## Tuesday, January 30, 2007

### Home field advantage seems to disappear in 3-run games

The first article in the new issue of JQAS is a baseball paper on home field advantage (HFA), by William Levernier and Anthony Barilla. Unfortunately, the authors appear to be unfamiliar with some pertinent sabermetric results, and there are, in my opinion, a couple of problems with their analysis.

They start by examining run scoring: they find that in games of 2004-2005, the home team scored .093 runs per game more than the visiting team. This number looks small, and so the authors conclude this "little supports" the explanation that home teams are "more proficient at scoring runs."

Of course, .093 runs per game is reasonably significant. Using the rule of thumb that 10 runs equals one win, the effect the authors found is about 1.5 wins per season -- or a winning percentage difference of .009. Given that the entire home field advantage in 2004-5 (as found by this study) was .036, the run differential explains 25% of it.

But the authors didn't take into account the fact that home teams often don't bat in the bottom of the ninth inning. That is, the home team scores only .093 runs per game more than the visiting team, but *in fewer opportunities*. If we make a rough guess that home teams lose the equvalent of 36 full innings over an 81-home-game season, and that they score 5 runs per nine-inning game on average, that's 20 runs right there -- another two wins out of 81 home games, or 4 wins in 162. That brings home teams up to about .534, almost exactly what the authors found.

(The difference is some combination of the home team both scoring more runs and preventing opposition runs.)

The authors then note that the observed HFA is higher in close games, and lower in blowouts:

.602 Games decided by one run
.539 Games decided by two runs
.500 Games decided by three or more runs

This surprised me a bit; I didn't expect to see this kind of effect. Why can it happen? I can only think of two explanations:

First, you have a small effect caused by walk-off games where the home team doesn't get to pile on more runs (but the visiting team does). Second, blowout games are disproportionately won by the better team, and better teams have smaller home field advantages than average teams. (I think Bill James showed this once, and started by observing that a 1.000 team must have a home field advantage of zero.)

It seems to me that these two factors alone shouldn't be enough to account for home teams' .500 record in 3+ run games. But I don't know. Are there other explanations?

In any case, the authors run a logistic regression on home/road, runs scored, run differential (unsigned), and roster size (25 or 40). They find everything significant except home/road. I'm not sure how to interpret that, but I think the idea is that if you know that the home team scored 7 runs, you're pretty much assured that they won, home or road. If they scored 1 run and it was a two run game, you know that they lost, home or road. The leftover games may be sufficiently few that a statistically significant result doesn't appear -- especially considering that runs scored aren't adjusted for innings.

In any case, it's a bit weird trying to predict home field advantage based on the run differential of the final score of the game. Shouldn't the predictions go the other way? Following the authors' logic, you could say the HFA is infinite in games won by walk-off home runs.

It may be true that teams were only about .500 in games decided by more than two runs. But the statement "HFA is non-existent in games decided by more than two runs" is false. There is a home field advantage in those games, but selective sampling makes it look like there isn't.

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At Tuesday, January 30, 2007 1:32:00 PM,  Tangotiger said...

I responded on my site.

Phil must be on the same mailing list as I am, as I got a notice about bepress last night.

I'm not sure how the peer review process works, but the points that Phil and I brought up need to make their way directly to the authors in a two-way street.

I know Ben is pretty good about communication, so maybe he'll stop by and explain it.

At Thursday, February 01, 2007 8:26:00 PM,  Unknown said...

"... better teams have smaller home field advantages than average teams. (I think Bill James showed this once, and started by observing that a 1.000 team must have a home field advantage of zero.)"

I don't know if this is the only place he discussed it, but in the 1984 Baseball Abstract, pp. 252-3, James looked at 5 years of data and found that better teams had greater home field advantages. His data only extended to .600 teams, and as you note he argued that a hypothetical nearly perfect team would have to have a smaller home field advantage. He speculated that home field advantage might start to decrease for .700 teams.

Have there been other studies supporting the idea that good teams actually have a smaller home field advantage?

At Friday, February 02, 2007 6:19:00 AM,  Fifth Outfielder said...

I can't access the article, but it seems like the authors really didn't make much effort to research the HFA. Is there no mention of balls and strikes? I did a piece for THT 2 years ago and found that HFA was mostly BB and K, with a slight HFA in fielding and essentially no HFA from hitting last.

I think if we parsed the retrosheet data we'd figure out the margin of victory stuff pretty easily. Off the top of my head, winning big is probably highly linked to a high differential in BABIP, so the impact of HFA - again, mostly balls and strikes - would be expected to be less pronounced in the outcomes of these games. Maybe I'm off base, though.

The basic James argument about good teams having less HFA makes good sense, and that could be a part of it. I once observed that the Braves always had a pretty small HFA in their recent run, but didn't follow up on how/why.

One somewhat off-topic note: if you're researching HFA, always run another set of numbers that exclude any Colorado games (both Colorado at home and on the road). The difference between Colorado's HFA and everyone else's is huge, and this of course may be composed more by the 'hangover effect' - i.e., Colorado's road disadvantage.

At Friday, February 02, 2007 9:53:00 AM,  Anonymous said...

Tom:
I'm a little surprised by your BABIP finding. I thought the home vs. road DER difference (which is what your really want) was generally pretty significant. I think Pinto has posted these #s at some point. I thought the DER gap was nearly as impactful (in run terms) as Ks/BBs. But I could certainly be remembering this incorrectly.

In general, I think the extent of the HFA is largely a function of how idiosyncratic the park is. An unusual hitting background will give you a bigger BB/K edge. Unusal dimensions/features (e.g. Green Monster) should enhance the fielding/BABIP edge. Short/deep fences should give a HR edge (if roster construction exploits it).
So Atlanta's small HFA might just mean they have a relatively generic park, as opposed to being a function of how good they were.

At Saturday, February 03, 2007 8:17:00 AM,  Anonymous said...

I found Tom's THT article (great analysis), and it appears that BBs/Ks are about 2/3 of the HFA, while BIP (including HRs) makes up the other 1/3. An interesting question is how much of the BB/K difference is park --hitter familiarity with background, pitcher familiarity with mound -- as opposed to subtle umpire bias. I suppose players could also simply be more motivated at home.