The Detroit Pistons broke the NBA record for most consecutive losses in a season last night, with their 27th loss in a row. This morning I was puzzling over the following. A team’s record is, roughly speaking, a function of two factors:
(1) The team’s quality. By “quality” I mean everything about the team”s performance that isn’t an outcome of random factors, aka luck — the ability of the players, individually and collectively, the quality of the coaching, and the quality of the team’s management, for example.
(2) Random factors, aka luck.
Now what I’m wondering about is, how do we disentangle the relative importance of these two factors when evaluating a team’s performance to some point in the season? This of course is critical for predicting its performance going forward.
The best predictor ex ante of team performance is the evaluation of people who gamble on that performance. I realize that occasionally gambling odds include significant inefficiencies, in the form of the betting public making sentimental rather than coldly rational wagers, but this is very much the exception rather than the rule. Certainly when bookmakers set the odds for something like a wager on how many games the Detroit Pistons are going to win in the 2023-24 NBA regular season, sentiment, either on their part or of the betting public, has nothing to do with it.
Now the even money over/under for Detroit’s eventual winning percentage this season was, before the first game was played, a winning percentage of .340. To this point, a little more than third of the way through the season, Detroit’s winning percentage has been .0666.
What are the odds that a .340 team would lose all 27 games in any particular 27 game stretch? The answer would seem to be .660 to the 27th power, which is about 75,000 to 1. This suggests that Detroit is not actually a .340 team that has just had really really really bad luck so far.
Conversely, the team’s current 2-28 record projects to a final record of 5-77. Now this would be a good bet to the extent that the team’s current record is solely a reflection of its quality, apart from random factors. To the extent that the team has had unusually bad luck, then one would expect the team’s final record to be better. But how much better? Here we can again turn to the savants of Las Vegas et. al., who currently set the even money odds of the team’s final record on the basis of the assumption that it will have a .170 winning percentage in its remaining games. A .170 team could be expected to lose all 27 games in a 27-game stretch about once in every 150 such stretches, which, while highly unlikely, is worlds more probable than a .340 team doing the same, i..e, once every 75,000 times.
Now how did they get this latter estimate? I have no idea, but I asked my brother — a scientist and not a statistician by training as he wishes me to emphasize before Andrew Gelman gets to the end of this post — and he used the preseason odds and the team’s current record to construct the following graph:
What’s striking here is that if we have just two pieces of information — a prior assumption of a .340 team, and the subsequent information of a .066 performance through thirty games — the combination of these two pieces of information yields a posterior prediction of a .170 winning percentage going forward, which remarkably enough is exactly what the current gambling odds predict!
In other words, it appears that the estimate being made by professional gamblers is that about two-thirds of Detroit’s worse than expected record is a product of an ex ante overestimate of the team’s quality, while the other third is assumed to be accounted for by bad luck.
Now a complicating factor here in predicting future performance is whether team quality could be thought of as a fixed variable going forward. I think it can, because any changes in team quality going forward this season — because of the improvement of young players as the season goes on, and/or because of better coaching decisions in terms of lineup composition, and/or because of changes to the composition of the roster because of management decisions — can be considered things that were inherent attributes of the players, coaches, and management at the beginning of the season, that gamblers can take into account at that time in terms of possible future changes to present team quality. Also if we don’t make this assumption then the math gets really hard and we’re not going to do that.
As for luck, that’s definitionally stochastic, as Alan Iverson once implied.
A final note: the whole NBA is set up, via the salary cap and the structure of the draft, to make these kinds of outlier results extremely unlikely. But not unlikely enough apparently.
Anyway I hope some of you have fun with this.