SITE NEWS: We are moving all of our site and company news into a single blog for Sports-Reference.com. We'll tag all PFR content, so you can quickly and easily find the content you want.
Also, our existing PFR blog rss feed will be redirected to the new site's feed.
Pro-Football-Reference.com » Sports Reference
For more from Chase and Jason, check out their work at Football Perspective and The Big Lead.
ShareThisTen thousand stories
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.
|
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.
This entry was posted on Friday, June 2nd, 2006 at 4:16 am and is filed under Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.
OK, Browns fan here. I'll bite. I am as much of a freak as Doug. Interesting stuff.
But, I'd like to see how this all plays out under my division-less, conference-less NFL reorganization. My guess is that best teams would fare better.
Maybe I'm missing something (I probably shouldn't read this site before my morning coffee) but for the first 10 teams ranked by true-strength, why do they end up 5th seed more often than 4th? Is it some anomaly of the NFL's seeding system, or is something else at work here?
silentdibs, that made me do a double-take as well. But I think it makes sense. The fourth seed is the division champion with the worst record. The fifth seed is the team with the best record among non-division-winners.
So roughly speaking, if you're the best team in football you're more likely to have a good record but lose your division than to have a mediocre record and win your division.
Meanwhile, at the bottom of the list, a #4 is more likely than a #5, which means that bad teams are more likely to win their division than to get a wildcard.
Bears fan here, I'm willing to admit I felt a tinge of pride yesterday when I saw my "worst team in the nfl" scrapped their way to an 8-8 record and gutted their way to the superbowl. Nice to know I'm not insane. Or at least I'm not the only one.
Btw, I'll take KC with the points and the under
Doug Man! Bills 15-1. Nice
What's the money line on the Bills winning the SB? Oh, shoot... i forgot, they lost to the Chiefs. Darn.
Were the Bills the best team in that simulation?
Also, in your simulations, did games have scores, or was it just win-lose? If it was, how did you compute the ratings for the next simulation? (I thought point differential was a key aspect of the power ratings)
This blog/site is great! Now I check it before I check my email every day!
Finally you are speaking my language. Before I bet on the superbowl I must know, is Montana playing for the 49ers or KC?
I read somewhere that in all 32 NFL markets they surveyed people to name their favorite NFL team and their least favorite NFL team. In all 32 markets except Dallas, The Dallas Cowboys ranked #1 for most favorite (local teams excluded) and #1 for least favorite. I am wondering if I am becoming to fit into both groups. I love making fun of cowboys fans but after 25 years in Dallas, I am actually starting to care if they win. God. Go Redskins.
So the best team makes the playoffs 89.53% of the time, gets a bye 57.28% of the time, and wins the Super Bowl 23.99% of the time.
That means in each playoff game it plays, it is better than a 2-1 favorite, on average, against some pretty good competition.
When it makes the playoffs, it wins .2399/.8953 = 26.8% of the time.
(.5728)*(.677^3) + (.4272)(.677^4) = 26.8%
So if it's 67.7% to win each individual playoff game, it'd win the Super Bowl 23.99% of the time overall.
Does 67.7% seem high?
I don't know where to find historical moneyline data for NFL playoff games, but last year the Steelers were an implied 56%-58% to win over the Seahawks based on moneylines of +160/-180 or +165/-190.
I'll ask this (again) on this post, because the data is almost there in the above. What distribution of strength ranking is more likely to produce championship over a multi-year period?
For example: Does being ranked 1,1,15,15 produce more championships on average than being ranked 8,8,8,8? (same total amount of true strength just distributed evenly, vs. highs and lows). Should a team stop trying to go get those last players to "put them over the top" (boom and bust, ala the Titans) or shoud they just be "good enough" for a longer period and wait for chance (schedule, etc.) to do the rest? I'd guess it's the latter.
The team that is 1,1,15,15 would win more championships than the team that is 8,8,8,8.
The team that is 1,1,33,33 (i.e., it completely forfeits half its seasons) would win the championship 12% of the time (since the #1 team wins 24% of the time).
The team that is 8,8,8,8 will make the playoffs about 57% of the time. In order to win the championship 12% of the time like the 1,1,33,33 team will, it would have to win the championship 21% of the time that it makes the playoffs. (21% * 57% = 12%)
That's way too high. Since there are 12 teams in the playoffs, the average playoff team has a 1/12 = 8.33% chance of winning the Super Bowl. That's far less than the required 21%, and the #8 team is not likely to be much better than the average playoff team, if it is better at all.
Oops. I didn't need to do all of that work. The answer is in the Ten Thousand Seasons article.
The 1,1,15,15 team will win 12.7% of the time and the 8,8,8,8 team will win 3.88% of the time.
Re: silent dibs and Doug's comments. I noticed that two, and it sort of added to my thought that the current playoff/division setup makes it more likely that a bad team can make the playoffs, compared to previous setups. Now, you only have to beat out 3 other teams, and if you happen to have a group of 4 where none is significantly above average, a bottom dweller could get in (with a home game). Further, teams used to play the same amount of teams from the other divisions in conference, now, if the bad teams happen to be concentrated in one half of the conference that plays each other, it increases the chances as well.
Doug, one of the questions you had posed in the original post was in regard to looking at different playoff formats. Is that coming up? I am guessing that it was harder for bad teams to make the playoffs and advance under previous formats. We've only had 4 years of the current format so far, but can we expect higher chances of bad teams succeeding due to the setup?
If you are going to run other simulations, I would be interested in comparison of the current system to the following:
1) 28 teams (6 divisions) that was in place throughout the 80's, along with whether it mattered whether the best team was in a 4 team division like NFC West or not, while others had to play in 5 team divisions;
2) 30 teams (6 divisions) in place after Jacksonville and Carolina joined the league;
3) Current divisions structure, but with the Chiefs' proposed 7 team playoff structure, with only top seed getting bye;
4) Current divisions structure, 6 team playoff; but playoff seeding by the following--top 2 division winners get byes, remaining 2 wildcards and 2 division winners seeded by record/tiebreakers, so top wildcard could host first round game if it had better record than division winner (similar to the system NBA is going to next year).
You think this is freaky? I've set up tournaments on Madden, sat back and watched the games, and cheered. Yes, cheered. For a video game.
When I walk the dog, I do a lot of thinking. Tonight was no exception. It now makes perfect sense to me that you can expect the BEST football team to win the Super Bowl once every four years on the average. Given that fact, what is the point of the Super Bowl? What does it prove? It is about as useful as preseason for weeding out and/or showcasing who the best team is. Worse yet, it often makes heroes of a team that isn't the best team while the best team is just one of the other 31. Screw the Super Bowl... it is pointless!! Anybody got any thoughts?
In comment #7 above, I wrote:
I am having trouble recreating my error so I don't know exactly where I goofed -- but that is an error.
A moneyline of Seahawks +160 / Steelers -180 means that the Steelers should win between 180/280 = 64.3% of the time and 1 - 100/260 = 61.5% of the time. (The precise number would be 62.57% of the time. The Steelers are 180/280 = 64.3% to win, and the Seahawks are 100/260 = 38.46% to win. But because of the vigorish, those add up to 102.57% rather than 100%. So the Steelers are really 64.3%/102.75% = 62.57% to win.) A moneyline of Seahawks +165 / Steelers -190 means that the Steelers should win 63.45% of the time.
So I should have said 62%-64% instead of 56%-58%. Which makes the 67.7% figure look better.
I wouldn't say the Superbowl is pointless, I'm quiet content in calling the winner the league's best team. If only because you let it be decided on the field, and the tournement format seems the best way to do that.
RE seeding:
Thats a good point about the problem with 4 divisions. Let me second the motion to see this simulation run for different formats.
also i've definitely watched my share of simulated madden games, but creating a tournament? that ain't right.
I've been thinking about the way your model works, and it made me wonder:
What would happen if you tweaked your model a bit, like
-increasing/decreasing home field advantage (for the entire NFL, or for specific teams, if they have an especially high/low home field advantage)
-increasing/decreasing ratings of certain teams at random points in the season to account for key injuries
-Assigning ratings based on a team's actual overall record instead of randomly assigning a number
-increasing/decreasing ratings of certain teams for several years at a time, to account for an extremely good/bad player or coach
-taking into account the behavior of teams that play their second string players in the last games of the regular season if they have already clinched home-field advantage for the playoffs
This is really interesting stuff, and I look forward to the next post.
I'm ashamed to say that in the random season I immediately began by saying, "I wonder how philly did?" before realizing that was an idiotic thing to ask.
It would be useful to know what the intrinsic strengths of each team was in the random season when discussing it, though. Coding the real tiebreakers probably wouldn't change things much, but it might. For instance, when a bad team finds itself in contention for a division title it's pretty likely it did this by beating its also mediocre division mates, and might win tiebreakers more often than a coin flip. Maybe. It isn't strange to think there might be biases like this in some cases.
Of course, it's important to recognize that the absolute numbers here are a function more of the model (intrinsic strengths are normal w/ SD=6) and the win/loss predictor, than the NFL. But, I suspect that the relative implcations of different divisional setups might be less model dependent than the SB winner stats in any one setup.