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More on backup quarterbacks

Posted by Doug on June 14, 2006

Last week, I took a quick look at how top wide receivers do when a backup quarterback is playing. I decided to expand that look to second receivers, running backs, and tight ends. Then I wrote it up for my other site: footballguys.com. Here's the link.

While we're on the subject, I hope you'll forgive me a brief commercial message, because this seems like an appropriate time for me to point out that if you play fantasy football, a $25 subscription to footballguys is the best value out there. But everything is free until July 15th, so go check it out.

1 Comment | Posted in Fantasy, General

Roethlisberger’s decision

Posted by Doug on June 13, 2006

I'd better post something about Ben Roethlisberger's motorcylce accident.

First of all, I have yet to hear anyone criticize Roethlisberger for riding a cycle. No, everyone is on him for riding a cycle without a helmet. Why is riding the cycle OK, but riding it without a helmet is not? Because riding with the helmet is safer, I guess. But driving in a car is safer than either. I don't have data, but I'd guess that the marginal difference in severe injury probability between a car trip and a helmeted cycle trip is greater than that between a helmeted cycle trip and an unhelmeted one. (Feel free to chime in with data if you've got it.) It seems arbitrary to focus on the helmet. But that's not what this rant is about.

And while I do agree with the sentiment for the most part, this is not a libertarian-style "it's his life and he can do whatever he likes as long as he doesn't infringe on others' rights to do the same" rant. No, I am actually going to argue that Big Ben's decision to continue to ride his cycle sans helmet was, in fact, not a stupid one at all.

As everyone knows, getting out of bed in the morning is a risk. You probably got in your car and drove to work this morning, knowing full well that there was a small probability that that decision would be the direct cause of your grisly death. That is exactly what Roethlisberger did when he hopped on the bike with no helmet yesterday. Yes, you're saying, but I have to drive to work. Ben doesn't have to ride without a helmet. He could simply take the same ride with a helmet, and be 42% safer.

I'll grant that Roethlisberger would not literally shrivel up and die if he were forced to wear a helmet. But everyone has certain psychological needs, and it's just plain as day to me that one of Ben Roethlisberger's is satisfied by riding a motorcycle without a helmet.

Whatever you think about his decision, he is one of the best in the world at a job that requires a lot of decision making, so it is at least clear that he is not a stupid person. When Kellen Winslow was hurt in a bike wreck last May, Bill Cowher lectured Roethlisberger about the need to wear a helmet, but Ben refused to start wearing one.

When a smart person consciously makes a decision like that --- especially after so recently seeing a colleague demonstrate the potential consequences --- there is a reason for it. Having a very cautious personality myself, I can't begin to fathom what that reason is, but there is one and I think we ought to respect it. To use the usual words --- risk-taking, thrillseeking --- is to vastly oversimplify an incredibly complicated issue, but Ben Roethlisberger needs that thrill. You may not need it, but he does.

I believe that, in almost all cases, the good aspects of our personalities are inextricably tied to the bad ones. I don't understand the exact connection, but there is no doubt in my mind that whatever it is that compels Big Ben to bike without a helmet also plays a crucial role in his being such a great football player. Is it really surprising that a successful football player would be wired in such a way that he has an inner drive to do things that might not be in the best interests of his physical health?

Steeler fans, the choice is not between a helmetless Big Ben and a helmeted one. It's between a helmetless Big Ben and no Big Ben at all. The Big Ben that wins Super Bowls at age 23 is the very same Big Ben as the one who consciously chooses not to wear a helmet when he rides. You could try to separate the two with contractual obligations, but I guarantee that aspect of his personality would manifest itself some other way. It's part of the package.

35 Comments | Posted in Rant

Coaching changes and lurking variables

Posted by Doug on June 12, 2006

Lots of teams changed head coaches this year.

I have a crazy theory that changing coaches just for the sake of changing coaches is usually a good thing. Maybe not every year, but unless my team's record is good and getting better, I'd be inclined to fire the coach and start afresh every two or three years. I realize this is contrary to the coaching-continuity-is-everything line of thinking that the Steelers' Super Bowl title has wrought, so I probabaly should take a full blog post to explain it more clearly sometime. But for today, let's just do a quick investigation of how teams do after changing coaches.

Since 1990, we have seen 80 teams change head coaches between seasons. On 53 of those occasions, the team improved its record, and another four times the team's record stayed the same. If we count those four as half improve and half decline, then we get that 55 of the 80 teams improved. That's 68.8%. During the same span, teams that did not change coaches improved their record only 45.7% of the time. [Technical note: I have thrown out teams that changed coaches in mid-season in either year N or year N+1. My intent was to focus on situations where a conscious between-seasons choice was made between continuity and a new direction.]

Despite the fact that it appears to support my point, that is an extremely misleading statistic. While there is unquestionably an association between changing coaches and improving your record, there may or may not be a causal relationship. There is a lurking variable here, and its name is team quality. In the NFL, bad teams tend, as a group, to improve their records more often than good teams do. Bad teams also tend to change coaches more than good teams do. These two facts might lead to the statistic we saw above even if there is no causal relationship at all between changing coaches and improving your record.

One simple way to remove this bias would be to group the teams into groups of roughly equal quality. So let's do that.


YrN === changed coaches ===+=== did not change ======
Wins Imp Same Dec Imp% | Imp Same Dec Imp%
=====+========================+=========================
0-3 | 14 1 0 96.7 | 9 1 1 86.4
4-5 | 15 0 1 93.8 | 27 5 9 72.0
6-7 | 14 0 8 63.6 | 42 6 23 63.4
8-9 | 8 1 9 47.2 | 34 10 38 47.6
10+ | 2 2 5 33.3 | 23 17 93 23.7
=====+========================+=========================
53 4 23 68.8 | 135 39 164 45.7

From 6 wins on up, there is no difference between the improvement rate of the teams that changed coaches and those that didn't. For the 10+ win group, the percentages appear to be different, but a switch of just one team from the improved to the declined column would make them almost identical.

For the really bad teams, though, the story might be different. I'm too lazy to run the appropriate statistical tests, but it is notable that bad teams that change coaches improve "almost always" while bad teams that don't change coaches only improve "usually." Obviously, what's needed now is to see if that improvement sticks. Perhaps all the gains from the first year are given back in the next year. I'll put an investigation of that on the to-do list.

18 Comments | Posted in General

Asterisk

Posted by Doug on June 9, 2006

I've gotten a couple of emails in the last few weeks alerting me to a situation that I'm sure many others were already aware of. But this is the first I'd heard of it. Friday is rant day, and I think this deserves a rant. Here is one of the emails:

Why are the New York Giants of 1930 listed in first place, while the Green Bay Packers won the title that year, and have a better record?

First let me say that this is a completely appropriate email, and that nothing I write in this post should be interpreted to mean that the emailer was in any way out of line.

I get emails like this every so often. Normally they alert me to a legitimate error in my data or in my programs. I fix it, thank the emailer, and move on. But this time is a little different. The page in question is the 1930 standings page, which does indeed show the following:


W L T PF PA
New York Giants 13 4 0 308 98
Green Bay Packers 10 3 1 234 111

So I went to Total Football to verify. Those are indeed the correct W-L-T numbers for each team, but Total Football lists them in the opposite order. The problem boils down to this:


  • 10/13 = .769

  • 13/17 = .765

  • 10.5/14 = .750

Instead of being counted as half a win and half a loss, ties were simply discarded before computing winning percentage back in those days, which is Just Plain Wrong, and that's the nicest way I know how to put it. If you disagree, then consider that your system would rank a 1-0-15 team ahead of a 15-1-0 team. That's a contrived example, but it is illustrative. Discarding ties would be appropriate if tie games conveyed no information about which team was stronger. But that's not what tie games do. They convey information that the teams were equally strong on that day, which is a very different thing.

Someone please tell me if there is something that I'm missing here. Did forfeits used to count as ties or something like that?

The NFL eventually figured out the error of its ways, because ties are now apparently counted as half a win and half a loss in computing the winning percentages. As best as I can figure it, the change occurred between the 1971 and 1972 seasons. Total Football lists Washington's 9-4-1 record as .692 in 1971, which indicates that the erroneous system was still in place at the time. But it lists the Eagles' 2-11-1 mark in 1972 as .179, which is in compliance with the new (correct) way of counting ties.

Correct me if I'm wrong, but my understanding is that they didn't have a postseason back in 1930. The team with the best record was simply declared the champion. It should have been the Giants, but it was the Packers. Sports fans and pundits really love their asterisks, generally too much, but this is a rare case where an asterisk is completely appropriate.

As I said, I am quite sure I am not the first person to notice this. But it was something of a shock to me. I haven't yet decided whether I should "fix" the standings at the site.

17 Comments | Posted in History, Rant

When bad QBs happen to good receivers

Posted by Doug on June 8, 2006

So I've got Chad Johnson in a keeper league and I'm wondering how much this Carson Palmer situation ought to concern me. On one hand, Johnson's best year was when Jon Kitna was quarterbacking the Bengals. On the other, I don't think Anthony Wright, Doug Johnson, and Dave Ragone are even as good as Kitna. How big a dropoff --- if any --- should we expect from Johnson in the first four games of the season? (It's pure speculation on my part, obviously, but I'd bet money that Palmer doesn't return until after the week five bye.)

My first instinct in this situation is look for comparable situations and see if there are any obvious answers. So that's what I did. I looked for all teams since 1996 that had a quarterback who ranked in the top 10 in fantasy points per game while playing between 8 and 14 games. I then identified the team's top wide receiver, in terms of fantasy points per game, and examined how that receiver did with and without his main quarterback.

I threw out a number of teams because it just didn't feel right to include them. I threw out the 2000 Rams, who split the year between Warner and Green. I threw out all the Viking seasons that were split between some pair of Brad Johnson, Jeff George, and Randall Cunningham. I threw out a few others, trying to keep only the teams that had a typical Backup Quarterback [TM] step in.

Since there are obviously a lot of factors to consider, I won't try to summarize the data. I'll just present it and let you sift through it. Some fine print is at the bottom. Enjoy.


2005 Arizona Cardinals
Main QB: Kurt Warner
Top WR: Anquan Boldin

WK QB R Y T
================================
3 Josh McCown 6 88 0
4 Josh McCown 8 116 1
5 Josh McCown 10 162 1
7 Josh McCown 0 0 0
8 Josh McCown 3 69 1
15 John Navarre 8 134 1
16 Josh McCown 9 81 1
17 Josh McCown 8 81 0
Points per game in 8 games with Warner: 9.9
Points per game in 8 games with other QBs: 12.9

2005 St. Louis Rams
Main QB: Marc Bulger
Top WR: Torry Holt

WK QB R Y T
================================
6 Jamie Martin 6 70 0
12 Ryan Fitzpatrick 10 130 1
13 Ryan Fitzpatrick 6 75 0
14 Ryan Fitzpatrick 10 95 0
15 Ryan Fitzpatrick 3 16 1
16 Jamie Martin 10 163 1
17 Jamie Martin 4 40 0
Points per game in 7 games with Bulger: 15.7
Points per game in 7 games with other QBs: 11.0

2004 St. Louis Rams
Main QB: Marc Bulger
Top WR: Torry Holt

WK QB R Y T
================================
13 Chris Chandler 10 160 1
14 Chris Chandler 6 151 1
15 Jamie Martin 6 95 0
Points per game in 13 games with Bulger: 11.1
Points per game in 3 games with other QBs: 17.5

2003 Denver Broncos
Main QB: Jake Plummer
Top WR: Rod Smith

WK QB R Y T
================================
2 Steve Beuerlein 5 71 0
6 Steve Beuerlein 4 70 1
7 Steve Beuerlein 3 24 0
8 Danny Kanell 4 23 0
9 Danny Kanell 4 58 0
Points per game in 10 games with Plummer: 7.2
Points per game in 5 games with other QBs: 6.1

2003 Minnesota Vikings
Main QB: Daunte Culpepper
Top WR: Randy Moss

WK QB R Y T
================================
3 Gus Frerotte 3 85 0
4 Gus Frerotte 8 172 3
5 Gus Frerotte 5 81 2
Points per game in 13 games with Culpepper: 15.5
Points per game in 3 games with other QBs: 21.3

2003 San Francisco 49ers
Main QB: Jeff Garcia
Top WR: Terrell Owens

WK QB R Y T
================================
9 Tim Rattay 2 17 1
11 Tim Rattay 8 155 1
12 Tim Rattay 5 49 1
Points per game in 13 games with Garcia: 9.5
Points per game in 3 games with other QBs: 13.4

2003 Tennessee Titans
Main QB: Steve McNair
Top WR: Derrick Mason

WK QB R Y T
================================
12 Billy Volek 4 47 0
15 Billy Volek 9 137 0
17 6 90 2
Points per game in 13 games with McNair: 10.7
Points per game in 3 games with other QBs: 13.1

2002 Philadelphia Eagles
Main QB: Donovan McNabb
Top WR: James Thrash

WK QB R Y T
================================
12 Koy Detmer 2 45 0
13 A.J. Feeley 2 16 0
14 A.J. Feeley 5 23 1
16 A.J. Feeley 1 34 0
17 A.J. Feeley 1 8 1
Points per game in 10 games with McNabb: 8.7
Points per game in 5 games with other QBs: 4.9

2001 Minnesota Vikings
Main QB: Daunte Culpepper
Top WR: Randy Moss

WK QB R Y T
================================
13 Todd Bouman 7 158 1
14 Todd Bouman 7 144 2
15 Spergon Wynn 3 34 0
16 Spergon Wynn 2 10 0
17 Spergon Wynn 2 9 0
Points per game in 11 games with Culpepper: 11.8
Points per game in 5 games with other QBs: 10.7

2000 Denver Broncos
Main QB: Brian Griese
Top WR: Rod Smith

WK QB R Y T
================================
4 Gus Frerotte 8 134 0
12 Gus Frerotte 11 187 1
13 Gus Frerotte 4 82 1
14 Gus Frerotte 2 25 0
15 Gus Frerotte 5 82 0
16 Gus Frerotte 6 101 0
17 Gus Frerotte 8 80 0
Points per game in 9 games with Griese: 14.8
Points per game in 7 games with other QBs: 11.6

1997 Arizona Cardinals
Main QB: Jake Plummer
Top WR: Rob Moore

WK QB R Y T
================================
1 Kent Graham 7 96 0
2 Kent Graham 6 108 0
3 Kent Graham 3 27 0
5 Kent Graham 8 147 1
6 Kent Graham 8 108 0
7 Stoney Case 4 87 0
8 Stoney Case 6 101 0
Points per game in 9 games with Plummer: 14.8
Points per game in 7 games with other QBs: 10.5

1997 Jacksonville Jaguars
Main QB: Mark Brunell
Top WR: Jimmy Smith

WK QB R Y T
================================
1 Rob Johnson 6 106 2
2 Steve Matthews 8 117 0
Points per game in 14 games with Brunell: 8.7
Points per game in 2 games with other QBs: 17.1

1996 Oakland Raiders
Main QB: Jeff Hostetler
Top WR: Tim Brown

WK QB R Y T
================================
1 Billy Joe Hobert 4 31 2
2 Billy Joe Hobert 8 96 0
17 David Klingler 5 65 0
Points per game in 13 games with Hostetler: 10.2
Points per game in 3 games with other QBs: 10.4

1996 San Francisco 49ers
Main QB: Steve Young
Top WR: Jerry Rice

WK QB R Y T
================================
5 Elvis Grbac 7 72 1
6 Elvis Grbac 7 108 1
7 Elvis Grbac 7 84 2
9 Jeff Brohm 5 36 0
11 Elvis Grbac 5 49 0
12 Elvis Grbac 6 58 1
Points per game in 10 games with Young: 10.9
Points per game in 6 games with other QBs: 11.8

Fine print: this was done only by looking at game logs, so every game was defined as either a "starter" game or a "backup" game. For example, even though Marc Bulger started the Rams' week 6 game in 2005 and played part of it, the game counts as a Jamie Martin game because Martin threw more passes than Bulger in the game. This pollutes the data a bit, but it's the best I can do with just game logs.

8 Comments | Posted in Fantasy

Who is throwing to whom?

Posted by Doug on June 7, 2006

I had intended to continue the ten thousand seasons experiment for another day or so, by investigating different playoff formats. The programming for that has proved more challenging than I thought it would. It's not so challenging that I can't get it done at some point, just challenging enough that I can't get it done right now. I'll get back to it soon.

In the mean time, my thoughts are starting to turn more and more toward fantasy football, so much so that I am considering the idea of possibly starting to think about doing some projections. Maybe. Anyway, for me, the first step on that road is to collate some team data. In particular, one thing I always like to look at is what percentage of each team's passing yards went to wide receivers, tight ends, and running backs. And then break that down further into primary wide receiver, next wide receiver, and so on.

Another thing I like to do is try to squeeze as much data as I can into preformatted text tables, so here is my latest effort. The top line tells you that in 2003, the Cardinals leading wide receiver (by yardage) accounted for 42% of the team's receiving yardage. Their next wide receiver accounted for 13%. Under the T (for total) you'll see that the wide receiver group as a whole accounted for 70% of the team's yards. Likewise, tight ends contributed 18% and running backs 12%.

At the bottom are the league averages for the past three years.


==== WR =====|=== TE ===|=== RB ==
TM YR 1 2 3 T | 1 2 T | 1 2 T
============================================
ari 2003 | 42 13 6 70 | 16 2 18 | 6 3 12
2004 | 25 20 17 69 | 13 2 15 | 6 5 16
2005 | 30 30 9 77 | 6 3 9 | 5 5 14

atl 2003 | 32 14 5 55 | 21 3 24 | 13 5 21
2004 | 21 14 10 49 | 29 1 30 | 11 8 21
2005 | 21 17 15 55 | 30 1 31 | 8 4 14

bal 2003 | 25 18 7 50 | 28 6 34 | 8 5 16
2004 | 16 15 13 55 | 12 9 30 | 7 5 15
2005 | 32 14 4 52 | 25 5 31 | 9 6 16

buf 2003 | 25 24 19 72 | 11 3 15 | 5 3 13
2004 | 35 29 5 75 | 7 3 13 | 6 4 12
2005 | 29 26 16 80 | 5 1 6 | 6 4 15

car 2003 | 34 26 12 73 | 6 2 10 | 6 5 17
2004 | 36 19 13 70 | 8 3 12 | 10 4 17
2005 | 45 13 8 71 | 6 4 10 | 11 4 19

chi 2003 | 25 20 12 75 | 15 3 18 | 3 2 7
2004 | 26 18 9 59 | 11 3 14 | 16 5 27
2005 | 34 16 11 75 | 10 1 11 | 6 3 13

cin 2003 | 38 23 8 69 | 9 6 17 | 5 4 13
2004 | 36 28 11 81 | 6 2 9 | 5 2 10
2005 | 36 24 11 80 | 5 2 8 | 8 2 12

cle 2003 | 27 21 19 71 | 5 3 12 | 11 4 17
2004 | 26 18 14 69 | 9 8 19 | 6 3 11
2005 | 30 15 13 68 | 12 5 17 | 11 2 15

dal 2003 | 23 20 16 60 | 10 6 16 | 15 4 23
2004 | 27 11 7 60 | 27 0 27 | 6 3 13
2005 | 31 23 9 66 | 21 1 22 | 6 3 12

den 2003 | 27 20 6 55 | 25 2 28 | 10 3 17
2004 | 28 27 9 67 | 14 5 20 | 6 3 13
2005 | 33 23 6 65 | 14 5 20 | 6 5 15

det 2003 | 15 13 11 54 | 15 5 20 | 11 8 26
2004 | 26 17 8 62 | 12 3 15 | 10 6 22
2005 | 23 14 12 60 | 17 1 19 | 9 6 22

gnb 2003 | 21 18 15 59 | 7 7 16 | 11 6 25
2004 | 30 27 8 71 | 8 2 11 | 6 6 19
2005 | 31 14 9 59 | 7 6 18 | 9 7 22

hou 2003 | 34 16 14 67 | 13 3 15 | 12 2 17
2004 | 32 18 12 73 | 5 1 6 | 17 2 21
2005 | 26 18 16 69 | 6 1 8 | 13 7 23

ind 2003 | 30 20 11 67 | 13 8 21 | 7 4 12
2004 | 26 24 23 72 | 9 7 16 | 10 1 11
2005 | 27 25 13 71 | 12 5 18 | 8 2 11

jax 2003 | 22 17 13 67 | 8 4 13 | 10 6 21
2004 | 35 16 8 70 | 5 3 13 | 10 5 17
2005 | 31 20 13 77 | 5 4 10 | 7 2 13

kan 2003 | 21 18 10 53 | 22 1 24 | 17 4 24
2004 | 23 17 5 52 | 27 3 30 | 6 5 18
2005 | 27 13 11 59 | 23 1 25 | 9 5 16

mia 2003 | 32 12 9 57 | 20 4 24 | 12 6 19
2004 | 27 19 11 62 | 23 3 27 | 4 2 11
2005 | 32 20 13 70 | 17 2 18 | 7 3 11

min 2003 | 39 13 11 63 | 10 1 10 | 15 3 23
2004 | 21 16 14 59 | 15 2 18 | 8 5 23
2005 | 18 15 11 63 | 16 5 22 | 10 4 15

nor 2003 | 27 16 13 63 | 12 8 21 | 14 1 15
2004 | 37 20 15 76 | 10 3 12 | 6 5 12
2005 | 26 18 14 69 | 11 5 17 | 8 3 14

nwe 2003 | 21 14 13 64 | 11 8 18 | 12 3 18
2004 | 23 21 12 67 | 10 5 18 | 7 6 15
2005 | 23 17 11 65 | 10 5 17 | 6 5 18

nyg 2003 | 29 17 9 61 | 15 4 21 | 13 3 18
2004 | 24 14 6 49 | 22 1 23 | 19 4 23
2005 | 33 19 5 58 | 24 2 27 | 14 0 15

nyj 2003 | 31 18 8 63 | 10 4 14 | 12 7 23
2004 | 26 24 12 69 | 6 3 9 | 11 8 22
2005 | 28 24 8 67 | 11 9 21 | 5 4 12

oak 2003 | 29 19 12 65 | 8 4 15 | 13 4 20
2004 | 25 17 14 65 | 8 4 15 | 7 6 19
2005 | 26 24 14 74 | 8 1 9 | 14 3 18

phi 2003 | 18 17 15 53 | 10 9 19 | 12 10 29
2004 | 29 16 9 58 | 9 6 16 | 17 3 25
2005 | 20 15 14 58 | 17 2 20 | 16 2 22

pit 2003 | 34 25 10 76 | 4 3 8 | 9 3 16
2004 | 34 24 20 82 | 3 3 6 | 5 3 11
2005 | 31 18 15 69 | 15 2 17 | 7 4 14

ram 2003 | 40 23 12 80 | 6 3 9 | 7 2 11
2004 | 30 28 11 82 | 4 1 5 | 7 4 13
2005 | 31 18 12 79 | 3 2 6 | 7 7 15

sdg 2003 | 27 9 8 55 | 12 4 18 | 22 2 26
2004 | 19 11 9 52 | 27 2 32 | 12 2 16
2005 | 25 19 9 55 | 29 1 30 | 10 4 14

sea 2003 | 29 23 16 71 | 13 2 15 | 8 6 15
2004 | 32 13 13 72 | 9 6 19 | 5 3 9
2005 | 21 19 13 74 | 15 2 18 | 5 2 8

sfo 2003 | 31 17 11 65 | 12 3 16 | 9 6 20
2004 | 19 16 12 55 | 24 3 28 | 6 4 17
2005 | 33 17 13 69 | 3 2 7 | 11 6 24

tam 2003 | 30 15 11 64 | 6 2 9 | 15 5 26
2004 | 33 12 9 65 | 10 3 15 | 11 6 20
2005 | 39 11 9 63 | 11 3 18 | 9 7 20

ten 2003 | 32 20 13 74 | 9 4 18 | 4 3 9
2004 | 32 30 7 70 | 8 5 17 | 4 4 14
2005 | 20 8 8 49 | 14 14 36 | 9 3 15

was 2003 | 37 18 11 73 | 3 1 6 | 6 5 22
2004 | 33 23 7 71 | 11 2 17 | 8 4 12
2005 | 44 6 6 60 | 23 4 30 | 6 2 9

NFL 2003 | 29 18 12 65 | 12 4 17 | 10 4 18
2004 | 28 20 11 66 | 12 3 17 | 8 4 16
2005 | 29 18 11 66 | 14 3 18 | 9 4 15

In some cases, injuries and other circumstances cause these numbers to be a bit misleading. The Eagles' #1 wide receiver last year was Terrell Owens, of course, and the number listed is 20% of their receiving yards. But it was more like 35 or 40 when he was actually playing.

Off the top of my head, here are a few situations worth watching:


  • Will the addition of Javon Walker and apparent lack of a tight end in Denver turn the Broncos into a Cardinal/Bengal type team, where more than 75% of the yardage goes to wide receivers?
  • New Rams coach Scott Linehan has some history of utilizing tight ends, but the Rams top three tight ends --- rookies Dominique Byrd and Joel Klopfenstein and second year man Jerome Collins --- have zero career catches.
  • The Ravens lost most of their RB receiving yards when Chester Taylor left for Minnesota. Taylor was replaced by Mike Anderson, who has never caught a ton of balls. Will they essentially abandon the passes to running backs, as Seattle and Washington have done?
  • Will Keyshawn Johnson catch any passes in Carolina? If so, will that eat into Steve Smith's numbers?
  • Will Brandon Loyd's and Antwaan Randle El's numbers (if any) come at the expense of Chris Cooley? Or will they come at the expense of Santana Moss, whose percentage of team yards was almost as high last year as Steve Smith's?

14 Comments | Posted in Fantasy, General

Ten thousand 2005s

Posted by Doug on June 6, 2006

Prerequisite reading material:

How often does the best team win?

Ten thousand seasons

Ten thousand seasons again

In the previous posts, I simulated ten thousand generic NFL seasons. In some of those seasons the "Seattle Seahawks" were great. In some they were terrible. In some they played a tough schedule, in others an easy one. In this post, I'll simulate ten thousand 2005 NFL seasons. The Seattle Seahawks will be a very good team in each of them, and they will play an easy schedule in each of them.

Mechanically, the procedures are similar, but philosophically there is a world of difference. The generic seasons had teams whose strengths I knew, so I could say things like "the best team" and "Chicago was not very good." I knew who the best team was and I knew how good Chicago was or wasn't. Exactly. Only because I knew those team strengths could I assign the proper probabilities to each game.

But if I want to simulate the 2005 season, I've got a problem: I don't know the team strengths. Neither do you. We have to guess. The guess I'm going to use is the team's rating from the simple rating system. I'm not going to spend time here making a case that that's the best guess or even necessarily a good guess. If you don't think the simple rating system is an adequate representation of team strength, that's fine. No hard feelings. But you'd better stop reading now, because that's the foundation this post rests on.

For those still with me, I'll make one more disclaimer. If I happen to say something like:

Seattle was the 4th-best team in football.

What I actually mean is:

According to the measurement of team strength that we have agreed upon --- which we acknowledge is imperfect in some obvious and some non-obvious ways --- Seattle appears to be the 4th-best team in football.

I am not trying to quash discussion of the merits of the various ways of estimating team strength and I am well aware of the weaknesses of the one I have chosen. But we've got to pick something and go with it, and the prose just seems to flow a bit better if you allow me to use the above shorthand notation. As you know, I can use all the help I can get with making the prose flow.

Now let's get to it. I'll just throw this summary out and then we'll discuss it.

Rating is the team's rating, which is my guess as to its true strength. Avg Wins is the average number of wins each team had over the course of the 10,000 seasons. Div is the number of division titles each team won. WC is the number of times each team got into the playoffs as a wildcard. PO = Div + WC. It is the number of times each team made the playoffs. SB is the number times each team made it to the Super Bowl and Champ is the number of times they won it.


TM Rating AvgWins Div WC PO SB Champ
=====+=========+========+================+===========
ind | 10.8 | 11.2 | 7128 1572 8700 | 2688 1640
sea | 9.1 | 11.1 | 8936 395 9331 | 3461 1780
car | 5.1 | 10.4 | 6304 1818 8122 | 1681 741
den | 10.8 | 10.4 | 4342 2797 7139 | 1825 1092
pit | 7.8 | 10.3 | 5741 1543 7284 | 1469 778
nyg | 7.5 | 10.1 | 5083 2534 7617 | 1785 817
sdg | 9.9 | 9.9 | 3190 2907 6097 | 1343 797
jax | 4.8 | 9.6 | 2727 2951 5678 | 674 321
kan | 7.0 | 9.4 | 2298 2842 5140 | 737 371
cin | 3.8 | 9.3 | 3015 1974 4989 | 516 242
was | 6.0 | 9.2 | 2986 2765 5751 | 989 416
chi | 1.4 | 9.1 | 5653 793 6446 | 721 256
nwe | 3.1 | 8.7 | 5001 476 5477 | 425 194
tam | -1.0 | 8.5 | 1969 2333 4302 | 315 103
dal | 3.2 | 8.3 | 1552 2249 3801 | 409 166
atl | -1.2 | 8.2 | 1652 2122 3774 | 236 73
mia | -0.8 | 8.0 | 3385 481 3866 | 165 52
rav | -1.8 | 7.4 | 773 829 1602 | 61 22
min | -3.5 | 7.3 | 1864 774 2638 | 113 36
gnb | -3.7 | 7.1 | 1616 755 2371 | 93 29
ram | -5.1 | 6.9 | 528 1013 1541 | 59 10
cle | -4.2 | 6.8 | 471 518 989 | 32 9
crd | -5.0 | 6.7 | 481 884 1365 | 46 9
phi | -2.3 | 6.6 | 379 878 1257 | 61 16
rai | -2.8 | 6.3 | 170 427 597 | 22 9
det | -6.7 | 6.3 | 867 417 1284 | 27 6
buf | -5.8 | 6.2 | 889 179 1068 | 20 7
nyj | -6.4 | 6.0 | 725 136 861 | 18 6
oti | -7.6 | 5.8 | 108 256 364 | 4 2
htx | -10.0 | 5.1 | 37 112 149 | 1 0
nor | -11.1 | 4.9 | 75 139 214 | 4 0
sfo | -11.1 | 4.7 | 55 131 186 | 0 0

Indianapolis averaged 11.2 wins per season in the simulation. They won the AFC South 71.2 percent of the time, they made the playoffs 87% of the time, they made it to the Super Bowl about 27% of the time and won it 16.4% of the time.

If you were to translate this into an English sentence, it would not be: at the beginning of the season, we should have estimated that the Colts had a 16.4% chance of winning the Super Bowl. It would be something more like: knowing what we now know in hindsight about how good these teams were in 2005, if we were to play the season again with those strengths remaining the same, the Colts would have a 16.4% chance of winning the Super Bowl. Alright, that's pretty bad English but I hope you get the point.

The probability of winning the Super Bowl depends two things: the team's strength and their schedule (including the playoff schedule). You can see the effect of both in the table. Denver and Indianapolis were essentially equally strong, but the Colts' chances of winning the Super Bowl were significantly higher. And Seattle's were even higher, despite being a weaker team. Carolina had a title chance that was disproportionately high (compared to their true strength) and San Diego's was disproportionally low. We'll revisist them in a moment.

Also note that the spread on average wins --- from Indy's 10.8 to Houston's 4.7 --- is much smaller than the spread on actual wins in the 2005 season. This makes sense. I think it's safe to say that there is almost never an NFL team that is morally a 14-2 team or a 2-14 team. There are, though, probably three or four teams each year --- maybe more --- that are capable of going 14-2 if things break right for them, and there are another few that might slip to 2-14 if things don't. And the result is that we see 14-2 teams and 2-14 with some regularity. This idea might strike some people as controversial, but it's really no different from pointing out that no basketball player truly is a 50-point-per-game player even though certain players do score 50 from time to time.

OK, time to play god. Let's move the Chargers to the NFC South and the Panthers to the AFC West and see what happens.


TM Rating AvgWins Div WC PO SB Champ
=====+=========+========+================+===========
sdg | 9.9 | 11.7 | 8209 1158 9367 | 3344 1790
clt | 10.8 | 11.3 | 7255 1615 8870 | 2881 1610
sea | 9.1 | 11.1 | 8921 398 9319 | 2879 1520
den | 10.8 | 10.6 | 5370 2328 7698 | 2134 1196
pit | 7.8 | 10.4 | 5795 1684 7479 | 1563 787
nyg | 7.5 | 10.1 | 5063 2508 7571 | 1478 727
jax | 4.8 | 9.7 | 2592 3360 5952 | 731 317
kan | 7.0 | 9.6 | 2980 2784 5764 | 902 441
was | 6.0 | 9.3 | 3015 2879 5894 | 827 366
cin | 3.8 | 9.3 | 2979 2222 5201 | 570 256
chi | 1.4 | 9.0 | 5504 754 6258 | 522 184
nwe | 3.1 | 8.7 | 4984 487 5471 | 476 195
car | 5.1 | 8.5 | 1385 2076 3461 | 388 179
tam | -1.0 | 8.3 | 979 2862 3841 | 173 63
dal | 3.2 | 8.3 | 1530 2287 3817 | 306 138
atl | -1.2 | 8.0 | 782 2516 3298 | 147 38
mia | -0.8 | 8.0 | 3298 551 3849 | 180 56
rav | -1.8 | 7.4 | 778 960 1738 | 62 23
min | -3.5 | 7.3 | 1933 661 2594 | 88 19
gnb | -3.7 | 7.0 | 1681 634 2315 | 86 22
ram | -5.1 | 6.9 | 559 1011 1570 | 36 6
cle | -4.2 | 6.8 | 448 593 1041 | 25 6
phi | -2.3 | 6.7 | 392 924 1316 | 49 19
crd | -5.0 | 6.6 | 458 793 1251 | 37 12
rai | -2.8 | 6.5 | 265 524 789 | 33 10
det | -6.7 | 6.3 | 882 369 1251 | 28 6
buf | -5.8 | 6.2 | 935 222 1157 | 32 10
nyj | -6.4 | 6.0 | 783 152 935 | 18 2
oti | -7.6 | 5.9 | 113 315 428 | 4 1
htx | -10.0 | 5.1 | 40 127 167 | 1 1
nor | -11.1 | 4.8 | 30 133 163 | 0 0
sfo | -11.1 | 4.7 | 62 113 175 | 0 0

Interesting.

21 Comments | Posted in Statgeekery

Ten thousand seasons again

Posted by Doug on June 5, 2006

You'd better read Thursday's post and Wednesday's if you haven't yet. Thanks to the many who posted thoughtful comments during the weekend, and apologies for not giving them the thought they deserve. I had a a busy weekend. But I will do my best to address some of them when and if I get a chance.

Today will just be a few more observations from the same experiment, but note that there will be a subtle shift in focus. Last week, I was asking questions about how often the actual best team won the Super Bowl. Today, I'll be investigating how often a team with a given record wins its division or a Super Bowl.

How often will a team with a sub-.500 record win its division?

In 10,000 seasons, a division winner had a sub-.500 record 870 times. If the league structure remains as it is now, we can expect this to happen about once every 11 or 12 years on average. I find this tolerable, I guess. We'll see shortly how often these teams go on to win the Super Bowl.

Amazingly, on two occasions teams won their division with a 5-11 record. This is pretty hard to arrange. Both times, the four teams in the division won a total of 17 games. Since there are 12 intradivision games, this means that those divisions must have been 5-35 in interdivision games.

Again, 10,000 years is a long time.

Because the teams' true strengths were rigged to be symmetric about zero --- which is a very reasonable assumption in general but might possibly break down at the extremes --- there is no point in computing how often a division produces four teams with winning records. It will be (theoretically) the same as the above.

How often will we see a four-way tie in a division?

I think a four-way tie would be cool. It happened 109 times in 10,000 simulated seasons, or once every 92 years on average. In one of the simulated seasons (#2702, if you must know), there was a four-way tie at 11-5 in the AFC West. The Broncos were left out of the playoffs despite having the best true strength in the division and having the best record in the AFC. The Bills won the AFC East at 8-8 and went on to beat the 9-7 Cardinals in the Super Bowl, which makes up for that time they went 15-1 but were bounced from the playoffs early. Strange year.

How often will a team with a sub-.500 record win the Super Bowl?

Fourteen times in 10,000 years. There is about an 13% chance of this happening at some point in the next 100 years. I find this to be tolerable also.

When this format was announced five years ago, I thought the small divisions created too much opportunity for a losing team to get into the playoffs, and hence win the title. But I'm finding that there is something aesthetically pleasing about the small divisions, and a 0.14% chance of a team with a losing record winning the Super Bowl is a price I'm willing to pay.

Here is the full list of the how often the Super Bowl champ had a given number of wins:


Wins Times
===========
7 14
8 135
9 665
10 1541
11 2344
12 2499
13 1728
14 779
15 255
16 40

How often will we see an undefeated team?

We saw 115 undefeated regular seasons, which means roughly one every 87 seasons. As you can see from the table above, 40 of those 114 undefeated teams won the Super Bowl. That might seem low, but it's about 35%. In the comments of the last post maurile computed that, when they make the playoffs, the best team in football wins the Super Bowl about 27% of the time. An average 16-0 team was probably a bit better than an average best-team-in-the-league. So 35% is in the ballpark of what we'd expect.

The moral of the story: going 19-0 is hard. It's probably even harder than the media folks who write and blab every November about how hard it is even realize. I am 34 years old right now. If I live to be 100, and if the NFL remains just as it is now, there is about a 23% chance that I will see a 19-0 team.

12 Comments | Posted in Statgeekery

Ten thousand stories

Posted by Doug on June 2, 2006

Following up on a 15-year-old idea of Bill James, I decided to simulate 10,000 NFL seasons and see what would happen. Well I'm going to milk that idea for several posts. So if the idea doesn't intrigue you, you might want to check back in in a week or so. I'll still be here when you get back.

Today I'm just going to post one gnarly table and let you find interesting things in it if you're so inclined. Then, in keeping with Friday tradition, I'm going to get a bit silly.

Here is the table. It shows how often the team whose true quality was ranked Nth in the NFL finished the regular season with each given seed in their conference. Rank is the true quality rank, #1, #2, etc denote how many times the team with the given rank earned that seed, and OOP is the number of times they missed the playoffs:


========= seed ============
Rank #1 #2 #3 #4 #5 #6 OOP
========================================
1 3822 1906 1106 469 1083 567 1047
2 2634 1827 1160 634 1235 753 1757
3 2039 1672 1192 740 1193 865 2299
4 1692 1435 1161 798 1325 879 2710
5 1356 1383 1118 818 1195 978 3152
6 1128 1245 1126 870 1186 952 3493
7 991 1156 1116 880 1087 952 3818
8 881 1008 1050 814 992 953 4302
9 789 957 949 886 954 907 4558
10 672 850 942 896 910 896 4834
11 532 758 882 928 823 901 5176
12 498 651 819 868 802 875 5487
13 447 657 824 797 789 845 5641
14 401 580 769 775 719 809 5947
15 361 540 633 796 665 726 6279
16 282 477 635 757 622 743 6484
17 247 445 572 692 572 683 6789
18 218 386 492 680 517 703 7004
19 174 333 448 695 463 680 7207
20 178 288 410 660 446 573 7445
21 146 263 435 602 412 543 7599
22 102 239 370 592 368 480 7849
23 105 222 298 566 307 461 8041
24 81 164 312 484 298 452 8209
25 58 137 282 459 242 374 8448
26 58 133 214 432 205 320 8638
27 36 88 197 367 189 297 8826
28 27 70 169 332 149 273 8980
29 20 54 106 264 106 225 9225
30 13 38 103 172 84 173 9417
31 9 31 73 165 38 107 9577
32 3 7 37 112 24 55 9762

If you put a decimal point in there you've got percentages. So the best team in football missed the playoffs about 10.47% of the time, roughly once every ten seasons on average. The best team in football got a bye roughly 57% of the time. The worst team in football made the playoffs about 2.4% of the time.

Now we're going to going to play a game called "Am I as much of a freak as Doug is?"

To start with, I am going to pick one of my ten thousand seasons, totally at random, and I'm going to post a summary of it right here. I want you to spend a few minutes looking over it before reading on.


buf 15- 1
nwe 7- 9
mia 6-10
nyj 4-12

bal 9- 7
cle 8- 8
pit 6-10
cin 4-12

jax 12- 4
ten 8- 8
hou 7- 9
ind 7- 9

den 10- 6
sdg 9- 7
kan 8- 8
oak 7- 9

was 10- 6
dal 9- 7
phi 5-11
nyg 1-15

det 11- 5
gnb 10- 6
chi 8- 8
min 8- 8

car 10- 6
tam 9- 7
nor 8- 8
atl 5-11

sfo 13- 3
sea 10- 6
stl 6-10
ari 6-10

AFC Playoffs:
Wildcard: KC over Denver, SD over Baltimore
Divisional: KC over Buffalo, Jacksonville over SD
Championship: KC over Jacksonville

NFC Playoffs:
Wildcard: Washington over Seattle, Carolina over Green Bay
Divisional: San Fran over Carolina, Washington over Detroit
Championship: San Fran over Washington

I know I have a reader who's a Browns' fan, did you notice that your team missed the playoffs on a tiebreaker? Did anyone notice that an 8-8 team beat a 15-1 team in the playoffs, and that that 8-8 team made it to the Super Bowl? Do you have a mental picture of what that 15-1 Buffalo team looked like, what they played like? What about the 8-8 Super Bowl Chiefs? Do you think they were a running-and-defense team or do you think they won those playoff games 45-38? Did you find yourself thinking that the AFC West and NFC North were probably a lot of fun from start to finish that year?

Did you check to see what your favorite team's record was? Did you check to see if it was better than their main rival's record? If I invented an emoto-scope and hooked you up to it, would it have detected some tiny bit of happiness when you saw your team's record was better?

Finally, did you notice that I didn't tell you who won the Super Bowl? Did you find yourself wanting to know who won it?

If you answered yes to any of the above, you might just be as much of a freak as Doug is. The only possible way you could be more of a freak than Doug is, is if you had an urge to gamble on this Super Bowl.

If I were more eloquent, I'd have something really great to say here about the grip that sports has on our minds. You're all smart people, and you were fully aware that the output above was generated by a bunch of random numbers. But because the random numbers were collated in a specific way and attached to some city names, I'm willing to bet that at least a few of you found them interesting.

If I were more familiar with math history and/or the philosophical side of math, I might have something really great to say about the incredible efficiency of numbers in their ability to tell a story. The standings above are essentially a labeled table of numbers containing roughly 200 characters. Is there any way to write 200 characters of prose that would evoke as clear or as many mental images as those standings did?

In my program that plays out these simulated seasons, I built in a flag that alerts me when something odd happens, like a team with a losing record winning the Super Bowl or a team going undefeated. When I go in to check out those flags, I find myself scrolling up to the season above or down to the season below, about which there is nothing special. But somehow those seasons are always just as fascinating as the flagged ones.

These make-believe seasons were intended to simulate reality in the present day NFL. If you're like me, and you find a random made-up season interesting, then I think the lesson here is that the present day NFL is incapable of producing an uninteresting season. There may be a 24% chance that the best team will win and a 10% chance they'll miss the playoffs, but there is apparently a 100% chance that I will enjoy the NFL in 2006.

Unless Dallas wins.

17 Comments | Posted in Statgeekery

Ten thousand seasons

Posted by Doug on June 1, 2006

You'd better read yesterday's post if you haven't yet.

So the plan is to simulate an NFL season a bazillion times and observe what kind of wacky stuff happens. Here are the particulars.

For each simulated season, I will assign each team a true strength which is a random number from a normal distribution with mean 0 and standard deviation 6. This means that the teams' true strengths are mostly somewhat close to zero. In particular, roughly two-thirds of all teams will have true strengths between -6 and +6, about 95% of all teams will have true strengths between -12 and +12. As you probably guessed, these numbers were rigged so that they generally agree with the values that the simple rating system produces for real NFL seasons in this decade.

You'll note that, even though it will be true for a real NFL season, I am not requiring that the teams' strengths in a given year average zero. Even though we can't observe it (at least not easily), there must surely be years when the league is stronger and years when it's weaker. And in any case, since we are primarily interested in questions like "how often does the best team in football (for that year) win the Super Bowl," it doesn't matter much.

Each simulated season had the same league structure and schedule as the 2005 NFL. That is, there were 32 teams divided into eight divisions of four teams each, and the schedule is just like that of the 2005 NFL.

There is one potential complication here, but I think it's minor. In the simulated world, each season is independent of the previous one, so the two intra-conference games in each team's schedule that are determined by last season's finish are instead essentially against random teams. In the real NFL, the seasons are not independent and good teams probably end up playing very slightly stronger schedules in general than bad teams do. Fortunately, this effect isn't nearly as dramatic now as it was in the 80s and 90s.

Also, I was too lazy to program the tiebreakers. All ties were broken by coin flip. I don't think this will affect anything, but let me know if you think I'm wrong about that.

Finally, the individual games are played by using the same formula we used in this post:


Home team prob. of winning =~ 1 / (1 + e^(-.438 - .0826*diff))

where diff is the home team's true strength minus the visiting team's true strength.

OK, that's that. Let's get to the question of the day, which is: how often does the best team in the NFL win the Super Bowl?

The answer is roughly 24% of the time.

I simulated 10,000 seasons. The table below shows that the best team won the Super Bowl 2,399 times, the second-best team won it 1,448 times, and so.


Tm# SBwins
==========
1 2399
2 1448
3 1060
4 846
5 670
6 584
7 464
8 388
9 327
10 285
11 231
12 189
13 188
14 151
15 141
16 122
17 113
18 72
19 70
20 55
21 42
22 35
23 36
24 22
25 22
26 15
27 12
28 4
29 4
30 3
31 1
32 1

[NOTE: if you thought this table looked slightly different earlier, you're not seeing things. I accidentally inlcuded the wrong table at first, so I updated it about an hour later.]

Very nearly 50% of the time, the Super Bowl champion was one of the best three teams in football. And let me reiterate that when I say "the best team," I am not necessarily talking about the team with the best record. I am talking about the best team. Remember, we're omniscient here. We know which team really was the best.

I'm sure what caught your eye was that the 32nd-best (i.e. the worst) team in the NFL won the title once. Let me tell you about that season.

It was simulated season #6605. The Seattle Seahawks were truly a great team (true strength +15.1) and they played up to their potential, posting a 15-1 regular season record. The Chicago Bears were the worst team in football, but with a true strength of -9.0, they really weren't that bad, at least by worst-team-in-football standards. The NFC North was relatively weak, and Chicago took the division with an 8-8 record.

The Bears' first round playoff opponent was the Carolina Panthers, who were not great (+2.8) but had posted a 10-6 record to finish second in the NFC South. The game was in Chicago, of course, and it was therefore only a mild upset when Chicago won it. Chicago then beat the Saints in New Orleans and the Seahawks in Seattle to reach the Super Bowl.

The AFC was weak in 6605. The best they had to offer was the Jets (+7.2) who had gone 12-4 in the regular season and had beaten the Colts on the road to reach the Super Bowl. The Bears beat the Jets to win the title.

As James points out in his article, there is no single event here that is too hard to believe. It's not unlikely that there wouldn't be any truly terrible teams in the NFL in a given year. It's not unlikely that an entire division would be weak, and it's not unlikely that the worst team in such a division could win the title with an 8-8 record. In their four playoff games, their probabilites of victory were 37%, 10%, 8%, and 21%. That they'd win those four games is certainly unlikely, but no more unlikely than, say, an NL team getting four straight hits at the bottom of their batting order, and I'll bet you've seen that.

No one of those things is terribly bizarre. Yet they all come together to create an almost-unbelievable occurrence. Almost unbelievable. Ten thousand years is a long time. Most of you have probably been watching NFL football for 20 or 30 years, and think of all the crazy stuff you've seen in that time. If you lived another 500 lifetimes, you'd see some even crazier stuff.

Do you think you'd ever see a team like the 2005 Jets win a Super Bowl? And I'm not talking about the Jets if Pennington and Curtis Martin had stayed healthy. I'm talking about the Brooks Bollinger Cedric Houston 2005 New York Jets. If you gave that team 10,000 tries, would they win a Super Bowl? Before you say no, think about all the times you've seen a really bad team rattle off three or four unexpected victories; think of the Craig Krenzel-led Bears during that stretch in 2004, for example. Such runs are unlikely, but you've seen lots of them. Don't you think that, in 10,000 years, some team could string a couple of those runs together, get some breaks from the schedule, and then fluke out in the playoffs?

It could happen.

25 Comments | Posted in Statgeekery

How often does the best team win?

Posted by Doug on May 31, 2006

In the 1989 Baseball Abstract --- yes, there was a 1989 Baseball Abstract; I'll bet I am one of no more than ten people on the planet who has it on his bookshelf right now --- Bill James wrote an essay called How Often Does the Best Team Actually Win? Here is a passage from the introduction:

Yes, we know that the luck evens out in a 162-game schedule, but how consistently? Does the best team win the division, in a 162-game schedule, 90% of the time? 75%? How often? Does the best team in baseball win the World Championship nine years in ten, or two? Is it possible for a team which is in reality just average --- a .500 team --- to win its division (and therefore possibly even the World Series) by sheer luck?

Note that he was not asking how often the team with the best record wins the World Series, or how often a team with a .500 record would win. He was asking how often the team that really and truly was the best wins the World Series, and how often a team that was morally a .500 team would win the world series (most likely lucking into a better-than-.500 record in the process).

Questions like the former can't be answered by looking at real life results, but only because we don't have enough of a sample size. Questions like the latter, though, cannot be answered using real life results even if we live to see a million seasons. We don't know how often the best team wins the World Series or the Super Bowl because we don't know --- we can't know --- who the best team is. Pittsburgh may have been the best team in the NFL last year, or they may have been the 3rd best or the 14th best. We don't know how often a .500 team wins the Super Bowl because we don't know who the .500 teams are.

If you want to know how often the best team wins the title, you have to build a model. In that model, you can create teams whose strengths you know, because you defined them. James did just that, and he concluded that in Major League Baseball, structured as it was in the late 1980s, the best team wins the World Series 29% of the time. The best team in a division wins that division about 53% of the time. The best team in all of baseball missed the playoffs about 29% of the time.

These results seemed to make him a little uneasy. He closed the essay with this:

The belief that in a 162-game schedule the luck will even out is certainly unfounded --- but that unfounded belief may also be essential to the health of the game. Would people lose interest in baseball if they realized that the best team doesn't win nearly half the time? Would it damage the perception of the World Series if people realized that the best team in baseball only emerges with the crown about 30% of the time?

For me, no. It would not damage my interest, and for most of you also, I suspect. I am afraid that for some people, the answer would be the other one. I've learned a lot of surprising things in running these simulations, and I'm happy to have that knowledge....But I don't think it's something I'm going to talk about a whole lot.

I think he's got it backwards. I think it's the stat geeks who are concerned about the best team winning. The rest of the public, in my experience, doesn't give much thought at all to the notion of "the best team," or is content to define the best team to be the one that wins and/or to appreciate the unpredictability for unpredictability's sake. Furthermore, I don't think that, in a 26-team league, 29% is all that low. If the best team in baseball is morally a .600 team, say, then most years there are probably two or three more teams pretty close to that. If a third-best team that is within a few percentage points of the best team happens to win a title because of luck, I don't think anyone considers that a travesty.

In any event, I --- like James --- find the topic fascinating, and have for years been meaning to replicate this study for the NFL. Yesterday's post was not exactly like the James study, but was in some ways similar. And it prompted me to roll up the sleeves and get the simulator built. So I did. And I'm going to spend the next post or five discussing what kinds of things it spits out. Discussion will include, but not be limited to, the followng:


  • I'll answer the same questions James did. How often does the best team in football win the Super Bowl? How often does the best team in football fail to make the playoffs? How often does a sub-.500 team win the Super Bowl? It's not clear how the answers will differ from MLB circa 1989. On one hand, baseball plays ten times more games, which gives the luck more of a chance to even out. On the other hand, football simply doesn't have as much luck built into it as baseball does. If the worst team in baseball beats the best team, it barely raises an eyebrow. In football, that almost never happens.
  • I want to examine various playoff configurations and see how much the answers to the above questions change. For example, what if we eliminated the wildcard and simply let the eight division winners play a standard tournament? Would that increase or decrease the chances of the best team winning? It's not clear, not to me anyway. Sometimes the wildcard lets weak teams in, sometimes it lets strong teams in. What if we had four divisions of eight instead of eight divisions of four? How would that change things? What if, as a friend of mine advocates, we have two conferences of 16 teams each and no divisions at all?
  • I also want to briefly investigate questions along the lines of, how often does a sub-.500 team win its division? Unlike the first bullet, here I'm not talking about teams that were morally sub-.500. I'm talking about teams whose record was under .500. Similarly, we can investigate question like, how often should we see an undefeated team? How often should we see a winless team? What are the chances of a four-way tie in a division?
  • James didn't do this, but I think it will be fun to take a look at some specific teams in specific years. In the previous post, I talked about what would happen if we switched the 2004 Colts and Falcons prior to the playoffs. Now I'll talk about the what would have happened if we had switched them before the season started. This will require an extra step (i.e. leap of faith) which I'll explain when the time comes. As another example, I talked last week about the Chargers having a rough schedule last year. What if they had played the Panthers' schedule last year and the Panthers had played theirs?

Many of these ideas were touched upon in the comments to yesterday's post. If you have more suggestions of questions to ponder, bung them down in the comments.

27 Comments | Posted in Statgeekery

Conference imbalance and playoff fairness

Posted by Doug on May 30, 2006

Last week I posted some quick lists of bad teams that made the playoffs and good teams that didn't.

In the comments of the former appeared this:

2004 really was a bad year for the NFC! I can see at least 4 teams on the list [of below average teams that made the playoffs], and the Falcons are 16th, despite IMO being clearly the second best team in the conference that season.

Four of the six playoff teams in the NFC that year were indeed below average according to the simple rating system. In fact, according to that system, 14 of the 16 teams in the NFC were below average. The average rating of all AFC teams was +7.8, which means the average rating of all NFC teams was -7.8, which means that an average AFC team was 16 points better than an average NFC team in 2004. I'll do a full post (or more) on conference imbalance someday, but for now I'll just say that that differential is the highest since the merger. The NFL was an absurdly imbalanced league in 2004.

This is probably the place to remind everyone, self included, that the ratings are just rough estimates and we should be attaching some mental error bars to them. In particular here, I think the Eagles' rating is likely an understatement of their strength because they mailed in their last three games. This would have a ripple effect on the rest of the NFC, which might mean that, really and truly, only 11 of 16 teams being below average instead of the 14 we're estimating above. Or something like that. Anyway, it doesn't change the fact that the NFL was an absurdly imbalanced league in 2004.

Consider the Colts and the Falcons, for example. In order to reach the Super Bowl, the Colts would have had to first beat a Denver team that was arguably better than any team in the NFC. Then they would have had to beat a 14-2 team and a 15-1 team --- both of which compiled their records against tougher-than-average schedules, I might add --- on the road. That's rough. All the Falcons had to do was win two games, one of them against a below-average opponent. If you believe that teams who accomplished more in the regular season should be rewarded with an easier postseason road, something which is implicitly assumed in the postseason structure of every sports league I'm aware of, then you have to consider this unfair.

I decided to investigate just how unfair it was. The basic idea is this: estimate the Colts' chances of reaching and/or winning the Super Bowl, and compare it to what their chances would have been had they been in the other bracket.

The first thing we need to do is find a formula that relates two teams' ratings to their chances of winning a game between the two of them. I'll skip the details, but here is the formula I used:


Home team prob. of winning =~ 1 / (1 + e^(-.438 - .0826*diff))

where diff is the home team's rating minus the visiting team's rating. If the home team is 7 points better than the road team, this model gives the home team a 73% chance of winning. If the home team is 7 points worse, this model gives the home team a 46% chance of winning. I wouldn't go to war with any bookies using this alone, but it should serve our purpose here, which is to give us the rough estimates needed to simulate the playoff tournament a few bazillion times. That will then give us a rough estimate of each team's probability of winning the Super Bowl.

Here were each team's estimated chances of reaching and winning the Super Bowl at the beginning of the playoffs in 2004:


ReachSB WinSB
===================
1. pit 35.4 22.1
2. nwe 35.7 24.6
3. ind 13.5 9.2
4. sdg 9.2 5.9
5. nyj 3.4 1.8
6. den 2.8 1.8

1. phi 56.3 22.4
2. atl 19.5 5.4
3. gnb 11.5 3.5
4. sea 6.4 1.6
5. stl 2.4 0.6
6. min 3.9 1.1

Anyway, let's see what happens if you switch the Colts and Falcons, giving the Colts the two seed in the NFC and the Falcons the three seed in the AFC:


ReachSB WinSB
===================
1. pit 37.7 19.8
2. nwe 41.7 24.9
3. atl 2.0 0.6
4. sdg 9.9 5.3
5. nyj 3.8 1.8
6. den 5.0 2.6

1. phi 41.2 17.1
2. ind 47.1 24.8
3. gnb 5.2 1.6
4. sea 3.3 0.8
5. stl 1.2 0.2
6. min 2.1 0.5

The Colts' chances of reaching the Super Bowl would have been about three to four times greater had they been in the other league. The Falcons' chances would have decreased by a factor of 10 had they been in the other league. The Bills missed the playoffs in the AFC. Had they been the #6 seed in the NFC, they would have had a 15% chance of getting to the Super Bowl.

Finally, this comes from the comments of the "best non-playoff team" post:

Don’t forget, that 1991 San Francisco team lost to the Falcons on a Hail Mary pass (Tolliver to Haynes, I believe for 44 yards). If that pass is incomplete, SF goes 11-5 and wins the division, NO is a wildcard team and Atlanta misses the playoffs entirely.

Had things played out that way, San Francisco would have had an estimated 16% chance at reaching the Super Bowl and a 10% chance of winning it, and those numbers would be quite a bit higher had the 1991 Redskins not been such a juggernaut.

Yes, yes, I know. That's the way the ball bounces, that's why they play the games, great teams will find a way to overcome bad breaks, and so on and so forth. Anyone with the urge to post, "the Patriots won the 2004 title on the field and that's all that matters" will not be telling me anything I don't know. I get that. I am aware that it's meaningless to say that being in the AFC cost Indianapolis .156 Super Bowl titles in 2004.

For some reason, it's something I wanted to know anyway.

9 Comments | Posted in History, Statgeekery

Tough schedules, lucky teams, and Simpson’s paradox

Posted by Doug on May 29, 2006

These two posts gave me occasion to whip up a program that tells me what every team's record was against playoff teams and against non-playoff teams. Lots of interesting tidbits in there.

For example, the 1998 Cardinals were one of 16 teams since the merger to make the playoffs without having any wins over playoff teams. They were 0-2 against playoff teams. But perhaps more shameful are the 2004 Vikings, who made the playoffs despite going 0-5 against playoff teams. Like the Cardinals, though, they somehow managed to win an actual playoff game.

The 1998 Cardinals and the 1998 Saints provide a very nice example of Simpson's paradox. Check out this table:


Cards Saints Better Record
==================================================
vs playoff teams 0-2 1- 9 Saints
vs non-playoff teams 9-5 5- 1 Saints
Total 9-7 6-10 Cards

The Saints had a better record (percentage-wise) than the Cardinals against playoff teams. The Saints had a better record than the Cardinals against non-playoff teams. But the Cardinals had an overall record that was three games better. In case you're curious, there have been 42 instances like this since 1970. Where else are you going to get info like that?

More trivia:


  • The 1999 Jaguars were winless (0-2) against playoff teams and undefeated (14-0) against non-playoff teams. They are the only team to hold that distinction.
  • The 1989 Browns were 5-1 against playoff teams and 4-5 against non-playoff teams.
  • Ten teams have been undefeated against playoff teams, with the 2003 Patriots having the most wins (5) among those teams.
  • The 1993 Bucs are the only team to play against 11 playoff teams. Four years later, the 1997 Bucs became one of only two teams to make the playoffs despite playing against 10 playoff teams. The 1994 Lions were the other.
  • With the schedule set up as it currently is, every team is guaranteed to play at least two playoff teams each year. Back in the old days, four teams played against just one: the 1970 Cowboys, the 1974 Steelers, the 1976 Rams, and the 1987 Redskins. I don't know enough about historical scheduling practices to know if it was ever theoretically possible to get through a season without playing a playoff team. In any case, no team ever did. [CORRECTION: the 1976 Rams, 1975 Vikings, and 1972 Dolphins did.]
  • The 1997 Packers and 1998 Jets were 7-1 against playoff teams.
  • Two Super Bowl winners, the 1974 Steelers and 1999 Rams, did not beat a playoff team during the regular season. [CORRECTION: add the 1972 Dolphins to the list.]
  • Among Super Bowl winners, the worst record against non-playoff teams belongs to the 1988 San Francisco 49ers, who were 7-4.

11 Comments | Posted in History, Statgeekery

The worst playoff team in history

Posted by Doug on May 26, 2006

This is a companion post to yesterday's best non-playoff team in history.

The worst playoff team in history is, as some of you guessed, the 1998 Arizona Cardinals. They played the weakest schedule in the league and were still outscored by 53 points. They only played one team with a winning record (Dallas. They did play them twice, losing both times.) According to the simple power ranking scheme, the Cardinals were the 26th-best team (out of 30) in the league in 1998. Here are their nine wins:


  • Week 3 - they beat the 3-13 Eagles
  • Week 4 - they beat the 4-12 Rams
  • Week 6 - they beat the 4-12 Bears
  • Week 9 - they beat the 5-11 Lions
  • Week 10 - they beat the 6-10 Redskins
  • Week 12 - Redskins again
  • Week 15 - Eagles again
  • Week 16 - they beat the 6-10 Saints
  • Week 17 - they beat the 5-11 Chargers

Cardinal fans might point out that, by definition, you can't be the worst playoff team in history if you actually won a playoff game. And this team somehow did manage to do that, beating Dallas in Dallas before losing in Minnesota. I don't care. This team was so bad that they take the title anyway.

I'll close with a list of all playoff teams since the merger that the simple rating system says were below average. For obvious reasons, there are a lot of 1982 teams here. For reasons that are not obvious (to me, anyway), the vikings appear eight times on the list.


TM YR Rating
================
ari 1998 -7.4
ram 2004 -6.0
atl 1978 -4.6
cle 1982 -3.7
pit 1989 -3.7
chi 1977 -3.6
atl 1982 -3.6
sea 2004 -2.9
tam 1979 -2.8
den 1983 -2.8
stl 1982 -2.7
nwe 1982 -2.7
hou 1989 -2.5
min 1987 -2.5
nyj 1991 -2.4
atl 2004 -2.2
chi 1994 -1.9
phi 1995 -1.7
min 2004 -1.7
ind 1996 -1.6
min 1977 -1.6
jax 1996 -1.5
nyj 1986 -1.4
ind 1995 -1.3
mia 1970 -1.3
nor 1990 -1.3
cle 1985 -1.3
cin 1990 -1.1
tam 2005 -1.0
car 2003 -0.9
buf 1995 -0.9
sea 1988 -0.7
rai 1993 -0.7
ram 1979 -0.6
dal 2003 -0.5
hou 1978 -0.4
det 1993 -0.3
min 1980 -0.3
min 1978 -0.2
min 1996 -0.1
min 1993 -0.1
min 1997 -0.1
pit 1983 -0.1
chi 1979 -0.0

16 Comments | Posted in General, History

The best non-playoff team in history

Posted by Doug on May 25, 2006

It might just be the 2005 San Diego Chargers.

If you go by the basic power rating system, the Chargers were the third best team in the NFL last year with a rating of +9.9, which means that, if you adjust for the schedule they played, they were about 9.9 points better than an average team. According to that metric, the Chargers were the third-best team since the merger to be watching the postseason on TV:


TM YR Rating
================
sfo 1991 10.4
cin 1976 10.0
sdg 2005 9.9
ram 1970 9.3
mia 1975 8.9
buf 2004 8.1
mia 1977 7.4
stl 1970 7.3
den 1976 7.2
kan 2005 7.0
buf 1975 6.6
sea 1986 6.5
cin 1989 6.5
kan 1999 6.4
ram 1971 6.3
oak 1999 6.2
hou 1975 6.1
min 1986 6.1
bal 2004 6.1
kan 2002 6.1
mia 2002 6.1
hou 1977 6.0
nwe 1980 6.0

Using this rating system to compare across years requires a bit of interpretation. This doesn't say the 2005 Chargers were a better team (or a worse team) than, say, the 1977 Oilers. It says that the 2005 Chargers were better, relative to their league, than the 1977 Oilers were, relative to theirs. It seems to me that's an appropriate metric by which to judge meaningless trivia like "best non-playoff team in history."

If you click on the 1991 49ers and the 1976 Bengals, you'll see that each of them has pretty strong claim to this title as well. The 49ers were third in the NFL in points scored and fourth in points allowed. The Bengals ranked sixth and seventh in those two categories. They were 10-4, with all four losses coming against playoff teams, including two to the eventual Super Bowl champion Steelers.

But I think the simple rating system I'm using actually understates the Chargers' strength. If memory serves (correct me if I'm incorrect), the loss to Denver in week 17 was essentially an exhibition game, as both teams' postseason destinations were already sealed. Further, the Chargers' loss to Philadelphia looks like a bad loss to the computer, but at the time, the Eagles still had Owens and McNabb and were among the best teams in the NFC. Likewise, there is little shame in their loss to the Dolphins, who were in the middle of a six-game win streak when they beat San Diego.

On the flip side, who is the worst playoff team of all time? Unlike the above, where you could reasonably argue for a few different teams, this one is not debateable. I knew who it was before running the numbers, but the numbers confirmed it. I'll write about them in a future post.

16 Comments | Posted in General

Why is 3rd-and-2 a passing down?

Posted by Doug on May 24, 2006

Let's start with just theory. No data.

On 3rd-and-anything, shouldn't the leaguewide success rate on runs and the success rate on passes be roughly equal? On say, 3rd-and-3, if running plays succeeded 70% of the time and passes succeeded only 53% of the time(these are made up numbers), then wouldn't teams start to run the ball more often on 3rd-and-3? Then the fact that teams were running more than they used to in that situation would cause defenses to expect more runs and fewer passes, which would cause them to gear their defenses more toward stopping the run, which would cause the success rate on runs to go down and the success rate on passes to go up.

How far would the success rate on running plays go down? It seems to me it would go down --- and the success rate on passes would go up --- just until the point where they are the same. If the success rates on the two kinds of plays are the same, then offenses don't have any incentive to shift their play-calling mixture. Thus, defenses don't have any reason to shift their expectations, and the success rates should stay the same. Equilibrium.

And we should stay in that equilibrium until the system gets a shock from outside. A rule change that favors the run over the pass (or vice versa) could throw it out of balance. A new play-calling innovation in one aspect of the game could do it.

But even then, we should rather quickly settle down into a new equilibrium. Imagine, for example, that everything is cruising along with a leaguewide 3rd-and-3 success rate of 58% on both runs and passes. Now some hotshot defensive coordinator creates a new scheme that allows defenses to achieve standard 3rd-and-3 pass coverage while at the same time making it very difficult to run the ball. Such an innovation would spread throughout the league, and would generally make running on 3rd-and-3 much less attractive than it used to be. Say the passing success rate stays at 58% while the running success rate drops to 40%.

If you're an offensive coordinator and you can succeed 40% of the time with runs and 58% of the time with passes, what are you going to do? You're going to pass more. The defense will notice this and will start to play the pass a bit more, which will open the run back up a little. But as long as the pass is more profitable, offenses should shift from running to passing. As long long as offenses are shifting from running to passing, defenses will adjust accordingly and make the pass less profitable. As soon as the pass is no longer more profitable than the run, all this shifting stops. Equilibrium.

I was using 3rd-and-3 as an example, but the same reasoning should apply on 3rd-and-anything. On 3rd-and-5, for example, the run has a chance to succeed largely because of the surprise factor, so runs will only succeed if they aren't tried too often. Therefore, it may be an 80/20 pass/run mix that achieves equal success rates. On 3rd-and-1, it may be a 30/70 mix. I am not saying that the number of runs and passes should be equal in any given situation, just that the success rate on runs and passes should be equal.

[I should probably stop short of saying 3rd-and-anything. On 3rd-and-16, for instance, teams use the run as a sort of pre-punt to try to improve their field position rather than as an instrument to pick up the first, and my theory isn't applicable.]

Anyway, that's how it ought to be in some sort of idealized world with perfect information and rational choices and homogeneous teams whose only goals are to get the immediate first down or to stop the other team from doing so. In the real NFL, however, this is how it plays out. This is 2003--2005 data.


Rush (success rate) Pass (success rate)
=================================================================
(3rd-or-4th)-and-1 76.5% (71.5%) 23.5% (53.9%)
(3rd-or-4th)-and-2 41.6% (57.1%) 58.4% (48.9%)
(3rd-or-4th)-and-3 25.5% (55.9%) 74.5% (51.8%)
(3rd-or-4th)-and-4 19.2% (50.2%) 80.8% (47.1%)
(3rd-or-4th)-and-5 15.8% (38.1%) 84.2% (42.1%)

To make sure we're clear, the second line says that on 3rd-and-2 (or 4th-and-2) during the past three seasons, teams have passed the ball 58.4% of the time and run it only 41.6% of the time. When they've passed, they've picked up the first 48.9% of the time. When they've run, they've picked it up 57.1% of the time.

The data fits the theory fairly well on 3rd-and-3, 4, and 5. But it's not even close on 3rd-and-1 and 3rd-and-2. That brings us to the title of the post: why is 3rd-and-2 a passing down? An alternate title might be, why does my theory stink so bad?

Maybe my theory doesn't stink, but the pace of innovation casuses the equilibria to be so short-lived that they can't be captured with a 3-year snapshot.

Maybe my theory doesn't stink, but the equilibria show up at the team level and not at the league level. This would be tough to verify, as the sample sizes get pretty smallish if you look at things one team at a time. For the record, here are the three-year average run/pass rates and overall success rates on 3rd-and-2:


TM R/P ratio ConvRate
========================
dal 62 / 38 44.2
den 60 / 40 52.3
buf 59 / 41 44.4
car 54 / 46 50.0
sdg 52 / 48 52.1
nwe 52 / 48 65.5
sea 48 / 52 66.0
stl 46 / 54 38.0
pit 46 / 54 47.5
atl 46 / 54 49.1
jax 45 / 55 54.7
sfo 44 / 56 40.0
nyj 44 / 56 50.0
min 44 / 56 58.0
bal 43 / 57 50.8
mia 42 / 58 54.2
nor 40 / 60 67.3
chi 40 / 60 52.7
hou 40 / 60 49.1
phi 40 / 60 53.5
ari 39 / 61 57.1
ind 39 / 61 52.9
oak 39 / 61 63.3
cin 39 / 61 70.5
was 38 / 62 55.1
kan 37 / 63 58.1
nyg 36 / 64 53.3
cle 35 / 65 40.0
gnb 35 / 65 57.8
ten 28 / 72 44.0
tam 20 / 80 43.1
det 11 / 89 44.3

Are you kidding me Steve Mariucci? You're passing 89% of the time on 3rd-and-2?

I always thought running was standard procedure in short yardage, and I always thought 2 is short yardage. Yet teams pass more than they run on 3rd-and-2. This would make sense if teams were having more success with the pass on 3rd-and-2. But they're not. Why are teams passing in a running situation even though it's not working?

It is possible that the success rates are skewed in favor of the run because of quarterback run-pass option plays or unplanned scrambles. That is, quarterbacks on such plays tend to run only if they know they can get the first, and throw it away otherwise. This would cause the successes to get counted as runs and the failures to get counted as passes, even though it's the same play. But there can't be enough of those plays to make too much difference.

Maybe teams are interested in more than just the immediate first down. On 3rd-and-(1-or-2), 7.3% of pass plays went for 20 more yards, while only 2.4% of running plays did. Maybe, contrary to David Romer's findings, teams will trade in a surer chance at a 2-yard first down pickup for a chance at a long gainer.

13 Comments | Posted in General

More on rating systems: margin of victory loss

Posted by Doug on May 23, 2006

Back in this post, I described a simple iterative ranking scheme. Like all rating systems, that one has its strengths and weaknesses.

That system is not one of the systems actually included in the BCS selection process, because a few years ago the BCS mandated that all their computer ranking algorithms must completely ignore margin of victory. This is a controversial topic among aficianados of ranking algorithms.

One one hand, the margin of victory contains extra information. If you know that Team A beat Team B, that tells you something about the relative strengths of the two teams. But if you know that Team A beat Team B by 31 points --- or by one point --- you know more about the relative strengths. You don't know everything, of course, but you know more, and it just makes good sense to include more data rather than less. On the other hand, using margin of victory is in some abstract sense contrary to the point of almost all sports, and football in particular. The only purpose of the score is to determine a winner. The team that wins by 31 may have looked more impressive than the team that wins by a single point, but The Institution Of Sport does not recognize them as having accomplished anything different. A win is a win.

In general, I can see the merits of both sides of the debate. But in the particular case of using mathematical algorithms to help determine which teams play in the official national championship game, as with the BCS, it certainly does make sense to remove margin of victory from consideration. Otherwise, teams would have incentive to run up the score needlessly in a game that is already essentially over, which is almost universally considered poor sportsmanship (I don't necessarily agree with that almost-universally-held view, by the way, but that's another post.) But whether it's bad sportsmanship or not, incentives change behavior. And at the very least, including margin of victory gives teams incentive to attempt to inject false information into the equations.

Anyway, a reader named Vince posted this in the comments to the above-linked post:

My dad and I used to argue that teams should be measured on 1) W-L %, 2) Strength of schedule, and 3) Margin of loss. This came about in one college season where two teams who played similar schedules each had one loss, but one team lost by seven and the other by a huge margin.

Would it be possible to do a ranking that puts a margin of one point on all wins, but has no such limits on losses?

Vince and his dad are a couple of sharp dudes. By treating all wins --- but not all losses --- equally, we can capture some of the information contained in the score without giving teams any incentive to run it up. So I starting playing around to see if I could figure out a way to make it mathematically feasible. And I think I did. Here is the plan:

  1. Figure out the average margin of victory in all games during the course of the season. In the 2005 NFL, it was about 11.7. That is, the winning team scored, on average, 11.7 more points than the losing team.
  2. Count every win as +11.7 points, and every loss as -N points, where N was the actual margin of the game. So a one-point loss is -1, and a 20-point loss is -20. A one-point win is +11.7, and a 20-point win is +11.7.
  3. Compute each team's average point margin using to the strange accounting system described above. For example, the Chargers were 9-7 last year. Their seven losses were by a total of 43 points, so their average point margin would be (11.7 * 9 - 43) / 16, which is about +3.9. A team that went 16-0 would have a margin of +11.7, while a team that went 0-16 might have a margin anywhere from -1 to -40 depending on how lopsided their losses were.
  4. Now you've got a collection of average point margins that sum to exactly zero, so you can plug into the same system we used previously. Simply adjust the ratings repeatedly until they stabilize.

Here are the ratings for the 2005 NFL using this scheme:


TM Rating StrOfSched
=============================
1. den 9.6 1.9
2. ind 7.2 -1.5
3. sdg 6.8 2.9
4. sea 6.3 -1.8
5. nyg 6.1 0.9
6. was 5.8 1.9
7. kan 5.5 1.8
8. jax 5.2 -1.6
9. pit 4.8 -0.8
10. dal 4.7 1.7
11. car 4.3 -1.9
12. nwe 3.4 0.7
13. cin 2.6 -1.2
14. tam 2.5 -1.9
15. chi 2.1 -1.9
16. mia 1.3 -0.5
17. atl -0.4 -1.0
18. phi -1.8 2.3
19. min -2.6 -0.9
20. oak -2.7 2.6
21. bal -2.9 -0.2
22. ram -3.2 -1.1
23. cle -3.4 -0.5
24. ari -4.5 -0.3
25. gnb -4.7 -0.6
26. buf -5.1 0.5
27. nyj -5.1 1.1
28. det -5.5 -0.7
29. ten -7.8 -0.4
30. nor -9.1 -0.0
31. sfo -9.1 0.7
32. hou -10.1 0.0

Remember I said there is no incentive to run up the score? In fact there is a disincentive to do so. If you run up the score, you do nothing to your average point margin (because all wins are counted the same), but you do hurt your opponent's point margin. This weakens your strength of schedule, which actually lowers your rating. Here is some "proof." The Colts beat the Cardinals 17-13 in the last game of the season last year. If we change that score to 57-13, here are the new ratings:


TM Rating StrOfSched
=============================
1. den 9.9 2.0
2. ind 7.1 -1.7
3. sdg 7.0 3.0
4. sea 6.0 -2.3
5. nyg 6.0 0.7
6. was 5.7 1.8
7. kan 5.7 1.9
8. jax 5.1 -1.8
9. pit 5.1 -0.7
10. dal 4.6 1.5
11. car 4.4 -1.8
12. nwe 3.7 0.9
13. tam 2.8 -1.7
14. cin 2.8 -1.0
15. chi 2.3 -1.8
16. mia 1.6 -0.3
17. atl -0.2 -0.8
18. phi -1.9 2.1
19. min -2.4 -0.8
20. oak -2.5 2.8
21. bal -2.7 -0.1
22. cle -3.2 -0.4
23. ram -3.6 -1.5
24. gnb -4.5 -0.4
25. buf -4.8 0.7
26. nyj -4.9 1.4
27. det -5.5 -0.7
28. ari -7.1 -0.4
29. ten -7.9 -0.6
30. nor -8.9 0.1
31. sfo -9.5 0.3
32. hou -10.3 -0.2

The Cards drop four spots, as Vince and his dad think they should, but the Colts' rating also dropped just a hair. Instead of giving teams incentive to score, score, score in the closing moments of an already-decided contest, this system would actually give teams incentive to let the other team score. It's a kindler, gentler rating system. Hooray for everyone!

In all seriousness, though, I can't envision that becoming a practical problem if a system like this were installed as part of the BCS formula. One question I have is whether this system would produce college football ratings that look reasonable to most people. I think it would, but we'll have to run the numbers to find out for sure. I'll put that on the to-do list.

6 Comments | Posted in BCS, Statgeekery

More home cookin’

Posted by Doug on May 22, 2006

Last week I posted this breakdown of success rates at home versus on the road on third (or fourth) and one when the play was close. I'm just going to throw out a few similar breakdowns here. As I said in the previous post, I don't think it's possible to determine from the stats whether there is an officiating-related home field advantage, so I'm going to refrain from commenting much. I just thought you might be interested in the numbers.

First, here is the dual breakdown to the one I presented last week. The first column is the exact data I presented in the last post. The second column contains the conversion rates on plays that were not close (and hence where a spot couldn't have made a difference).

Success rates on rushing plays on (3rd-or-4th)-and-1


When the play is close When not close
=========================================================
home team 48.7% 87.2%
road team 40.8% 86.7%

And here is some further detail:

All (3rd-or-4th)-and-1 rushing attempts


Gain<0 Gain=0 Gain=1 Gain>1
=============================================
home team 8.3% 17.7% 16.9% 57.0%
road team 8.2% 22.8% 15.7% 53.3%

Finally, these data should give us an idea of what the overall home field advantage is on 3rd down (and 4th down) plays.

Success rates on all (3rd-or-4th)-and-N plays


N Home Road
========================
1 68.6% 66.0%
2 53.3% 51.2%
3 52.7% 53.0%
4 48.1% 47.3%
5 42.6% 40.4%
6 44.9% 40.8%
7 36.2% 39.0%
8 32.1% 31.5%
9 33.2% 29.2%
10+ 21.0% 19.2%

3 Comments | Posted in Home Field Advantage

Home cookin?

Posted by Doug on May 19, 2006

You know what I hate?

The quarterback sneak.

I acknowledge that it's generally a pretty effective play if you need to pick up two inches. But it's really ugly. And besides that, it puts the refs in a tough spot. On most quarterback sneaks, it's impossible to get a decent spot because no one --- not the refs, the fans, or even the TV cameras --- can see through the pile of bodies well enough to pinpoint the exact spot of the ball (which you can't see) at the time that the knee (which you can't see) touches the ground (which you can't see) or figure out when the forward momentum of the ball carrier was stopped. It just can't be done. And the result is that the ref has to arbitrarily decide whether to award a first down or not.

That makes me wonder whether the arbitrary spots that the home team gets might be different from the arbitrary spots that the road team gets. I decided to take a very incomplete preliminary look at some data to see if anything interesting would turn up. And, though I started this post talking about quarterback sneaks, I'm going to open up the data to the broader topic of short-yardage situations.

So here is what I did. I looked at all 3rd-and-1 and 4th-and-1 situations during the past three seasons in which a rush was attempted and where the rush gained either zero or one yard. Inasmuch as we can tell from the play-by-play data, those would be the plays where a spot could make the difference. Here is the data:


attempts successes success rate
===============================================
home team 357 174 48.7%
road team 390 159 40.8%
===============================================
TOTAL 747 333 44.6%
===============================================

Given the sample sizes involved, it's very unlikely that such a split would happen by chance if the true success rates were equal. So we have pretty good evidence that the success rates are not the same. It's pretty likely that something is going on here.

I need to state clearly that this does not necessarily say anything about the refs and whether their spotting guesses are influenced by the home crowd. The refs are just one of many possibilities for the something that is going on. Teams in all sports do all sorts of things better at home than on the road, so this could be just another non-officiating-related manifestation of that slippery character named home field advantage.

Or maybe it's not. This data isn't merely saying that the home team converts more often on 3rd-and-1. It's saying that they convert more often on 3rd-and-1 when the play is close. I don't think it's possible to statistically separate the officiating-related home field advantage (if any) from the non-officiated-related home field advantage, so we'll never know. But this looks a bit suspicious to my paranoid eye.

I think sports rooting is a good outlet for me to release all my irrationality. Most people who know me consider me pretty logical and level-headed, and generally I am. As I sit here typing this, I truly believe that "this does not necessarily say anything about the refs and whether their spotting guesses are influenced by the home crowd. The refs are just one of many possibilities for the something that is going on." But the first time a team I'm rooting for gets a bad spot on the road, this data will become iron-clad evidence of widespread conspiracy.

That's healthy, right?

10 Comments | Posted in Home Field Advantage

Team quarterbacking through the years

Posted by Doug on May 18, 2006

The end of the Joey Harrington era in Detroit gave sports economist Dave Berri a chance to observe that no Lion quarterback has made the pro bowl in 35 years. That's pretty bad, but according to what I'm about to show you there are a few other teams that can make a case as having had worse overall quarterback play than Detroit over the course of the "modern era for passing" (1978--present).

Here is the plan:


  1. Compute each team's passer rating (just for quarterbacks --- passing attempts by others have been discarded) for each season since 1978. I'm not a fan of the NFL's passer rating formula and I'm not sure what possessed me to use it here, but you'll get similar results if you use yards-per-attempt or, I suspect, any other reasonable metric.
  2. Compare it to league average and get a Passing Effectiveness Index for each team for each year. For example, Detroit's quarterbacks posted a 69.1 passer rating last season. League average was 80.0. Dividing the Lions by the League gives you about .863, which I'll multiply by 100 to make it more easily digestible. The Lions Passing Effectivness Index for 2005 was 86.3.
  3. Average each team's Passing Effectiveness Index over all the years they've been in the league (since 1978). When you do that for the Lions, you get 92.9. This means that Detroit's quarterback's have been, on average, about 7.1% less effective than average (according to passer rating) over the past 28 years.

You get no prize for guessing what franchise has the highest average Passing Effectiveness Index. It's the 49ers, who boast an extremely impressive 115.4. The second best franchise has a 105.8. In fact, the difference between San Francisco and #2 is bigger than the difference between #2 and #24.

As foreshadowed above, last place belongs not to the Lions, but to their divisional rivals: the Chicago Bears. This is a grim list indeed:


YR PEI Main QB
===========================
1978 72.6 Bob Avellini
1979 96.2 Mike Phipps
1980 78.9 Vince Evans
1981 73.0 Vince Evans
1982 93.2 Jim McMahon
1983 98.6 Jim McMahon
1984 98.6 Jim McMahon
1985 103.1 Jim McMahon
1986 79.9 Mike Tomczak
1987 99.4 Jim McMahon
1988 98.0 Jim McMahon
1989 91.1 Mike Tomczak
1990 94.3 Jim Harbaugh
1991 97.2 Jim Harbaugh
1992 91.8 Jim Harbaugh
1993 85.0 Jim Harbaugh
1994 100.0 Steve Walsh
1995 117.9 Erik Kramer
1996 93.7 Dave Krieg
1997 85.8 Erik Kramer
1998 97.5 Erik Kramer
1999 99.5 Shane Matthews
2000 85.7 Cade McNown
2001 94.6 Jim Miller
2002 91.5 Jim Miller
2003 77.8 Kordell Stewart
2004 75.7 Chad Hutchinson
2005 76.7 Kyle Orton

Only thrice in the last 28 years have the Bears even been above average in the passing game. Also below the Lions are the Texans, the Buccaneers, and the Cardinals, but all those teams are very close.

I'll post the full list later today, but I wanted to first give you the opportunity to impress me by guessing who is #2 on the list after the 49ers.

Addendum: Good guessing by monkeytime. Here is the list. PEI is the franchise's average Passing Effectiveness Index, PctOverAvg is the percentage of that franchise's seasons in which they've been above average in PEI.


Franchise PEI PctOverAvg
===================================
49ers 115.4 85.7
Jaguars 105.8 72.7
Dolphins 105.2 64.3
Vikings 104.4 57.1
Cowboys 103.3 64.3
Broncos 103.1 57.1
Bengals 102.2 53.6
Packers 102.2 50.0
Chiefs 102.1 57.1
Oilers/Titans 101.1 57.1
Redskins 101.0 50.0
Jets 100.9 42.9
Rams 100.9 50.0
Raiders 100.9 46.4
Bills 100.9 60.7
Eagles 100.4 57.1
Browns 100.3 40.0
Colts 99.8 39.3
Falcons 99.7 46.4
Seahawks 99.6 50.0
Patriots 98.6 42.9
Chargers 97.6 35.7
Panthers 97.4 54.5
Steelers 97.2 46.4
Saints 95.6 46.4
Giants 95.2 42.9
Ravens 94.2 20.0
Lions 92.9 21.4
Cardinals 92.8 28.6
Buccaneers 91.9 21.4
Texans 91.1 25.0
Bears 91.0 10.7

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