Sunday, March 18, 2007

Do women's basketball teams have better stats on the road?

While looking through some references for academic studies my library has access too, I found a very confused study of home field advantage: "Team Quality and the Home Advantage."

The authors define home field advantage (HFA) as "the consistency with which home teams win over 50% of ... games." That can be interpreted many different ways. But it seems that what they mean by HFA is actual home team winning percentage, so that if teams are .600 at home, the HFA is 60%. That's reasonable, I suppose, when applied to a .500 league, but obviously not when applied to an individual team. The 1998 Yankees had the league's best home record (.765), but that doesn't necessarily mean they had the best home field advantage, at least in the normal sense of how people use the expression.

But the authors don't make the distinction, and throughout the paper, they usually treat "home field advantage" and "record at home" as interchangeable. Indeed, they go out of their way to inform us that better teams would be expected to have better home records – and they quote other studies confirming this, as if it's an important finding. It never seems to occur to them to treat HFA as a function of a team's difference between home and road record.

The main part of the paper is a regression on the results of single games. The authors chose a decade's worth of NCAA women's basketball, and used game data for four teams – the two best over the decade, and the two worst. (Since each team played two games against each opponent per season – one at home, and one on the road – the schedule is balanced.)

Then, they ran a regression on whether or not the home team won the game.

(Why did they use a full decade's record to choose the best and worst teams? Because, they say, a single season's record might be flawed, since some players might have been absent part of the season due to injury. But why would that matter? And, besides, doesn't their method have the same problem? In their own data, every player will have been absent at least part of the decade due to, say, having graduated.)

The dependent variables in the regression were:

-- a dummy variable for whether one of the "two best" teams was involved;
-- attendance, expressed as a percentage of capacity;
-- distance the visiting team travelled;
-- who won the previous game that season between the two teams, if any;
-- the half-time score of the current game;
-- the difference between the number of rebounds for this team this game, and the number of rebounds for this team in the other game that season, even if that other game hadn't been played yet
-- the same as above, but for fouls, steals, field goal percentage, and free throw percentage.

This is quite muddled.

First, the half-time score doesn't cause home field advantage, it is caused by it. Do the authors really believe that the home field advantage doesn't have anything to do with scoring, that it can cause you to win games in which the other team scores more points than you do? Do they believe that there's no home field advantage until the second half of a game, so you can just take the first-half score as independent of HFA?

And what about the performance measures, like field goal percentage? Aren't those affected by home field advantage also? Or is the theory that teams play exactly as well at home as on the road, but magical scoring dust somehow makes that identical performance worth more points?

And, why take the difference between the home and road performance, anyway? If you hit for an 80% free throw percentage at home, why would you suspect your chances of winning this game are different if you only shot 70% on the road three weeks ago?

The authors do realize, after the first regression, that having half-time score in the model is perhaps not a good idea, and so they run a second one without it. But they still solemnly conclude that "the results clearly implicate the importance of half-time score on game outcome."

Anyway, I don't think any of the regression results can be taken seriously at all. But there's one very surprising result the authors found that didn't come from the regression: that the low-quality teams actually played better on the road than at home, at least according to certain statistics:

"... high quality teams had a higher field goal percentage at home when matched against the same opponent away for a particular year on 63 separate occasions, whereas they did worse at home than away on only 25 occasions. In contrast, low quality teams did better on the road 51 times and better at home on only 35 occasions."
They also made more steals and committed fewer fouls on the road (but rebounds and free-throw percentage showed no difference).

Can anyone explain this? The only thing I can think of is some kind of park effect. If the bad teams played in arenas with bad visibility, where overall field goal percentages were very, very low, that would explain why both they and their opponents have better stats away from that court.

That explanation seems very unlikely, though. I don't mean to sound disrespectful, but, given the other flaws in this study, is it possible that this particular finding might just be an error?

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At Sunday, March 18, 2007 7:39:00 PM, Anonymous Anonymous said...

-- the difference between the number of rebounds for this team this game, and the number of rebounds for this team in the other game that season, even if that other game hadn't been played yet

-- the same as above, but for ... field goal percentage

Argh. Rebounds and FG% are highly correlated. If you miss a lot of shots, you will have more offensive rebounds regardless of you offensive rebounding ability. If you don't miss shots, your rebounding decreases. And why didn't they separate offensive and defensive rebounding? They are two different skill sets at the player level, and two different philosophies at the team level. It's like having an Outs supercategory combining Caught Stealing and put-outs.

Jesus. This whole paper sounds like a mess. But that rebounding thing just pisses me off.

Slightly on the topic of this paper, I've looked at HCA at the NBA level, and found that distance traveled had no significant effect. In fact, once you account for the strength of both teams, and the number of days rest for each, you can pretty much explain most of the game results. You can even take out the days rest, use Ye Olde log5 with a .6/.4 HCA weight, and get pretty accruate results without reference to any other variables.

At Monday, March 19, 2007 3:35:00 PM, Anonymous Anonymous said...

I agree that this study appears pretty sloppy. I tried to come up with an plausible idea for the "bad teams better on the road on certain stats" hypothesis and here's my best shot:

In general, assume the worst teams will lose both home and away to a typical conference opponent - with the difference being that they lose a close game at home and get blown out on the road (on average).

Now, getting blown out on the road allows more time playing against scrubs, which beefs up fg% and steals, but doesn't affect FT (competitor-independent) or rebounds (fewer missed shots = fewer Off Rebound opportunities, which negates any rebound advantage held over scrubs).

This would assume that scrub-time is so powerful that those 10 min can outweigh effects of first 30 of poor play on the road, which is asking a lot. But that's the best I can do.

In general, I would expect the HFA (in terms of probability of winning) to be greatest for a home team that on a neutral court would be at parity or slightly inferior to the visiting team. Here, the incremental skill improvement has the biggest bang for the buck in marginal probability of winning. Whereas a heavy favorite or dog doesn't have the % winning changing much.


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