The regular season is in the books now, and I would say that congratulations are in order for the Patriots, Steelers, Chiefs, Colts, Ravens, Steelers, Falcons, Bears, Eagles, Seahawks, Packers, and Saints, but they don’t honestly care about my congratulations and I don’t think they should all be there anyway. Most people will focus on the Seahawks making the playoffs at 7-9, but would anyone outside of St. Louis really be that more pleased with the Rams making it? The Giants and Bucs both had better records; in the AFC, the Raiders, Chargers, and Jaguars all had better records as well and the Dolphins tied them. Of course, this analysis is based on win-loss records, which are known to not be the best option.
A better option would be point differential, or points scored minus points given up. By this criterion, the only change in the AFC playoffs (in terms of who gets in) would be the Chargers replacing the Chiefs. In the NFC, the Giants would get in over the Seahawks (and the Bucs would still stay home). But with such a short season in the NFL, even point differential is somewhat flawed. Relatively random occurrences, like kick returns or interceptions taken for touchdowns, increase scoring but don’t have enough time to even out across the league. Instead we can look at factors that are more stable and predictive of future performance, such as what my Luigi model uses. And thus we get to the regular season final power rankings and season predictions.
Above are the power rankings. Remember that they are based on a team’s average over the course of the season. According to these rankings, the AFC playoffs (with no regard for divisions) should have the Pats, Chargers, Steelers, Jets, Colts, and Ravens. Surprisingly, the system worked pretty well here, if you ignore the Chargers. In the NFC, it should be the Giants, Saints, Packers, Eagles, Bears, and Falcons. The best team in the NFC appears to be staying home, and the top two seeds are the worst playoff teams.
On the other hand, we could take into account a team’s schedule as well. Thus the season predictions:
Remember that the predictions essentially re-predict each game based on what we know about a team at the end of the year. Each team gets a probability of winning each game, and the expected win total is the sum of those probabilities. By this criterion, the best AFC teams are the Chiefs, Patriots, Steelers, Texans, Ravens, and Chargers. The Texans vastly underperformed this year, gathering good stats but failing to win games. In the NFC we would have the Saints, Packers, Giants, Falcons, Bucs, and Eagles. The Giants and Bucs also underperformed, but at least they were alive in the final week of the season. We can quantify this underperformance (or overperformance) by comparing a team’s actual wins to their predicted wins. The luckiest teams were the Patriots (3.8 extra wins), Jets (2.6), Falcons (3.8), Ravens (2.8), and Bears (2.3). The unluckiest were the Texans (3.4), Titans (2.5), Browns (2.2), Bengals (2.8), and Panthers (2.9).
You might have noticed that I called those teams ‘lucky’ or ‘unlucky’ instead of over or underachievers. That’s another way to think about their performance this season; they ‘should’ have won X games but instead won Y. We can’t say why the difference happened exactly except to say that it’s due to unrepeatable events; kick returns, bad bounces, who knows. It should even happen to very good teams. Let’s say there was a team that played well enough to have a 80% probability of victory in every game they played. This is unlikely; no team is that much better than every other team in the NFL, and the probabilities would vary from game to game with opponent and home field advantage (or the lack thereof). But 80% is about what you could expect for the best team in the league against the worst. Now we’ll say that each game played by that team is a coin flip with a 80% chance of a win. I can flip that coin 16 times, once for each game in the season, and count the heads. This is the same thing as sampling from a binomial distribution. If I do this season sample 1000 times, I get the distribution of wins below.
What we see is that most often, the team wins 16*.8 = 12.8 games. Of course you can’t win 12.8 games, so most often there are 13 wins, followed by 12. But even these win counts happen less than a quarter of the time. Around 10% of the time that team will win 11 games, and a bit more often they’ll win 15. And perhaps surprisingly, about 3% of the time they’ll only win 9 games (and a bit less often they’ll go undefeated). So dumb luck can easily swing a win total a couple games; a ‘12.8 win team’ will win 12 to 14 games about two thirds of the time, meaning they get more extreme results about a third of the time.
What should we take away from this? Don’t look at win totals, look at how your team played. Fans in San Diego and New York might be angry at their teams, but they played very well. It simply didn’t come out in the final results. Fans in Atlanta might want to start adjusting their expectations down. And fans in Seattle truly should just be happy to be there.