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Ten thousand seasons with no standards

Posted by Doug on June 29, 2006

In case you just stumbled in today, this post is the latest in a long string. Read these first: I, II, III, IV, V.

I got into a conversation yesterday with one of the two readers of this blog who I actually see in person on a regular basis. I conjectured, based on yesterday's results, that, assuming we keep the eight four-team divisions and demand that the winners of those divisions get seeds one through four in the playoffs, the current system (two wildcards) is the one that maximizes the chances of the best team in football ending up with the Lombardi Trophy. My reasoning: if you eliminate the wildcard, you will too often shut the best team out of the playoffs altogether (we saw this in yesterday's post). And if you have more than two wildcards, you will too often make the best team navigate an extra round of playoffs.

My friend then made this bold claim:

I'll bet that if you let all 16 teams from each conference into the tournament, then the best team's chances of winning it all would be greater than they are with the current system.

At first I thought this was ridiculous, but it didn't take too much thought to realize that he might be right. For one thing, letting everyone in would guarantee that the best team actually makes the playoffs. And in the usual case, where they win their division and post a good record, all it really does is add a game against the 16th seed and a game against the 8th or 9th seed. Not too much different from a couple of byes. Sure, there is a slim chance of an upset. But there is also a chance of an upset that knocks off the best team's toughest competition.

Only one way to find out.

I'm going to apologize in advance for the lack of decent formatting. I just don't have time to get it done the way it ought to be done. So it's going to be long and unwieldy. I will look at four different playoff formats, two of which will be review. For each one, I'll show the number of times (out of 10,000) that the true #1 team in the NFL won the Super Bowl, the number of times the true #2 won it, and so on. Then, I'll show how often the Super Bowl winner had each given number of regular season wins. I'll add some brief thoughts at the end.

The current system: two wildcards


Tm# SBwins Cumulative
=====================
1 2399 2399
2 1441 3840
3 1064 4904
4 826 5730
5 652 6382
6 559 6941
7 492 7433
8 386 7819
9 312 8131
10 293 8424
11 231 8655
12 210 8865
13 176 9041
14 162 9203
15 138 9341
16 120 9461
17 100 9561
18 73 9634
19 83 9717
20 58 9775
21 44 9819
22 50 9869
23 38 9907
24 24 9931
25 21 9952
26 14 9966
27 9 9975
28 12 9987
29 4 9991
30 8 9999
31 1 10000
32 0 10000


Wins Times Cumulative
======================
6 2 2
7 7 9
8 150 159
9 651 810
10 1528 2338
11 2413 4751
12 2502 7253
13 1674 8927
14 822 9749
15 214 9963
16 37 10000

If you can see that the 4th-best team in football won the Super Bowl 8.26% of the time, that a 9-7 team won the Super Bowl 6.51% of the time, and that one of the top four teams in football won it 57.3% of the time, then you're reading the tables right. You'll note that I've added a cumulative column to make things a bit easier to summarize. You'll also note that the numbers don't match those shown in the original posts. That's due to random variation, of course. Although, amazingly, the top team won exactly 2399 out of each run of 10,000.

No wildcards - four division winners play a standard tournament


Tm# SBwins Cumulative
=====================
1 2315 2315
2 1448 3763
3 1039 4802
4 853 5655
5 625 6280
6 533 6813
7 499 7312
8 406 7718
9 308 8026
10 288 8314
11 249 8563
12 228 8791
13 191 8982
14 162 9144
15 167 9311
16 96 9407
17 104 9511
18 88 9599
19 80 9679
20 55 9734
21 54 9788
22 53 9841
23 32 9873
24 32 9905
25 27 9932
26 15 9947
27 18 9965
28 15 9980
29 9 9989
30 7 9996
31 4 10000
32 0 10000


Wins Times Cumulative
======================
6 1 1
7 17 18
8 158 176
9 711 887
10 1600 2487
11 2368 4855
12 2462 7317
13 1607 8924
14 797 9721
15 242 9963
16 37 10000

Four wildcards - division winners get seeds 1 through 4, four next-best teams regardless of division get seeds 5--8. Straight 8-team tournament with no re-seeding between rounds.


Tm# SBwins Cumulative
=====================
1 2285 2285
2 1411 3696
3 1006 4702
4 795 5497
5 689 6186
6 572 6758
7 488 7246
8 400 7646
9 362 8008
10 311 8319
11 260 8579
12 217 8796
13 194 8990
14 156 9146
15 130 9276
16 136 9412
17 100 9512
18 74 9586
19 84 9670
20 72 9742
21 55 9797
22 52 9849
23 31 9880
24 34 9914
25 18 9932
26 26 9958
27 19 9977
28 9 9986
29 7 9993
30 5 9998
31 1 9999
32 1 10000


Wins Times Cumulative
======================
7 37 37
8 507 544
9 1239 1783
10 1874 3657
11 2099 5756
12 2032 7788
13 1335 9123
14 623 9746
15 223 9969
16 31 10000

Twelve wildcards (i.e. all teams make playoffs) - division winners get seeds 1 through 4. Straight 16-team tournament with no re-seeding between rounds.


Tm# SBwins Cumulative
=====================
1 2111 2111
2 1318 3429
3 999 4428
4 804 5232
5 635 5867
6 559 6426
7 489 6915
8 372 7287
9 344 7631
10 322 7953
11 268 8221
12 249 8470
13 189 8659
14 200 8859
15 159 9018
16 150 9168
17 147 9315
18 132 9447
19 106 9553
20 74 9627
21 79 9706
22 64 9770
23 56 9826
24 36 9862
25 41 9903
26 22 9925
27 27 9952
28 17 9969
29 13 9982
30 8 9990
31 5 9995
32 5 10000


Wins Times Cumulative
======================
2 2 2
3 4 6
4 23 29
5 83 112
6 151 263
7 358 621
8 728 1349
9 1296 2645
10 1686 4331
11 1889 6220
12 1807 8027
13 1209 9236
14 552 9788
15 176 9964
16 36 10000

Thoughts:


  • I am floored by how little the playoff format seems to matter.

  • While it doesn't matter much "morally," the 16-team free-for-all would lead to some embarrassment, as a .500-or-worse team would be a near-lock to win the Super Bowl every fifteen years or so. You probably noticed some 2-14 and 3-13 teams winning Super Bowls in that format. Those were really strange seasons, but a 6-10 Super Bowl winner would be a real possibility.

  • If we re-seeded between rounds of the 16-team free-for-all, I bet the best team would win more than 24% of the time.

This entry was posted on Thursday, June 29th, 2006 at 4:10 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.