample size (good), but a team with three more wins shouldn't be expected to lose very often, especially one playing as well as the Chiefs.

N.Y. Jets @ New England
Prediction: New York (+10) is a strong play. Road 4-4 teams are 8-8 against 6-2 teams since 1970, so getting ten points in a coin-flip game looks good.

Result: New York 17, New England 14. The Jets were actually in control of this one the whole way, and were never in danger of losing by double digits.

San Diego @ Cincinnati
Prediction: San Diego (-1). This game is almost a coin-flip, and it’s properly viewed as one. I’d stay away from betting on this one.

Result: San Diego 49, Cincinnati 42. This game was crazy, and went down to the final minute. Certainly a good game to avoid betting on, and the only reason I took the Chargers was because I'm a big fan of Rivers and Schottenheimer.

San Francisco @ Detroit

Prediction: San Francisco (+6) covers against Detroit. I’m pretty surprised to see a 2-6 team favored over anyone with a better record, but I’ll give the market some credit for this one. I’d expect Detroit to win (after all, road 3-5 teams are just 1-3) but six is a lot of points to give. I wouldn’t bet this game, but I think SF covers.

Result: San Francisco 19, Detroit 13. While I thought the 'Niners would -- and they won outright -- this is another good example of why we need more than technical analysis. I didn't know at the time that James Hall (in addition to Shaun Rogers) would be missing the game, which would of course had been irrelevant to the "system". But without those two, Frank Gore rushed for 148 yards in the first half. The sample size was pretty small, so I avoided betting on this one.

Washington @ Philadelphia
Prediction: Washington (+7) is what the numbers would tell me. Of course, Philadelphia could really be 7-1, so I’m not sure how similar they are to similar 4-4 teams of years past. The only thing I know is that there’s no way I’d want to bet on this one.

Result: Philadelphia 27, Washington 3. It was pretty obvious that the Eagles weren't your typical 4-4 team, I'm glad I didn't let the numbers sway me here. Remember, garbage in, garbage out.

Denver @ Oakland
Prediction: Oakland (+9.5). Yes, I know this sounds like near insanity. In fact, I didn’t type “Oakland (+9.5)” without bursting out laughing. ... Oakland is terrible, and Denver has had Oakland’s number, despite the Raiders being pretty good for a number of years. I wouldn’t want to bet a lot of money on Oakland covering, but I think they will.

Result: Denver 17, Oakland 13. This is actually the prediction I was most proud of this weekend. All the numbers seemed to indicate betting hard on the Raiders, but who in their right mind could do that? The Seahawks sacked Andrew Walter on three consecutive plays on Monday Night, but six days later the Broncos only brought Walter down three times all afternoon. The Raiders led for the majority of this game, and almost won it outright. Like the Tennessee game -- another prediction that would have seemed crazy -- the numbers really like the Raiders here. Score one for the system.

Dallas @ Arizona
Prediction: Bill Parcells doesn’t pull a Kevin Gilbride and Ray Rhodes on us, and Dallas (-7) wins easily. Ok, so I didn’t really follow my system there. Road 4-4 teams are just 3-2 against the 1-7 teams on the road, but two of those wins were by 57 points. Dallas covers the seven point spread.

Result: Dallas 27, Arizona 10. I wasn't nearly as happy with this prediction. History really wasn't on my side, but I just used some subjective thoughts: Bill Parcells is pretty darn good, and Dennis Green and the Cardinals are terrible. On the other hand, 40% of the previous games were blowouts in the good team's favor, and so was this one. Too small of a sample size to bet much on, but I did like Dallas even giving a TD.

New Orleans @ Pittsburgh (2-6)
Prediction: New Orleans (+4.5). History tells us this game is a coin-flip. Taking the points with a team that has won four more games seems like free money.

Result: Pittsburgh 38, New Orleans 31. This was the Steelers game from the opening kickoff. Pittsburgh was certainly one of the best 2-6 teams in recent memory, and history told us this game was a coin flip. That being said, you have to like getting 4.5 points on those type of games, because more often than not you'll be a winner. This was not one of those times.

St. Louis @Seattle
Prediction: Seattle (-3.5) covers; home 5-3 teams are 13-3 against road 4-4 teams. Sure the Seahawks record is inflated a bit, because Alexander and Hasselbeck were a big part of those five wins, and won’t play on Sunday. But 13-3 is pretty strong evidence, and I like Wallace and that home field.

Result: Seattle 24, St. Louis 22. The Seahawks won, which is good; they didn't cover though, which is bad. I wasn't surprised to see them win this one, but they came up a couple of points short.

Chicago @ N.Y. Giants
Prediction: New York (+1) wins. A 7-1 team has never beaten a 6-2 team since the merger. ... I know the Bears lost to Miami, and got outplayed by Arizona, but I’m a bit surprised to see a Giants team without its top two receivers favored in this one.

Result: Chicago 38, New York 20. Plaxico Burress ended up playing, and for most of the first half New York looked like the much better team. Things got out of hand after that though, and Devin Hester's touchdown return was the icing on the cake. Certainly a very ugly game for the "system".

Tampa Bay @ Carolina
Prediction: Tampa Bay (+9.5) covers. Sure, 2-6 teams are 3-14, and 1-6 on the road. But of those seven road games, only once did the 2-6 team lose by more than ten points.

Result: Carolina 24, Tampa Bay 10. Tampa was up 7-0 at halftime, but things went south quickly for the Bucs after that. This looked like a pretty good bet, but with just over three minutes to go the Panthers scored another TD.

Final results
Like every other system ever designed, this one got some of them right and some of them wrong. History gave us the Jets, Titans, Packers and depending on your risk tolerance (or gambling addiction), the Cowboys, Raiders and 49ers. Alternatively, all signs pointed to the Giants, Seahawks, Saints, Bucs and, depending on your risk tolerance, maybe the Redskins and Chiefs covering. Atlanta, Jacksonville, Indianapolis and San Diego were all in games that history said was too close to wager on.

On the positive side, history strongly pointed towards the Jets, Raiders, Ravens and Giants covering, and they did win three of those four. The Giants were depleted by injuries, and probably weren't really representative of a team that had won six of its first eight games. There were three games this weekend featuring 2-6 teams hosting 6-2 teams, and history said that those games were 50/50. All were close and decided by a TD.

On the negative side, some of the glaring defects of this system came out. The Giants and Seahawks (and to a lesser extent, Lions) were hit with some big injuries, and that wasn't taken into account. The Eagles were much better than your typical 4-4 team. The Steelers were worlds better than your typical 2-6 team. And comparing the Jaguars and Falcons to any average group of teams is a recipe for disaster.

Overall, I think the system had slightly more hits than misses this week. That's good. There are definitely some tweaks available for the system, and intuitively you would think that would improve the success of the system. But the fact that the Eagles weren't your typical 4-4 team, and the Giants were depleted with injuries, was reflected in the betting line. In games that are blowouts, it's easy to get frustrated with the system. I'll have to spend a bit more time stewing on ways to improve this.

Unfortunately, time constraints prevent me from running the numbers again this week, and most likely the week after as well. Depending on how things go, I might come back for week 13, which of course will have even more data available.

San Diego/Denver

There's a lot of content coming this week, so I'm just going to throw this tidbit at the end here today. Over the next four weeks, we'll see the Chargers and Broncos play twice. It's not that rare for two very good teams to come from the same division, but it's not exactly common either. Since 1970, there are 19 pairs of teams that played in the same division and won at least 75% of their games.

Interestingly enough, ten times there was a sweep of the season series. Five times the team with the better end of season record would sweep, twice the teams would have the same record, and two more times the worse team actually swept. In 1999, the Jaguars went 14-2 and the Titans went 13-3, but Tennessee swept the Jags. To add insult to injury, the Titans eliminated the Jaguars in Jacksonville in the AFC Championship game. In 2001, the Green Bay Packers (12-4) swept the Chicago Bears (13-3), but both teams lost in the second round of the playoffs.

Six of those nineteen pairs of teams would meet again in the playoffs, which of course could also happen this year. Twice -- the 1999 Titans/Jaguars, and the 1986 Giants/Redskins -- there was a season series sweep, and both times the previous victor would prevail again in the playoffs.

One last note: don't let the venue affect your thinking too much. Home teams are just 17-19 in these types of games. (Of course, it's very possible that one team will fail to reach 12 wins, which would put them out of the study.) We're lucky this game's on national television, and I think it will be one of the best of the season. The Chargers have scored the most points in the league (297) while the Broncos have allowed the fewest points in the NFL (111).

15 Comments | Posted in General

Close series

Posted by Doug on November 13, 2006

Rams fans have got to be smarting after another heartbreaking loss to the Seahawks on a last-second field goal. Perhaps you Ram-backers can take some solace in the fact that you're not alone. Here are all other instances (since 1970) of a team losing twice in the same season to the same team by two points or fewer each time:

TM1 TM2 YR Scores
kan sdg 1986 24-23, 42-41
buf nwe 1974 29-28, 30-28
cin pit 1980 30-28, 17-16
bal nwe 1981 23-21, 29-28
jax bal 1997 28-27, 29-27

While we've got the program fired up, here is a list of the opposite kind of series: those that were split, but with blowouts in both games:

TM1 TM2 YR Scores
kan sea 1987 41-20, 14-43
dal was 1986 14-41, 30- 6
nyg was 2005 20-35, 36- 0
cin hou 1990 17-48, 40-20
bal mia 1970 17-34, 35- 0
oak sea 1995 34-14, 10-44
dal was 1993 38- 3, 16-35
det min 1980 0-34, 27- 7
nwe nyj 1979 26-27, 56- 3
cin hou 1989 24-26, 61- 7
bal mia 1973 0-44, 16- 3
cin hou 1988 6-41, 44-21
mia nwe 1971 41- 3, 13-34
chi gnb 1980 6-12, 61- 7
cle pit 1989 51- 0, 7-17
buf nwe 2003 31- 0, 0-31
atl nor 1982 35- 0, 6-35
buf ind 1987 27- 3, 6-47
kan sea 1984 34- 7, 0-45

9 Comments | Posted in General, History

Rule change proposal: pick your playoff opponent

Posted by Doug on November 10, 2006

As you can see, I'm opening up a new category today: Rule Change Proposals. Maybe I'll make Fridays rule change proposal days. Some of them will relate to the mechanics of what goes on on the field. Some will have to do with league structure and playoff format. Some will be serious, others will be crazy. Others will be both crazy and serious.

This one is completely serious and I can think of absolutely no reason at all why it shouldn't be implemented immediately. I know exactly why it won't be implemented, but there's no reason why it shouldn't be.

The current structure of the NFL playoffs calls for the three seed to play the six seed, and the four to play the five. In the following round, the one seed plays the lowest remaining seed. My proposal is this: the three seed gets to choose whether it wants to play the five seed or the six seed. In the second round, the one seed gets to choose which of the first-round winners it wants to play.

Bill Belichick is clearly above questioning of any kind so I won't pretend that his decision to intentionally lose last year's week 17 game against Miami to gain a favorable playoff matchup wasn't the smart thing to do. But Bill is also a virtuous man, so I'm sure he wishes he wasn't forced to do it. Under my rule, he could have won the game and still gotten to play the Jaguar team he wanted to play.

Yes, tanking for playoff matchups is probably fairly rare. But it's not nonexistent, and this would put an end to it. Further, the fact that tanking is even a possibility in some cases indicates that the seeding system isn't achieving its desired purpose. The point of the seeding system is to reward the higher seed. So why not truly reward them with the easier matchup instead of giving the nominal reward of playing the team that probably is the easier matchup?

I'm pretty sure coaches would hate this rule, as it forces them to give their soon-to-be opponent the ultimate bulletin board material. But, as I see it, that's part of the fun. Speculating on who the Chargers are going to choose to play in the first round --- and then critiquing their decision --- would be a lot more interesting than most of what goes on in week 17 under the current system. And I guess if the three seed doesn't see sufficient advantage in naming their opponent, they should be allowed to pass that right/obligation to the four seed.

Give me one good reason not to implement this rule.

32 Comments | Posted in Rule Change Proposals

Predicting week 10 games (Part 2)

Posted by Chase Stuart on November 10, 2006

If you didn't read Wednesday's post, you should probably do that before reading this post. I'm going to analyze the rest of this weekend's games using that system.

San Francisco (3-5) at Detroit (2-6)
Old games: 3-5 teams are 5-3 against 2-6 teams, but six of those games were at home. 3-5 went 1-1 on the road. Example: 1981; the Cardinals (3-5) lost in Washington, 42-21. (This was Joe Gibbs' first season, and his Redskins started 0-5 but finished 8-8.)
New games: 3-5 teams are 1-7 against 2-6 teams, with three of those games being away. Road 3-5 teams are 0-3. Example: 2003; Chicago (3-5) lost at Detroit, 12-10.

Prediction: San Francisco (+6) covers against Detroit. I'm pretty surprised to see a 2-6 team favored over anyone with a better record, but I'll give the market some credit for this one. I'd expect Detroit to win (after all, road 3-5 teams are just 1-3) but six is a lot of points to give. I wouldn't bet this game, but I think SF covers.

Washington (3-5) at Philadelphia (4-4)
See the analysis in the Green Bay @ Minnesota game in Wednesday's post.

Prediction: Washington (+7) is what the numbers would tell me. Of course, Philadelphia could really be 7-1, so I'm not sure how similar they are to similar 4-4 teams of years past. The only thing I know is that there's no way I'd want to bet on this one.

Denver (6-2) at Oakland (2-6)
See the analysis in the Tennessee-Baltimore game in Wednesday's post.

Prediction: Oakland (+9.5). Yes, I know this sounds like near insanity. In fact, I didn't type "Oakland (+9.5)" without bursting out laughing. The Raiders have looked like a NCAA I-AA team in several games this year, and the Broncos are one of the NFL's elite teams. Of course, all of that is factored into the spread. What's probably not, is that road 6-2 teams are just 7-7 against 2-6 teams. Nine and a half is a lot of points to give on the road, especially when you have as anemic an offense as the Broncos have. Granted, Denver has scored 30+ in consecutive games, but they looked horrible for the first month and a half.

Everyone knows Mike Shanahan used to coach the Raiders, and he's pretty much owned them since joining the Broncos. Here are some quick stats:

Since 1995, Denver is 18-5 against Oakland, and including an 8-3 record in Oakland.
Average score: Denver 25.6, Oakland 17.3.
Average score in Denver wins: Denver 26.9, Oakland 13.6.
Average score in Oakland: Denver 26.3, Oakland 20.5.
Number of times (out of 23) that Denver has beaten Oakland by more than 9.5: Ten.
Number of times (out of 11) that Denver has beaten Oakland in Oakland by more than 9.5: Four.

Oakland is terrible, and Denver has had Oakland's number, despite the Raiders being pretty good for a number of years. I wouldn't want to bet a lot of money on Oakland covering, but I think they will.

Dallas (4-4) at Arizona (1-7)
Did you know Arizona is the only team in the league with fewer than 2 wins? Weren't they being touted as a sleeper team two months ago? Anyway...

Old games: 4-4 teams are 3-1 against 1-7 teams, but only one of those games (a win) came on the road. Example: 1985; Washington (4-4) won at Atlanta, 44-10.
New games: 4-4 teams are 3-3, and 2-2 on the road, against 1-7 teams. Example: Week 10, 1997, was when three of those four games occurred. Philadelphia and San Diego (4-4s) lost in Arizona and Cincinnati, 31-21 and 38-31, respectively; Washington (4-4) clobbered the Bears in Chicago, 31-8.

Prediction: Bill Parcells doesn't pull a Kevin Gilbride and Ray Rhodes on us, and Dallas (-7) wins easily. Ok, so I didn't really follow my system there. Road 4-4 teams are just 3-2 against the 1-7 teams on the road, but two of those wins were by 57 points. Dallas covers the seven point spread.

New Orleans (6-2) at Pittsburgh (2-6)
This line actually opened as high as Pittsburgh (-6) in some places. This is the third 6-2 @ 2-6 game of the weekend, along with Denver/Oakland and Baltimore/Tennessee. It's pretty interesting that the lines as of Thursday night are -9.5, -7 and +4.5 for the three games. Does one of those look a bit out of place?

This is a pretty intriguing matchup, because if features half of the league's teams that rank in the top ten in offense and defense (San Diego - 6th offense, 2nd defense and Dallas - 4th offense, 5th defense are the other two). Pittsburgh is without a doubt one of the best 2-6 teams in recent memory, ranking third in passing yards per attempt and sixth in rushing yards per attempt allowed. Willie Parker is ninth in the league in rushing, and the Steelers rank third in defensive interceptions. So sure, it's surprising to see them at 2-6. But...

Prediction: New Orleans (+4.5). History tells us this game is a coin-flip. Taking the points with a team that has won four more games seems like free money.

St. Louis (4-4) at Seattle (5-3)
Old games: 4-4 teams are 9-12 against 5-3 teams, with nine of those coming on the road. Away 4-4 teams are just 1-8 against 5-3 teams. Example: 1981; Cleveland (4-4) lost at Buffalo, 22-13.
New games: 4-4 teams are 8-9 against 5-3 teams, but only seven of those were road games. Road 4-4 teams are 2-5. Example: 2004; Detroit (4-4) lost at Jacksonville, 23-17.

Prediction: Seattle (-3.5) covers; home 5-3 teams are 13-3 against road 4-4 teams. Sure the Seahawks record is inflated a bit, because Alexander and Hasselbeck were a big part of those five wins, and won't play on Sunday. But 13-3 is pretty strong evidence, and I like Wallace and that home field.

Chicago (7-1) at N.Y. Giants (6-2)
Doesn't it feel like 1974 all over again? Just like the '74 Vikings, the '06 Giants are 6-2 and playing a 7-1 team that's coming off its first loss.

Old games: 7-1 teams are 0-6. That's mind-boggling, and even worse: the 7-1 team was home in four of those games. Example: 1975; Miami (7-1) lost in Houston, 20-19. Five of the six games were decided by four or fewer points.
New games: None.

Prediction: New York (+1) wins. A 7-1 team has never beaten a 6-2 team since the merger. The real winners are the fans though, as this pits the first time teams with those records have squared off since 1988. Of the six previous games, only once was there a rematch in the post-season. In 1974, the 7-1 Cardinals lost to the Vikings at home, and then got blown out in the rematch in Minnesota in the playoffs. I know the Bears lost to Miami, and got outplayed by Arizona, but I'm a bit surprised to see a Giants team without its top two receivers favored in this one.

Tampa Bay (2-6) at Carolina (4-4)
Old games: 2-6 teams are 2-8 against 4-4 teams, with six of those games at home. Road 2-6 teams are 0-4. Example: 1988; San Diego (2-6) lost in Seattle, 17-14.
New games: 2-6 teams are 1-6 against 4-4 teams, with three of those games on the road. Road 2-6 teams are 1-2 against 4-4 teams. Example: 2002; Houston (2-6) lost at Tennessee, 17-10.

Prediction: Tampa Bay (+9.5) covers. Sure, 2-6 teams are 3-14, and 1-6 on the road. But of those seven road games, only once did the 2-6 team lose by more than ten points.


I don't really know what to expect with this system. I don't think it will be excellent, because there are just too many flaws. The Giants aren't downgraded for losing Strahan and Toomer, for example. That's bad. And the sample sizes aren't as big as you'd like. I don't know what to make out of 6-2 teams winning all six times against 7-1 teams, but I'd imagine the results would be closer to 50/50 if they played 30 more times.

That being said, it's important to remember the benefits of this system. For one, people don't know these numbers. In the end, that's the only way you're ever going to beat the market. We've got three matchups of 6-2 and 2-6 teams this weekend with three different spreads. Why? Because the market thinks Oakland stinks and Denver's great, that Pittsburgh is good and who knows what New Orleans is, and that Tennessee/Baltimore is somewhere in between.

It always makes me laugh when I see a prediction about a game that goes something like this: Team X (-8) will cover this weekend; they're playing at home and against a rookie QB! Expect lots of turnovers and short fields for Team X.

The reason Team X is -8 is because they are at home and because Team Y has a rookie QB. We could all say "how can you bet on Oakland, did you see them on Monday night?" But the key point is that we all can say that. And that's factored into the point spread. Had the Raiders played well on MNF, the line might be Oakland +7.

This type of analysis intrigues me because it's objective data, and I don't really know what the results mean. Why have home 2-6 teams fared so well against road 6-2 teams? I have no idea. If you asked most football fans, I imagine they would guess that in fourteen matchups, 6-2 teams were 10-4 or 11-3 against 2-6 teams, and not 7-7. But the thinking is that whatever it is that makes 2-6 teams win, Tennessee (and Oakland and Pittsburgh) might have it too, and that's why they're more likely to win (or cover) than you might think.

In reality, the sample size for this would always be too small. My gut feeling is that if Tennessee and Baltimore played this game 100 times, the Titans would cover on 60-70 of those games. For this system to look successful, it's going to take a lot more than one or two or even eight weeks to really figure it out. But I'll be watching the scoreboard a bit more carefully on Sunday.

Comments Off on Predicting week 10 games (Part 2) | Posted in General

Another Thursday…

Posted by Doug on November 9, 2006

...another Big East game with major national championship implications.

Last week I predicted that Louisville would be playing for the championship if they win out, and I still think that's the case. That's the "will they?" side of the equation. I hadn't really thought about the "should they?" question. So I'll do that now.

Let's assume Louisville wins out and compare them to a top one-loss team. There is a possibility that the Ohio State - Michigan loser could be Louisville's main challenger, but my guess is that Florida will be the team with the most support from the public. If the Gators win out, they'll go to the SEC championship game. Let's assume that's against Arkansas and that they win that too.

I am a well-known SEC-hater, but I will try to be as objective as possible. Well, OK, I actually won't try to be objective. But, like Bart Simpson, I will try to try. Anyway, nothing is more objective than a mathematical algorithm, so I'll use that as my main basis of comparison. Jeff Sagarin's ratings are probably the most famous and most well-respected ratings out there, so I'll go with those.

There is a segment of the population that believes the SEC is head and shoulders above all other conferences every year because, well, I guess because it's the SEC. I really have never been given any other reason. If you're one of those people, then this analysis won't appeal to you. If, however, you're willing to regard Alabama as a team that lost to Mississippi State last week instead of as a team that is great because they're Alabama --- Alabama --- then you might find this of interest.

Here are the current Sagarin rankings for Florida's and Louisville's opponents:

Florida Louisville

opp rank opp rank
LSU 7 West Virginia 9
Auburn 11 Rutgers 15
Tennessee 14 Pitt 34
Arkansas 16 Kentucky 46
South Carolina 36 Cincy 51
Florida State 42 Kansas State 54
Kentucky 46 South Florida 55
Alabama 47 Miami 57
Georgia 48 Middle TN St. 65
Southern Miss 66 Syracuse 67
Vanderbilt 73 Connecticut 74
Central Florida 118 Temple 158
West. Carolina 214

Let's pair them up into roughly equivalent games:

  • They both beat Kentucky - so we cross that one off the list.
  • Louisville over West Virginia - Florida over Tennessee
  • Louisville over Rutgers - Florida over Arkansas
  • Louisville over Pitt - Florida over South Carolina
  • Louisville over Cincy - Florida over Southern Miss
  • Louisville over MTSU - Florida over Vanderbilt
  • Louisville over Temple - Florida over Western Carolina

In all the above cases, the two opponents are equivalent according to the Sagarin rankings. Louisville's opponents actually have a very slight advantage in all the above pairs, but I'm trying to try to be objective, so I'm calling it a wash.

Now, the thing that kills me about talking to SEC fans is that they are constantly saying things like this:

Man, there's just no off weeks in the SEC. It's brutal to have to play Alabama, LSU, Auburn, then Georgia.

LSU and Auburn are very good teams, no doubt. But even when Alabama loses at home to Mississippi State and Georgia loses to Vanderbilt and Kentucky, they still try to slip Georgia and Alabama into the conversation about how tough the SEC is. Alabama and Georgia rank 47 and 48 in the Sagarin rankings. Kansas State (who has won more games in the last several years than either Georgia or Alabama, if that's relevant) and South Florida rank 54 and 55. Those pairs are basically equivalent. I think it's fair to say that Miami and Florida State are a match given their histories and the fact that they played a very close game earlier this year.

So we've stripped out the parts of their schedules that are equivalent. What does that leave?

Louisville vs. Syracuse

Florida vs. Auburn and LSU

Beating Syracuse doesn't count for much. Beating LSU does. If Florida were undefeated, we wouldn't be having this conversation. The problem is that they have a loss.

After working through all this, I'm actually a little more sympathetic to Florida's case. If you want to make the case that a 10-0 record plus a 1-1 record against Auburn and LSU is more championship-worthy than an equivalent 10-0 record plus win over Syracuse, then I don't really have a problem with that. My objection is to the notion that the Georgia / Alabama / South Carolina part of the schedule is so much tougher than Cincy / Pittsburgh / Kansas State.

Of course, all these rankings will change --- in some cases drastically --- between now and the end of the season. But at that point I suspect that the relevant analysis will turn out similarly.

13 Comments | Posted in BCS, College

Predicting week 10 games

Posted by Chase Stuart on November 8, 2006

Earlier in the season I attempted to predict the week five games by looking at what had happened in previous seasons, when teams with the same records played each other. I'm going to do that again this weekend, and I expect better results for this weekend (to be fair, I didn't even calculate my results from the earlier time, so I'm not even sure how the system fared), for three reasons:

  • We now have five more weeks of data to analyze, which should eliminate some of the luck involved in a team's record. A 6-2 team is more likely to be a very good team than a 3-1 team. It's just more difficult to have sustained success (or lack of success) than it is to have a good or bad stretch.
  • We have more data to analyze now, since every team in the NFL has played eight games. I'm guessing you didn't know this, but when the Jets played the Browns in week 8, it was the first time in over 70 years that a 1-5 team played a 4-3 team in the NFL. While that sounds shocking at first, remember that the NFL didn't begin having a regular bye system until 1990. But now that every team has played a similar number of games, we can look at all matchups of 4-4 teams against 7-1 teams in either week 9 from 1990 to the present, or from week 8 from 1970 to 1989.
  • With three caveats. The 1982, 1987 and 1993 seasons were all thrown out, along with any game played before 1970. Why those three years? 1982 and 1987 were strike years, and 1993 was the one season where the NFL went with a two-bye system. It would have taken a bit more time programming my system to include that year, so I went the easy route and eliminated it.

Now that I have my caveats out the way, let's look at this weekend's games. I'm not sure how much success this system will have. Well I'm not an expert on the stock market, I believe this way of predicting NFL games would be similar to technical analysis, where you analyze trends to predict the future. This is in stark contrast to fundamental analysis, where you'd actually look at the specific business to predict its future stock price. To give an NFL example, technical analysis would say the Colts will beat the Bills because 8-0 teams are 10-1 since 1970*, with the only loss coming when the '77 Cowboys lost to a 5-3 Cardinals team. Since the Bills have a losing record, technical analysis says Indy wins in a romp. Fundamental analysis would lead me to say Peyton Manning is a lot better than J.P. Losman, no matter how many dropped interceptions Manning has thrown this year, and therefore the Colts will win.

*If you read yesterday's blog you might notice that there were 12 teams, not 11, to start 8-0 before the 2006 Colts. The difference is explained by the 1990 49ers, who at 8-0 played the 3-6 Cowboys. Remember, my study eliminates all teams that played an opponent with a different number of games played, since that won't happen in week 10 of the 2006 season.

There are flaws with technical analysis, and there are flaws with the way I'm going to try and predict this weekend's games. Here's the most obvious one: if Peyton Manning, Marvin Harrison, Reggie Wayne and Joseph Addai all get sick on Wednesday and are declared out for Sunday's game, my analysis wouldn't change. History would just see the Colts at 8-0, and give them a W. This is problematic, of course, and is why I caution putting too much emphasis on this system. But I can't help but run the numbers, especially when there are some interesting results. Today I'll look at eight games, and tomorrow I'll look at the remaining games and respond to the comments. If you have any suggestions on how to present the data in a better manner, let me know. This way just seemed right to me.

Last note: I'm going to list the results of all games from the "old era" and the "new era". This isn't because I think the analysis is better, but just because that's how my system is currently set up. The old era includes the week 9 games from 1970-1989* (with the strike seasons excluded), while the new era includes the games from 1990-2005, excluding 1993.
*For the most part. For example, in 1991 the Cardinals and Vikings game from week 9 is included, because both teams had byes very late in the season. The years are guidelines, not rules.

Baltimore (6-2) at Tennessee (2-6)
Old games: 6-2 teams are just 3-4, and hosted three of the seven games. Road 6-2 teams are 1-3. Example: 1989, Buffalo (6-2) lost in Atlanta, 30-28.
New games: 6-2 teams are 4-3, but hosted four of the seven games. Road 6-2 teams are 1-2. Example: 1999, Detroit (6-2) lost in Arizona, 23-19.

Prediction: Tennessee (+9) pulls the upset. History shows that 6-2 teams are 7-7 against 2-6 teams, and hosted exactly half of those games. Road 6-2 teams are just 2-5. This game's a coin flip, so the smart money would be on the Titans.

Buffalo (3-5) at Indianapolis (8-0)
Old games: 3-5 teams are 0-1, and hosted none of the games. Closest example: 1985, Green Bay (3-5) lost at Lambeau to the Bears, 16-10.

New games: 3-5 teams are 0-3, and hosted one of the games. Example: Cleveland (3-5) lost at Arrowhead to the Chiefs, 41-20.

Prediction: Colts (-11) win. Home 8-0 teams are 2-0 against 3-5 teams. Yes, you won't get this type of analysis anywhere else: 8-0 teams are good! Against the spread this one is a toss-up, and is a game I'd avoid.

Cleveland (2-6) at Atlanta (5-3)
Houston (2-6) at Jacksonville (5-3)

A pair of 2-6s against 5-3s, so I'll analyze them together.

Old games: 2-6 teams are 1-7, and were on the road for five games. Road 2-6 teams are 1-4. Example: 1972, Buffalo (2-6) lost on the road to the Jets, 41-3. (The next time the Bills went to New York, O.J. Simpson would become the first player to rush for 2,000 yards in a season.)

New games: 2-6 teams are 1-4, and were on the road for three of those games. Road 2-6 teams went 0-3. Example: 2005, week 10. Baltimore and San Francisco (2-6) lost in Jacksonville and Chicago respectively, by 30-3 and 17-9.

Prediction: Atlanta (-9) Jacksonville (-10.5) in romps. Road 2-6 teams are just 1-8 against these opponents. Against the spread, I'd probably avoid both of these games. Of those nine previous matchups of road 2-6 teams, the margin of victory was between 8 and 11 points in four of them. (For those curious, the one team to win was the 1978 Chargers in Oakland.)

Green Bay (3-5) at Minnesota (4-4)
Old games: 3-5 teams are 6-6, and hosted six of the games. Road 3-5 teams are 2-4. Example: 1970, Chicago (3-5) lost at Green Bay, 20-19. Note: The 3-5 team won the last four games (1985-1991), but three of those were at home.

New games: 3-5 teams are 5-4, and hosted only three of those games. Road 3-5 teams are 3-3. Example: 2001, Tennessee (3-5) beat Cincinnati, 20-7.

Prediction: Green Bay +5. 3-5 teams have actually won 9 of the last 13 matchups, and seven of those were on the road. Road 3-5 teams are 5-7 overall though, so this game is really just a coin-flip. I'd take Green Bay, with the five points.

Kansas City (5-3) at Miami (2-6)
Old games: 5-3 teams are 7-1 against 2-6 teams, but five of those games came at home (remember, this is just the flip-side of the Cle/Atl and Hou/Jac games). 5-3 teams are 3-0 on the road. Example: 1988, New York Giants (5-3) won in Detroit, 13-10.

New games: 5-3 teams are 4-1, but just 1-1 when on the road. Example: 2001, Philadelphia (5-3) won in Dallas, 36-3.

Prediction: Kansas City (-2.5) seems like a strong bet; road 5-3 teams are 4-1 all time. As is the case in this specific matchup, generally 5-3 teams are playing for the playoffs, while 2-6 teams have less at stake. History isn't a great guide here though, so be careful basing much on the sample size of just two games since 1990.

N.Y. Jets (4-4) at New England (6-2)
Here's something pretty fascinating. I started doing this Sunday afternoon, and at the time I had pegged the Pats to beat the Colts. If this was a matchup between a 4-4 team and a 7-1 team...

Old games: 4-4 teams were 1-9 against 7-1 teams, and 0-4 on the road.
New games: 4-4 teams were 1-4 against 7-1 teams, and 0-3 on the road.

Conclusion: The 4-4 team was just 2-13 (and one of those wins was a one-point squeaker), and an ugly 0-7 on the road. This would look like the lock of the week. But since New England lost...

Old games: 4-4 teams were 5-5 against 6-2 teams, with six of those games on the road. In those games, the away 4-4 teams went 3-3. Examples: 1978, week 9. Minnesota (4-4) won in Dallas, 21-10; Tampa Bay (4-4) lost 9-7 at Green Bay.

New games: 4-4 teams were 5-7 against 6-2 teams, with ten of those games on the road. But, away 4-4 teams were 5-5 on the road. Example: 2005, St. Louis (4-4) lost in Seattle, 31-16.

Prediction: New York (+10) is a strong play. Road 4-4 teams are 8-8 against 6-2 teams since 1970, so getting ten points in a coin-flip game looks good. Of course, in a lot of ways this is where the technical analysis breaks down. If the Colts beat the Pats, NE has only a 50% chance of beating New York (8-8); but if NE beats Indianapolis, the Pats have a 100% chance of beating the Jets (7-0).

But I'm of the opinion that the Jets had a much better chance of beating the Patriots if New England had beaten Indianapolis, because an angry Pats team is going to beat New York. The Jets have lost eight straight to New England. But giving 10 points is enough for me to like New York in this one.

San Diego (6-2) at Cincinnati (4-4)
Old games: 6-2 teams are 5-5 against 4-4 teams, and 2-2 on the road (remember, this is just the flip side of the Jets/Patriots game). Examples: 1979, week 9; San Diego (6-2) lost in Oakland, 45-22; Tampa Bay (6-2) won in Minnesota, 12-10.

New games: 6-2 teams are 7-5 against 4-4 teams, and 2-0 on the road. Example: 2001; Chicago (6-2) won in Tampa Bay, 27-24.

Prediction: San Diego (-1). This game is almost a coin-flip, and it's properly viewed as one. I'd stay away from betting on this one.

6 Comments | Posted in General

The Colts / Andre Johnson

Posted by Doug on November 7, 2006

I've spent a few recent posts (I, II) talking about the Bears' great start. Let's now take a look at the Colts.

Indianapolis is the 13th team since the merger to start the season 8-0. Of those teams, the 2006 Colts have the smallest collective margin of victory and they are the only one of those teams with no 20+ point wins. On the good side, they have had the toughest schedule of any 8-0 team (tied with the 1990 Giants, actually).

Marg = total margin of victory through 8 games
B = number of 20+ point wins in the first 8 games
SoS = collective winning percentage of opponents

TM YR Marg B SoS Record
was 1991 153 4 0.508 14- 2-0
mia 1984 150 4 0.438 14- 2-0
min 1975 134 3 0.304 12- 2-0
ind 2005 131 2 0.391 14- 2-0
chi 1985 125 1 0.445 15- 1-0
dal 1977 123 2 0.429 12- 2-0
kan 2003 116 3 0.430 13- 3-0
den 1998 114 2 0.453 14- 2-0
mia 1972 95 2 0.371 14- 0-0
nyg 1990 92 1 0.531 13- 3-0
min 1973 74 1 0.496 12- 2-0
sfo 1990 60 1 0.430 14- 2-0
ind 2006 59 0 0.531 8- 0-0

In other news, Andre Johnson has more receptions through nine weeks than just about anyone in recent history. Here is the most-receptions-through-nine-weeks list. It includes all seasons since 1995:

Player YR G REC
Rod Smith 2001 9 72
Marvin Harrison 2002 8 69
Andre Johnson 2006 8 65
Torry Holt 2003 8 63
Eric Moulds 2002 9 62
Keenan McCardell 2000 9 60
Peerless Price 2002 9 60
Keyshawn Johnson 2001 8 59
Eric Moulds 2000 8 59
Herman Moore 1996 8 59
Marvin Harrison 2000 8 58
Marvin Harrison 1999 8 58
Jimmy Smith 2001 8 58
Michael Irvin 1995 8 58
Eric Metcalf 1995 8 57
Terrell Owens 2000 8 57
Herman Moore 1997 8 57
Jerry Rice 1995 8 57
Terrell Owens 2001 8 56
Steve Smith 2005 8 55
Keenan McCardell 1996 9 55
Herman Moore 1995 8 55
David Boston 2001 8 55
Cris Carter 1999 9 55
Troy Brown 2001 9 55
Hines Ward 2002 8 55
Marvin Harrison 2003 8 55
Jerry Rice 1996 8 55

9 Comments | Posted in General, History

Curtis Martin and Terrell Davis

Posted by Doug on November 6, 2006

Curtis Martin announced last week that he is done for this season, and quite possibly for his career. About a week prior to that, the list of newly-eligible Hall of Fame candidates was released. These two events have a lot of people talking about Martin's career and, since Terrell Davis is a new eligible, about Davis' career as well.

I wrote awhile back that Hall of Fame debates don't interest me much, and they still don't. But general discussion of the merits of certain players' careers does interest me. So, while I won't spend much time worrying about whether both, neither, one, or the other should or will end up in Canton, I am interested in the general debate about the relative merits of Martin's long solid career versus Davis' short, brilliant one.

In this post about Jimmy Smith, I invented a quick-and-easy stat called Yards Over 1000 to measure a player's career value. We compute it by counting career yards, but that catch is that the only yards that count are the yards you get over and above 1000 in a season. A 600-yard season, a 100-yard season, and a 999-yard season all count the same: zero. The idea is that you get credit only for doing something above and beyond the ordinary, and anything less than a thousand yards is somewhat pedestrian (at least if we're trying to sort out the all-time greats, as we usually are when these sorts of discussions arise).

One problem with this is that a thousand 2005 yards are much different from a thousand 1976 yards --- especially receiving. We can correct both this by switching from Yards Over 1000 to Yards Over #10. Instead of counting yards over 1000, we'll count yards over the #10 rusher (or receiver, or passer, or whatever) of the given season. In 1996 for instance, the #10 rusher, Anthony Johnson, notched 1120 yards. Curtis Martin had 1152, so he gets credited with 32 Yards Over #10. Terrell Davis' 1538 rushing yards count for 418 Yards Over #10. Anyone under 1120 gets a zero.

Why make #10 the baseline? No good reason. Fifteen or 12 or 8 would be reasonable choices too, depending on what you think "above and beyond the ordinary" means.

Here are the top rushers in Yards Over #10. The list includes all players who debuted in 1970 or later. Before I post it, let me clearly state that this is NOT My Running Back Rankings. It doesn't take into account blocking, receiving, or even rushing touchdowns. And it doesn't take into account the offensive lines, quarterbacks, and coaching staffs these guys played with and for. It's just a simple way to try to measure rushing (yardage) outstandingness. The goal is not to create a definitive set of rankings. It's to create a list that makes us think a little bit. Here it is:

Player YardsOver#10
Barry Sanders 4723
Walter Payton 4461
Eric Dickerson 4074
Emmitt Smith 3307
Earl Campbell 2419
Thurman Thomas 1864
Terrell Davis 1846
Tony Dorsett 1696
Curtis Martin 1563
Gerald Riggs 1478
Edgerrin James 1327
Ottis Anderson 1323
Jerome Bettis 1314
Shaun Alexander 1280
Tiki Barber 1133
Curt Warner 1114
LaDainian Tomlinson 1093
Franco Harris 1038
William Andrews 999
Eddie George 903
Joe Morris 903
Lawrence McCutcheon 890
George Rogers 853
Wilbert Montgomery 851
Chris Warren 820
Clinton Portis 776
Marshall Faulk 765
Marcus Allen 756
Jamal Lewis 756
Billy Sims 750
Priest Holmes 701
Ahman Green 692
Lydell Mitchell 690
Corey Dillon 656

First, note that the list generally matches up with what most people believe a list of top rushers ought to look like. Next, it's worth remarking that Earl Campbell's short brilliant career ranks high, but so does Tony Dorsett's long solid career. There doesn't seem to be much of a bias toward one type of career over another. Of course, the relative merits of each type of career is subjective, so bias would be in the eye of the beholder anyway. What I'm saying is that I think this system does a decent job of balancing greatness and longevity. Truly great seasons are rewarded appropriately. Longevity is also rewarded appropriately, but compiling useless numbers is not.

Now, as far as Martin and Davis are concerned, they were both great and, as far as I'm concerned, roughly equally great. Looking at Scrimmage Yards Over #10 (instead of Rushing Yards) puts a little distance between Davis and Martin:

Player YardsOver#10
Walter Payton 4554
Barry Sanders 4234
Eric Dickerson 3219
Marshall Faulk 3147
Thurman Thomas 2979
Emmitt Smith 2923
LaDainian Tomlinson 2003
Tiki Barber 1958
Edgerrin James 1922
Terrell Davis 1805
Lydell Mitchell 1771
William Andrews 1745
Marcus Allen 1597
Priest Holmes 1580
Tony Dorsett 1536
Roger Craig 1527
Ottis Anderson 1512
Chuck Foreman 1465
Herschel Walker 1363
Curtis Martin 1294
Ricky Watters 1247
Earl Campbell 1105
Ahman Green 1010
Lawrence McCutcheon 1009
Billy Sims 1003

On the other hand, looking at Scrimmage Yards Over #15 (instead of #10) puts Curtis in the lead:

Player YardsOver#15
Walter Payton 6162
Barry Sanders 5221
Eric Dickerson 3883
Marshall Faulk 3870
Emmitt Smith 3709
Thurman Thomas 3611
Tony Dorsett 2760
LaDainian Tomlinson 2731
Tiki Barber 2621
Lydell Mitchell 2456
Edgerrin James 2435
William Andrews 2400
Ottis Anderson 2252
Curtis Martin 2179
Marcus Allen 2145
Roger Craig 2104
Chuck Foreman 2098
Terrell Davis 2056
Ricky Watters 2007
Priest Holmes 1989
Earl Campbell 1885
Herschel Walker 1780
Lawrence McCutcheon 1698
Billy Sims 1545
Wilbert Montgomery 1444
Ahman Green 1428
Shaun Alexander 1423
Franco Harris 1297
Eddie George 1236
Gerald Riggs 1166
Otis Armstrong 1165
Ricky Williams 1118
James Wilder 1093
Curt Warner 1079
Jerome Bettis 1077

9 Comments | Posted in General, History

BCS update

Posted by Doug on November 3, 2006

Before we get to the Big East BCS watch I wanted to call attention, on the eve of the Oklahoma State vs. Texas tilt, to one of the most remarkable splits ever:

First Half Second Half
2005 28-12 0- 35
2004 35-14 0- 42
2003 16-14 0- 41
TOTAL 79-40 0-118

Ouch. Hopefully my Cowboys will make some adjustments tomorrow and remove one more complication from the BCS picture.

Now, with Louisville's win over West Virginia last night, I'll go ahead and predict that the Cardinals will play for the national title if they win out. There are people who forecast these things more accurately than I can, but according to my margin-not-included power rankings, which I think are somewhat indicative of how the official BCS algorithms will act, Louisville is now #3 behind only Michigan and Ohio State. They trail Texas in the human poll right now, but have a huge lead over the Longhorns in the computers.

My rough eyeball calculations suggest that Louisville has a roughly equivalent schedule to Auburn, Florida, and Texas going forward, even possibly including a conference championship game. So I could be wrong about this, but I don't think an undefeated Louisville team will end up behind the SEC teams in the computer polls, and they will definitely end up ahead of Texas. Louisville also has a lead over Auburn and Florida in the human polls, so I think they'll be in Glendale in January if they win out.

It could be close, though, and we might see a lot of disgusting (but understandable) coach lobbying in the media. Sadly, it seems that that is now as much a part of a major college football coach's job description as recruiting and X-and-O stuff.

10 Comments | Posted in BCS, College

Rerun: The other Dungy Index

Posted by Doug on November 2, 2006

I've got a busy week this week, so here is a re-run. This one ran in January of 2006 at sabernomics:

Tony Dungy’s teams haven’t fared particularly well, relative to expectations, in postseason games. So when, in this other post, I created a metric to measure such performance, I named it after the man. That was something of a cheap shot.

I’ll right that wrong here by noting that Dungy has a superlative record of producing and maintaining very good teams. In his four years at the helm of the Colts, they’ve won 48 games. Since 1990, only three teams have bettered that number during a four-year stretch and three more have equalled it. Yeah, I know, he inherited Peyton, Edge, and Marvin. He also inherited a defense that was a complete wreck. To average 12 wins a year over a four-year span is remarkable under any circumstances.

Let’s now examine the fraud known as Bill Parcells. He seems to get lots of credit for turning losers into winners. Most recently, he took over a Cowboy team that had been dreadful for several years prior to his arrival. Immediately, they were contenders in the NFC. There was a bump in the road the following year, but the Cowboys were once again in the playoff mix in 2005.

But what has he done, really? In the three years prior to Parcells’ arrival, the Cowboys were 15-33. That’s pretty bad. In the three years since, they’ve been 25-23. Better. Is that Parcells, or is that just what bad teams naturally do in the NFL these days: get better? Since 1990, there have been 35 teams that won between 14 and 16 games over a three-year span. These teams, as a group, would have to be considered similar to the Cowboy team that Parcells inherited. Their performance during the next three years could serve as a yardstick against which to measure Parcells’ performance. During the next three years, the other comparably bad teams averaged 22 wins and 0.85 playoff appearances. Bill has notched 25 wins and one playoff appearance. Solid effort? Yes. Miraculous turnaround? No.

For various reasons — some “natural” and some due to NFL tinkering — teams with good records tend to regress while teams with bad records tend to get better. That’s a fact that will surprise very few readers of this blog, I’m sure. But it’s at the heart of why I believe Dungy has a more impressive record than Parcells — than just about anyone — over the last few years. His teams, despite being good, have not regressed. During their most recent stints, Parcells has been aided by the forces of nature while Dungy has been fighting against them.

On the other hand, even someone like myself who possesses a deep and irrational hatred of Parcells would acknowledge that Dungy did inherit a better team than Parcells did. It would therefore be unfair to simply compare their records.

I want to quantify these ideas a bit. The first step is to establish a baseline. If a team won X games in 2005, how many games should they be expected to win in 2006? Regression can provide us with an estimated answer. A plain old linear regression including all teams since 1990 produces the following formula:

Next Year Wins =~ 5.51 + .317 * LastYearWins

Some quick checks indicate that it passes the smell test: plug in 8 and you get out 8, plug in 12 and you get out 9.3. Teams since 1990 that have won twelve games have actually averaged about 9.2 wins the next year. The formula models reality fairly well (not surprising, of course, since it was built to fit reality).

But this same formula doesn’t model the reality of 1973 or 1985 very well. Those were different times, so they require different formulas. I simply ran a separate regression for each of the three time periods 1970–1979, 1980–1989, and 1990–present. I’ve got no good reason for selecting those cutoff points. Probably 1978 (a bunch of rule changes) and 1993 (free agency) would be better cutoffs. Even better, I could ask J.C. to tell me about some statistical whizbangery that would examine the data and tell me the best place to draw the cutoffs. But I’m lazy, so nominal decades it is.

The next step is to go through each coach’s record, year by year, and compare his expected wins to his actual wins. Here, for example, is Dungy:

Expected Actual
Year Team wins wins Diff
1996 tam 7.7 6.0 -1.7
1997 tam 7.4 10.0 2.6
1998 tam 8.7 8.0 -0.7
1999 tam 8.0 11.0 3.0
2000 tam 9.0 10.0 1.0
2001 tam 8.7 9.0 0.3
2002 ind 7.4 10.0 2.6
2003 ind 8.7 12.0 3.3
2004 ind 9.3 12.0 2.7
2005 ind 9.3 14.0 4.7

That’s about 84 expected wins and 102 actual wins, making +18 marginal wins. He gets some credit for turning around a bad Bucs team. But he scores most of his points by keeping his teams at (or near) the top of the league consistently.

Before we get to the full list, a couple of technical notes are in order:

1. Only seasons since the 1970 merger are counted. Guys like Don Shula, whose career started before 1970, are included but the games prior to 1970 are ignored. These guys are asterisked.

2. I didn’t want to order the list by Total Marginal Wins because that would weight long careers too heavily. Ordering the list by Marginal Wins per season, on the other hand, wouldn’t give enough weight to long successful careers. So I ordered the list by (an approximation of) the probability that chance would produce the given record or a better one.

Expected Actual Marginal
wins wins wins
*Don Shula 239 276 +36.5
Joe Gibbs 123 147 +23.6
Tony Dungy 84 102 +17.7
Mike Holmgren 117 138 +20.9
Marty Schottenheimer 159 183 +24.3
Bill Cowher 121 142 +20.8
Mike Shanahan 109 129 +19.8
George Seifert 97 114 +16.7
Bill Parcells 143 164 +20.9
Bill Walsh 83 96 +13.2
Andy Reid 60 70 +10.2
*Tom Landry 183 200 +16.5
*George Allen 77 88 +10.7
*Chuck Noll 191 208 +17.7
Marv Levy 129 144 +14.6
*John Madden 95 106 +10.8
Jon Gruden 65 73 +8.3
*Bud Grant 141 152 +11.3
John Fox 30 36 +5.7
Jimmy Johnson 71 80 +8.6
*Paul Brown 48 55 +6.9
Marvin Lewis 22 27 +4.8
Chuck Knox 185 198 +12.9
Bill Belichick 91 99 +8.3
Tom Coughlin 78 85 +7.1
Chuck Fairbanks 46 51 +5.3
Art Shell 42 47 +4.9
Bobby Ross 72 78 +6.2
Dennis Green 101 108 +7.0
Mike Sherman 52 57 +4.6
Jack Del Rio 23 26 +3.1
Barry Switzer 37 40 +3.4
Jeff Fisher 90 96 +5.6
Dick Vermeil 117 124 +6.4
Wade Phillips 41 45 +3.5
Mike Martz 53 57 +3.7
Mike Ditka 119 124 +5.5
Don Coryell 112 117 +5.3
Red Miller 39 42 +2.9
Brian Billick 58 62 +3.8
John Ralston 38 41 +3.0
Dan Reeves 189 195 +6.2
Jerry Burns 50 53 +2.9
Jim Mora 123 127 +4.2
Walt Michaels 42 45 +2.4
Bum Phillips 86 89 +3.1
*Joe Schmidt 28 30 +1.6
John Robinson 74 75 +1.6
Mike Tice 31 32 +1.1
John Mackovic 29 30 +1.0
Raymond Berry 44 45 +0.8
*Charley Winner 21 21 +0.6
Jim Fassel 58 58 +0.8
Tom Flores 103 104 +0.8
Jack Pardee 90 91 +0.7
Wayne Fontes 64 64 +0.5
Steve Mariucci 73 73 +0.3
Buddy Ryan 56 56 +0.1
Ron Meyer 60 60 +0.1
Jerry Glanville 61 61 +0.0
Forrest Gregg 84 84 -0.2
Ted Marchibroda 92 92 -0.4
Dan Devine 32 31 -0.7
*Nick Skorich 36 35 -0.7
Pete Carroll 34 33 -1.1
Rick Forzano 24 23 -1.0
Tommy Prothro 51 49 -1.7
Sam Rutigliano 56 54 -1.8
Don McCafferty 39 38 -1.4
Jack Patera 45 43 -2.2
Jim Haslett 47 45 -2.3
Jim Hanifan 46 43 -2.5
Herman Edwards 41 39 -2.5
Dick Jauron 38 35 -2.7
Monte Clark 59 56 -3.6
*Lou Saban 52 49 -3.5
Dave Wannstedt 89 85 -4.5
*Dick Nolan 71 66 -4.2
Joe Walton 58 54 -4.0
Neill Armstrong 33 30 -3.3
*Ray Malavasi 45 42 -3.7
Leeman Bennett 60 55 -4.7
*Norm VanBrocklin 40 36 -3.9
Bart Starr 65 60 -5.3
*Hank Stram 58 53 -4.9
Ray Rhodes 42 38 -4.2
Gene Stallings 28 24 -4.5
Butch Davis 30 25 -4.6
*Alex Webster 32 27 -4.7
John McKay 56 49 -7.1
Sam Wyche 93 84 -8.3
Norv Turner 67 60 -7.7
June Jones 24 19 -4.5
Ray Perkins 54 46 -7.7
John North 19 14 -4.8
Bill Johnson 29 25 -4.9
Mike McCormack 34 28 -6.5
Bill Arnsparger 17 11 -5.1
Dave McGinnis 21 16 -5.3
Dennis Erickson 48 40 -7.6
Gregg Williams 23 17 -5.6
Dom Capers 57 48 -9.4
Darryl Rogers 27 20 -6.8
Rich Kotite 48 40 -8.3
Frank Kush 18 12 -5.9
Abe Gibron 19 13 -6.1
Ron Erhardt 27 21 -6.1
Vince Tobin 37 29 -8.1
David Shula 34 26 -8.2
Paul Wiggin 20 14 -6.5
*Weeb Ewbank 32 24 -7.5
Mike Riley 21 14 -7.0
Lindy Infante 46 36 -10.1
Dave Campo 22 15 -7.2
Dan Henning 50 38 -11.8
Marion Campbell 53 39 -13.8
Bruce Coslet 58 44 -14.0
Joe Bugel 35 24 -11.5
Kay Stephenson 21 12 -8.9
Ed Biles 22 11 -11.3

How you weight the relative importance of regular season performance versus postseason performance is up to you. But either way, it’s tough to come up with a better candidate for best post-Merger NFL coach than Joe Gibbs.

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