The NFL might as well consist of 32 identical teams
Four games into the 2023 season, the standings look just as we'd expect if all 64 games had been coin flips instead
The National Football League consists of 32 teams, all of which have played four of the seventeen games on their 2023 schedules. There have been no tie games, meaning that every team's win-loss record is either 4-0, 3-1, 2-2, 1-3, or 0-4.
Assume for the moment that no team is any better or worse than any of the others: 100 percent parity across the league. What should we* expect the league standings to look like? That is, what is the anticipated distribution of undefeated teams, winless teams, and every level of success in between when wins and losses are generated at random?
Under these Harrison Bergeron-esque conditions, each game is tantamount to a coin flip. As there have been no games ending in ties this season, we can pretend these aren't allowed at all (as is the case in playoff games).
The number of combinations available in a given number of trials with random outcomes is the total number of outcomes per trial raised to the power of the number of trials observed. In the case of a coin flipped four times, this is two outcomes per trial (heads or tails) raised to the fourth power, or 2⁴. There are therefore 16 distinct “paths” a coin can take in the course of undergoing four flips.
Following convention and treating heads as wins and tails as losses, only one of these permutations, four consecutive heads, produces a spotless 4-0 record. Similarly, only four straight tails leads to a winless record.
There are four ways to tally three heads and a tail, or achieve a 3-1 record: H-H-H-T, H-H-T-H, H-T-H-H, and T-H-H-H. This means there are also four ways to go 1-3 (just reverse every letter in the above scheme).
With one way to go 4-0, four ways to go 3-1, four ways to go 1-3, and one way to go 0-4, ten of the sixteen available combinations are accounted for. By elimination, this means there are six ways to achieve two heads and two tails, or secure a 2-2 record.
If a lucky one in every 16 coins (or teams) manages to remain undefeated after four flips (or games), then in a 32-team league consisting of equally capable teams, we would expect two teams to be undefeated after four games, since 32 divided by 16 is exactly 2. We would also expect to see about eight teams with 3-1 records, about eight with 1-3 records, and about twelve with 2-2 records.
Two teams are 4-0, eight are 3-1, twelve are 2-2, eight are 1-3, and two are 0-4.
What this means is that there is no reason to play any more regular-season games, assuming there is a good reason for the NFL to exist in the first place. They should move Super Bowl LVIII from February 11, 2014 to Halloween, and invite two randomly selected teams along with 75,000 randomly chosen drunks to fill the stadium seats. As long as none of these teams makes any trades or loses anyone to injuries, felonies, or drug bans—and this might not matter anyway, because every position player could be as equal in ability as each team clearly is—all thirty-two of them would be closing in on 50-50 records if the season lasted 100 games. That would mean not merely boredom for fans but an intolerable burden of concussions and bad calls, like the ones that inspired me to write this last night.
As a statistical bonus, even though the 2-8-12-8-2 distribution of win-loss records observed would the most likely of all distributions in a league of truly coinlike teams, that doesn’t mean it’s probable, in the same way you wouldn’t have anywhere close to a 50-percent chance of getting exactly 50 heads and exactly 50 tails when flipping a coin 100 times. The odds of seeing the 2-8-12-8-2 distribution are around 11.4 percent, while you’d have about an 8 percent chance of getting exactly 50 heads (or tails) in 100 tosses of a fair coin.
(Social share photo: Shaquill and Shaquem Griffin, twin brothers who both played for the Seattle Seahawks for three seasons (2018-2020). Source: NFL.com.)