## Wednesday, June 25, 2008

### Did NBA playoff referees cheat in favor of the home team? Part II

In the last post, I looked at Kevin Hassett's analysis of home field advantage in the NBA playoffs. It occurred to me that it was possible that HFA should be higher in the playoffs because the teams are closer together in talent (since the worst teams don't play). However, before writing the post, I did some quick math and concluded that wasn't the case.

I was wrong. Brian Burke, over at Advanced NFL Stats, convinced me of that, with logic and empirical data. Here's his
original post, and a follow up on the topic.

My mistake (in my mind, not in the post) was assuming that HFA manifests itself in winning percentage. It does not. It manifests itself in better play – improved shooting, and defense, and rebounding. That turns into more points and fewer points against, and that's what causes the increase in wins.

But a fixed improvement in point differential translates into a different number of wins, depending on how close the two teams are in talent.

HFA in basketball is about 3 points. That means that the home team's advantage will only change the outcome of the game if, without the HFA, the visiting team would have won by 0-3 points. If the visiting team would have won by more than that, the three points wouldn’t have helped the home team. And, of course, if the home team would have won anyway, the HFA doesn't matter.

What's the probability that the visiting team would win by 0-3 points? That depends on the relative quality of the two teams. If the home team is way better than the visitors, it won't be very high. And if the visiting team is much better than the home team, it will win by more than 3 points so often that the probability again will be low.

So the closer the talent, the higher the home field advantage. That means HFA is higher in the NBA playoffs than in the regular season. How much higher? I'm not sure, but if you bump it up from .600 to .630, the significance level of what we saw in this year's playoffs (a home record of 64-22) goes from a 1 in 161 chance down to about a 1 in 40 chance.

That means that Hassett's evidence of abnormal home field advantage is even weaker than I previously argued.

In fairness, it also means that ignoring the first round, as Hassett did in his analysis, is not totally a case of "cherry picking" – HFA should indeed be higher in subsequent rounds as the relative talent tightens up with the elimination of the weaker teams. But, in that case, the HFA should increase in subsequent rounds as well, and, in that light, I doubt that even the 34-8 record in the second through fourth rounds is more significant than 2 SD.

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