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August 25, 2009

Ahead in the Count

Home-Field Advantages, Part Three

by Matt Swartz

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In trying to understand home-field advantage, we have asked what home-field advantage actually makes a team do better, and we have asked who has the biggest home-field advantage. The first article of this series answered the question of what home-field advantage actually makes you do better-everything, as home teams do better on walks, strikeouts, balls in play, and errors. They are better at pitching, hitting, baserunning, and defense, and all aspects of their games seem to improve. The second article of this series showed that most teams have pretty much the same size home-field advantage, with the exception of the Rockies. Even though natural luck can make a team look like they are particularly good or bad at home, the 29 non-Rockies teams are pretty much right around eight percent home-field advantage, plus or minus a little statistical noise.

However, that does not mean that every game has about an eight percent home-field advantage. In other words, if we know that the Yankees would beat the Dodgers in 52 percent of games they played against each other, we cannot infer that the Yankees would beat the Dodgers in 56 percent of the games at Yankee Stadium and the Dodgers would beat the Yankees in 48 percent of the games at Dodger Stadium. Certain types of games have a different degree of home-field advantage.

I divided the 27,613 games that did not result in a tie from 1998-2008 into a variety of subsets to evaluate the different magnitudes of home-field advantage. This is important to study because if we can understand where home-field advantage exists, we can better understand why home-field advantage exists and how it comes to be.

Home-field advantage is commonly attributed to the rigors of travel and familiarity with the ballpark. Therefore, I compared games played among teams within the same division to games played among teams in different divisions, since intradivision matchups occur more frequently and often require less travel. Home teams win just over 53.3 percent of intradivision games, which means that they have a 6.7 percent home-field advantage. In contrast, interdivision games showed an 8.7 percent home-field advantage. Although this seems like a large gap, it remains a little shy of statistical significance over the 1998-2008 period. The problem with statistical significance tests for this type of analysis is that to find anything conclusive among minor differences, we would need to look back over many years to be able to pinch the variance enough that home-field advantage differences were statistically significant. Doing so would risk losing meaning, by dipping into different eras where effects may be different. Instead, it seems safe to say that since the confidence interval of intradivision games (52.4-54.3 percent) and the confidence interval for interdivision games (53.6-55.1 percent) barely overlap, intradivision games probably involve smaller home-field advantages. This may be either because road teams are more familiar with the stadiums of their most frequent opponents, or because road teams suffer less when they travel shorter distances. There will be some evidence of both of these factors in what follows.

I also separated the home-field advantage for interleague games and intraleague games as well, in addition to interdivision games within the same league. Interleague games demonstrate a 10.1 percent home-field advantage, far larger than intra-league games, which show a 7.4 percent home-field advantage, although still not quite statistically significant. Specifically, interdivision games within the same league have a home-field advantage of 8.4 percent. This indicates that both distance effects and familiarity effects may be in play.

In summary, this means that we have the following home-field advantages:

Same Division, Same League: 6.68%
Different Division, Same League: 8.39%
Different League: 10.14%

Of course, interleague games may also have an extra home-field advantage, since the DH is only in place in AL stadiums (giving an added advantage to AL teams who construct their roster with this rule in mind), and no DH rule in NL stadiums (giving an added disadvantage to AL teams who construct their roster with a DH). Therefore, it is worth looking at different kinds of interleague games to determine the magnitude of this effect.

The first thing that I did to parse the set of interleague games was to compare the home-field advantage in interleague games among teams in the "equivalent" division in the opposite league (i.e. NL Central vs. AL Central) to interleague games among teams in different divisions. The results came out rather clean-home-field advantage in the equivalent division interleague games was only 7.95 percent, and home-field advantage among teams in different divisions was a whopping 13.42 percent. It certainly seems that familiarity may be in play, since the home-field advantage is smaller for same-division games within the same league (6.7 percent) than it is in equivalent division games in different leagues (7.9 percent), and it is also smaller for interdivision games within the same league (8.4 percent) than it is interleague, different-division games (13.4 percent).

Justification of the theory that familiarity is playing a role in home-field advantage comes from the fact that when I looked at "interleague rivals," the home-field advantage came out very small. Since interleague rivalries have changed over time, it was not easy to define who was encompassed by this term. To determine who these rivalries were, I simply found the 14 NL teams that had played the 14 AL teams the most frequently (Angels/Dodgers, White Sox/Cubs, Rays/Marlins, Indians/Reds, Rangers/Astros, Mets/Yankees, A's/Giants, Royals/Cardinals, Mariners/Padres, Twins/Brewers, Blue Jays/Nationals, Red Sox/Braves, Tigers/Pirates, and Orioles/Phillies). In those games, the home-field advantage is only 4.4 percent, even less than among teams in the exact same division. It certainly appears that familiarity is playing a role, since these teams play each other more frequently than other interleague games, even those within the same division, although it could also be attributed to distance.

Strengthening the argument that this might be the effect of familiarity rather than distance is that if you look at the three pairs of teams who play in the same metropolitan area (Yankees/Mets, Dodgers/Angels, and Cubs/White Sox), those matchups have a 15.8 percent home-field advantage, though in a sample of just 190 games. This also highlights another important fact, which is that crowd support is unlikely to be the primary cause of home-field advantage, since one would expect home-field advantage would smaller in a mixed-fan crowd. The "same city" argument for familiarity over distance is not very conclusive, as the confidence interval for those types of games is really large, (50.9-64.9 percent), but it does seem to point to distance or familiarity being a factor rather than crowd effects, since even this large interval rules out the possibility that there is no home-field advantage in the same metropolitan area.

As these "interleague rival" teams do not play each other any more frequently than teams in different divisions in the same league, it seems that distance may be playing a role too, since the home-field advantage is almost twice as large (8.4 percent) in those games. Another argument for the effect of distance on home-field advantage is that games between teams in the same division who travel further distances show a larger home-field advantage than teams who do not travel as far. To define "further" I had to resort to a small trick-rather than determine the mileage between each of the 450 pairs of major league cities, I gathered the degrees latitude and longitude for all 30 teams, and then used the Pythagorean Theorem (the one by the guy from ancient Greece, not the guy from Kansas) on the difference in latitude degrees and longitude degrees to figure out how far apart two cities were in degrees. The average distance in degrees for teams within the same division was 10, which is the distance between Seattle and San Francisco. Games among teams within the same division who were less than 10 degrees apart showed a home-field advantage of 5.5 percent, and games within teams who traveled further than 10 degrees was 8.1 percent. That is nearly as large as the home-field advantage among teams in different divisions of the same league (8.4 percent).

So, we have learned from this look at where home-field advantage exists that both travel distance and stadium familiarity are probably significant causes of home-field advantage. We found clear effects of familiarity since interleague rivals do better (even when geographically distant) than interleague teams in equivalent divisions, and since same city interleague rival games show a larger home-field advantage than other interleague rival games. We also found clear effects of distance, such as the fact that home teams within the same division win more frequently when the away teams have traveled further.

However, the differences in home-field advantage remain rather small. The difference between home-field advantage among intraleague games within the same division and between different divisions is less than two percent. Ignoring this effect and assuming that all games have an eight percent home-field advantage will only lead you to guess wrong on a couple of games more each year than you would if you had known this fact. Nonetheless, it gives us yet another insight into home-field advantage. Since travel seems to be playing a large part in home-field advantage, next week we will look at home-field advantage in different games within a series, as well as different lengths of series. We will also consider whether offdays and consecutive series at home or away play a role in home-field advantage.

Matt Swartz is an author of Baseball Prospectus. 
Click here to see Matt's other articles. You can contact Matt by clicking here

24 comments have been left for this article. (Click to hide comments)

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lionstar1964

Lionstar1964 -- Have you given any thought to jet lag as a cause? For example, an east coast team playing a night game on the west coast could easily find the game runs until 1 AM eastern time, when their brains may be less sharp.

Proving this would require isolating games where the road team is in a different time zone than the home team. It would also suggest that the advantage would be greater for the first game or two in the different time zone than the later games, as the brain acclimates to the different time zone. Similarly, it may suggest that west coast teams traveling east would be in better shape than east coast teams traveling west.

Aug 25, 2009 10:22 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

I will be getting to these issues in next week's article. Thanks.

Aug 25, 2009 11:06 AM
 
mgibson

What level of significance are you talking about? alpha=.05? .01?

Aug 25, 2009 10:44 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

alpha=.05

Aug 25, 2009 11:06 AM
 
j2avage

What if distance between teams were measured in terms of travel cost, such as average minutes in flight between airports?

Aug 25, 2009 10:53 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

I imagine that would be very complicated to do because there are over 400 different pairs of teams, and I'm not quite sure being that precise would help as much. Did you have something specific in mind?

Aug 25, 2009 11:07 AM
 
tallguyinwa

Just curious....did you make the adjustment for the fact that miles of longitudinal difference vary by degrees of latitudinal difference while degrees of latitudinal difference stay stable.


Holding longitude stable, a difference of one degree of latitude will always equal approx 69 miles.

At the equator a degree of longitude equals 69 miles but if I go and walk around the north pole, I would be moving many degrees of latitude with every step.

At 40 degrees of latitude (roughly the US center), a degree difference in longitude equals about 52 miles.

So if you are using a straight pythagorean calculation of degrees difference, it is going to overstate the distance calculations for teams on primarily E-W roadtrips and understate primarily N-S roadtrips.

Aug 25, 2009 11:29 AM
rating: 1
 
BP staff member Matt Swartz
BP staff

Very interesting. I did not know about the subtleties of latitude/longitude. I just went back and did the same thing but trying to get the mileage using Pythagorean Theorem, and the results were very similar. The average distance for divisional games was 594 miles. Games less than 594 miles had a 5.1% HFA and games greater than 594 miles had a 8.4% HFA, the same HFA as for league non-division games. Thanks for the tip.

Aug 25, 2009 11:49 AM
 
Tim Kniker

The "exact" equation, in terms of Great Circle distance, i.e., two points on a perfect sphre

EARTH_RADIUS * ArcCos[cos(lat1)*cos(lat2)*cos(lon1)*cos(lon2) + cos(lat1)*cos(lat2)*sin(lon1)*sin(lon2) + sin(lat1)*sin(lat2)]

where:
lat1 = origin point's latitude in radians (take degrees X PI/180.0)
lat2 = destination point's latitude in radians
lon1 = origin point's longitude
lon2 = destination point's longitude

and EARTH_RADIUS is 3986 miles (approximately).

This is typically what most airlines would do to get the crow-fly distance.

Aug 25, 2009 19:19 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

Awesome, thanks. This exchange just had a huge impact on HFA part 4 next week!

Aug 25, 2009 20:12 PM
 
Tim Kniker

If you need to do a check on code for distance, here's a couple of Great Circle calculators that you can use as a reference

gc.kls2.com/ (though this just does airport codes)

williams.best.vwh.net/gccalc.htm

http://www.gb3pi.org.uk/great.html

Aug 26, 2009 04:10 AM
rating: 0
 
tallguyinwa

No problem. I did the same thing myself the first time I tried a lat/long sample.

I have a question. If difference is statistically significant, shouldn't the Mariners be expected to have a higher HFA than east coast teams since they are so often playing against divisional rivals that are thousands of miles away....

Also, did you try doing a study of unusual stadiums vs cookie cutters. I know coming up with an exact definition would be difficult but I find it hard to believe that the Red Sox don't get at least some benefit off of the fact that they are more used to fielding balls off of the Monster and that a team with a normal left field wouldn't have the same effect.

I guess that is a whole different article but I'd be curious to see a Fenway only study of balls hit to left field by the home and road teams.

Aug 25, 2009 12:36 PM
rating: 0
 
tallguyinwa

There's been a lot of talk about the structural benefit from batting last. I wonder about this.

Again, the subject of a whole new article or set of articles, but it would seem to me to be overrated. The offense knows they only need one run so they vary their strategy. The problem is that the defense can vary their strategy as well. Honestly, I'd think that the defense would have more tools to stop a team from getting just one run than a team would from getting just one run. Taking away strategies like bunts which are somewhat overrated anyway, a team behind by a single run will still try to hit the ball more or less normally. Its the defense that can adjust by playing infielders up, etc.

I'd also point out that some people have been asking for a Monte Carlo simulation to see how many more games a team would win if both teams were exactly equal and the structure was the only thing that differed. I would think it would be exactly the same.

If we alternated flipping 10 coins 9 times a piece, it wouldn't matter who went last. Even if I didn't have to flip if I was already ahead after you flipped 9 times, it would be exactly the same.

I think the sample set is probably too small but there have been a handful of neutral site games. There have also been a handful of games where because of postponements and scheduling, the "home" team played at the away team's stadium and batted last. I'd be curious to see if the HFA was any different in these cases.

Aug 25, 2009 12:58 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

I agree with you that the away team easily has as much of a structural advantage in the bottom of the 9th has the home team does.

I don't think the neutral site idea would work, because that generally happens under pretty extenuating circumstances that are likely to severely bias the results. I'm generally wary of most "natural experiments" specifically because of this type of thing.

In response to your comments above, it may be that teams like the Mariners may have slightly higher HFA, but those effects (as I showed in the previous article) are probably very small. I do like the stadium idea to see if any team (park) specific HFA effects could be teased out a little more, though.

Aug 25, 2009 13:10 PM
 
Tommy Bennett

When you report the home field advantage in terms of a percent figure, are you reporting the percentage point difference in the win percentages or the percentage by which the home team's win percentage exceeds the away team's?

Aug 25, 2009 15:56 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

The latter, as in: if the home team wins 53.9% of games, then the away teams wins 46.1% of games, and the difference is (53.9 - 46.1) = 7.8%.

Aug 25, 2009 16:01 PM
 
nateetan

Also FYI, Oakland and SF are in the same metro area. Actually these are the only pair of major league ballparks that can see each other.

Aug 25, 2009 17:11 PM
rating: 0
 
Tim Kniker

One more thing I was thinking about on the john just now. One thing that you may want to consider (or at least something that I would be interested in) is if the HFA is stronger at the beginning of the series. Possibly if familiarity is one of the arguments, maybe the first game of the series at the ballpark for the visiting team is tougher than the 3rd/4th game of the series.

Taking this one step further, what about considering the game number of the season. If we looked at the same division, same league, is there a time effect in terms of familiarity? Maybe when the Rays-Orioles play their 15th game of the season the HFA is much smaller than in the first few games.

Or another thing is just a complete seasonal affect. Is HFA just bigger in April/May as teams are starting to get in the groove from ST versus August/September.

Aug 27, 2009 06:30 AM
rating: 0
 
sbnirish77

Great series ...

Aug 27, 2009 09:12 AM
rating: 0
 
drawbb

I don't understand the 4th paragraph from the bottom that begins "Strengthening the argument..." You talked previously about declining HFA percentages as the matchups progressively became closer and more familiar by divisions. Then you mention a 15.8% HFA in same-metro area matchups and say that strengthens the argument that familiarity reduces HFA. Doesn't the huge jump in that percentage right there WEAKEN the argument for familiarity?

Aug 27, 2009 10:26 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

Sorry-- I was trying to say that we see that the smallest home-field advantage is between interleague rivals, and that HFA seems to have a lot to do with stadium familiarity and distance. The fact that those rivals who are closer together among interleague rivals have a larger HFA than interleague rivals who travel further to each other's stadiums strengthens the case for familiarity vs. distance.

Aug 27, 2009 10:32 AM
 
Tim Kniker

On a completely different topic, any chance you want to drive cross-state to PNC Park and attend the BP event on Sept. 5th? I'm actually flying down from Boston and Brian C is going to be there as well. We can have a BP Idol Runner's Up side forum!

Aug 27, 2009 11:40 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

Argh, I'm moving this weekend and I'll still be setting up my new apartment then, so I can't do it. That would have been a cool reunion though :-)

Aug 27, 2009 12:36 PM
 
yetisnowman101

You forgot Oakland versus San Francisco in your metropolitan match-ups...and looking at the data I'd say it pretty thoroughly undermines that point. Watch out.

AWESOME analysis otherwise.

Apr 09, 2011 15:06 PM
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