More "Make-it, take-it" Data

At the suggestion of Tom Tango, I ran my basketball simulator with many different inputs to see what impact different scoring levels and game lengths might have on the change to a “make-it, take-it” rule for basketball replacing alternating possessions after scoring.
The short summary is that I find overtime games are much less likely under “make-it, take-it” (MITI), and while the difference is small, there does seem to be a real effect favoring the underdog, which tends to get larger as the difference between the teams gets bigger.
For each set of inputs, I ran 1,000,000 simulated games, totaling results for both alternating possessions and MITI. I used 11 different scoring probabilities for each team, from 0.45 to 0.55 with a 0.01 increment, yielding 66 total pairs. In addition I ran 5 different game lengths, 100, 200, 300, 400, and 500 possessions. For each game length, the overtime period was set to be the smallest even number greater than 10% of the game length, giving OT periods of 12, 22, 32, 42, and 52 possessions. In all this meant 660 different simulations, and 330 pairs of alternating/MITI runs.
The raw output data from these simulations is here, and the program used to generate it is here. The first observation I drew from the results was that under MITI there were fewer overtime games in every pairing, with the drop ranging from 1,492 in a 500 possession game between the most extreme teams (.45 success versus .55) to  44,198 in a 100 possession game between the two best shooting teams (both success of .55). This seems intuitive: longer games, especially between teams of greatly different strength, don’t have many ties to begin with, and MITI reduces the chances further; and shorter, evenly matched games have the most ties, and thus might see the biggest drop. Also it makes sense that the higher the chance of teams scoring, the bigger the impact MITI would have. Indeed when I looked just at 100 possession games between equal teams, and sorted by drop in OT games, I found that the order matched simply sorting by success.
Phil Birnbaum‘s hypothesis was that MITI favored the weaker team, and I think my data supports that conclusion across a wide range of trials. 55 pairs were between equal teams, but of the 275 other groups, 260 saw the underdog improve its winning percentage, and only one of the 15 where the underdog did worse was the difference more than 2 standard deviations, which is quite possible from random chance alone. When you run enough random trials, you ought to see some results that look like outliers. Also, 12 of the 15 cases where the underdog did worse were situations where the difference between team’s scoring success was just 0.01.
It does seem that the shorter the game the more the underdog is helped. The biggest improvements in winning percentage, 0.5%, were all in 100 possession games. Also, the gain tended to be bigger when the gap between teams was wider. While not part of this study, much wider gaps  in scoring chance become less interesting, as the favorite wins all the time. Even at .45/.55, the favorite won just under 99% of 500 possession games, compared to 84-5% of 100 possession games.
While the chances of winning don’t change much, the teams’ scoring averages do change, with the favorite’s rising, and the underdog’s falling, in a MITI format. As Phil suspects, this is mostly the better team having a bigger margin of victory when it would have won anyhow. And how much the scoring average changes is linked to the game length (more change from a longer game) and the difference between teams (more change from a bigger mismatch).
This is an interesting thought experiment, and it’s fun to find a genuine, albeit quite small, effect in winning percentage. There are two factors at play: the reduction in OT games favors the favorite, but that’s offset by the improvement in the underdog’s chances of winning, even though its’ scoring averages drop. MITI increases volatility and randomness, and when you’re the weaker team, that’s a good thing.

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