Another week, another Science Saturday featuring both football and math. This time explaining why going 16-0 in the NFL is so hard. Ever since 1978 when the NFL went to 16 games, there has only been one team to win all 16. That’s opposed to 6 teams to go 15-1, and 21 who went 14-2. Of course it’s harder to go 16-0 than 15-1, and harder to go 15-1 than 14-2, but it shouldn’t be that much harder, should it?
I mean think about it, there are 3.5 times as many 14-2 teams than 15-1, and 6 times as many 15-1 teams as 16-0. Wouldn’t you expect it to drop by only half or less? The difference between a 14-2 and 15-1 record is one win, and given that these teams are really good they’re more likely to win than lose that one game, so with 21 14-2 teams shouldn’t it be more like 15 15-1 teams and 10 16-0 teams? Why are these record so much more difficult to achieve than 14-2?
The answer is a quirk in how probabilities work. Calculating probabilities is basically counting at an extreme level. To go 16-0, you have to get wins in all 16 games. There’s only one way to do that. That’s a simple one.
To go 15-1 you have to win 15 games and lose 1, but the key is that 1 loss can come in any of the 16 games, so that 15-1 record gets an extra boost in probability because there are 16 combinations of 15 wins and 1 loss. When you go to 14-2, that explodes to 120 different possibilities. That means that for these elite teams, even though a win is far more probable than a loss in any given game, getting a couple losses is far more probable than all or almost all wins because there are more combinations with those losses.
As an example, let’s take a team that has a 80% chance of winning any given game. That’s huge, in reality that would be one of the biggest favorites of the season. But even getting that for all 16 games you only have a 2.8% chance of going 16-0. That jumps up to 11% to go 15-1, and 21% to go 14-2, and almost a 2/3 chance of going 13-3 or worse.
There’s another lesson from this other than explaining why these top records are so hard, that the teams who do achieve them might just be getting lucky rolls of the dice and actually aren’t any better than teams with more modest 13-3 and 12-4 records. About 1/3 teams to go 14-2 or better win the Super Bowl, compare to 1/5 for teams who go 13-3. While that’s a big jump, remember that those 13-3 teams are competing against themselves (for example, in 2017 the 13-3 Eagles beat the 13-3 Vikings and 13-3 Patriots in the playoffs) while there are rarely multiple 14+ win teams in the same season to prevent each other from winning the Super Bowl (1998 being a notable exception). Once you factor that in the difference becomes much more modest, if it even exists at all.
So while it’s fun to predict a 16-0 season for the Chiefs next year, the numbers show that they’ll probably lose at least once.