This is the fifth and final article in this series on home-field advantage. The first four parts of this series have revealed many things. In the first article of this series, we studied what home teams are able to do more frequently than road teams; we learned that they pretty much do everything better, hitting more home runs, reaching base more frequently on balls in play, walking more often, striking out less often, stealing more bases, making fewer errors, and recording more complete-game shutouts. In the second article, we learned that nearly all home teams enjoy relatively similar home-field advantages over time, with the exception of the Rockies, and that the vast majority of year-to-year fluctuations in teams’ home-field advantages are random fluctuation. The third time around demonstrated the important role of distance and familiarity in determining home-field advantage, and noted that home-field advantage was much larger in interdivision games than intradivision games, and was especially large in interleague games. We discovered something quirky in the fourth article of this series, that not only was the first game of the series not any more likely to exhibit home-field advantage, but the penultimate game was. More peculiarly, it was statistically significant, indicating that it is not all that likely to be merely noise. I received many e-mails and comments suggesting reasons that this peculiar effect may be real, or expressing skepticism that it is more than merely noise. This indicates that there is probably more to be learned about home-field advantage, and more that is not immediately obvious.

Although the second article taught us that team-specific home-field advantage is small, that does not necessarily mean that player-specific home-field advantage is as well. The first article taught us that home teams are more likely to succeed in hitting home runs, so we are left to wonder whether home-run hitters more likely to have a higher home-field advantage. A thoughtful commenter pointed out in the second article that team-specific home-field advantage seemed to be growing in recent years, and in fact, it has gone up, from about 6.6 percent in 1998-2002 to 8.9 percent in 2003-08. Perhaps teams have been able to improve their home-field advantage by acquiring players who better suit their stadiums. Furthermore, we know that if teams are more likely to hit home runs at home, we naturally are left to wonder whether players who hit more home runs will have higher or lower differentials between their home-run rates at home opposed to those on the road. In this article, we will test several statistics for this trend.

Naturally, testing these type of things requires knowing that players have persistent home-field advantage. This is definitely not something we can assume, because we know that teams do not. Only looking at players who did not switch teams and who were able to acquire 150 at-bats at home and on the road in two consecutive years between 2001-2008, we see that the difference in between OPS at home and on the road for a player has a year-to-year correlation of .1863, which is quite large given our sample of 960 players. It is worth checking whether park factors were playing a role here, so I used ESPN’s park factors for the year in question, and normalized the home statistics using park factors listed (hits, doubles, triples, home runs, walks). Since one-year park factors fluctuate a lot (there is no stadium that is going to be twice as likely as the average stadium to surrender home runs), I also developed regressed park factors that were merely halfway between the recorded park factor and 1.00. Either way, this correlation came out large: .1752 for given park factors and .1615 using regressed park factors. The year-to-year correlation for this set of hitters was also pretty high for various other statistics. (Note that all numbers from here out are normalized using the regressed park factors.)

Stat   Year-to-year
HR/AB      .0852
AVG        .1038
OBP        .1892
SLG        .1247
BB/PA      .1101
K/PA       .0914
BABIP      .0830

This year-to-year correlation was not as strong for pitchers who only had a slight tendency to continue being relatively better at home if they had the year before. Using regressed park factor-adjusted ERA on a sample of the 539 pitchers between 2001-08 who threw 40 innings or more both at home and on the road for the same team for two consecutive years, and we get a correlation of .0299. This was not much different with no park adjustments (.0394) and un-regressed park-factor adjustments (.0520).

Stat      Year-to-year
BB/9       .0521
HR/9      -.0348
K/9        .1261

It seems that if some pitchers do have a persistent ability to be particularly good at home, this would come primarily through their ability to strike people out., and somewhat through their ability to avoid walks.

Seeing as it is pretty clear that hitters and pitchers both have some sort of persistent ability to do better at home, it’s worth checking whether home-field advantage is going to be particularly helpful for players who have certain skills. Upon looking at the idea, this seems to be quite true, and for many skills. For example, the correlation between OPS and the difference between OPS at home and on the road (all normalized using regressed park-factors) is .1452 for the 1,824 hitters who got at least 150 at-bats at home and on the road in years between 2001-08. The correlation between ERA and the difference between ERA at home and on the road (again, all normalized the same way) is -.1048. It seems like better pitchers and better hitters will show larger home-field advantages. Consider the correlations between the following statistics and the differential between them at home and on the road, using the same normalized park factors:

         Correlation between itself &
Stat      its home/road differential
HR/AB      .0707
BB/PA      .1129
K/PA       .1127
BABIP      .1127
BB/K       .1429
ISO        .0696
SLG        .1216
OBP        .1517

For pitchers, we get the following:

         Correlation between itself &
Stat      its home/road differential
BB/9      -.0515
HR/9      -.0560
K/9        .0704

Looking at these, it seems pretty clear that players who have certain skills are particularly adept at employing those skills while at home. This seems particularly true for nearly all statistics, and especially for those related to strike-zone management.

As a side note, I thought it would be interesting to check the effect of age on home-field advantage. In discussions with David Cohen of about home-field advantage a while back, he questioned whether older players may have larger or smaller home-field advantages. On the one hand, they may be more familiar with batter’s eyes on the road and see the ball more clearly there. On the other hand, travel may be more difficult for them. In fact, the latter effect seems to be slightly more prevalent: the correlation between OPS home-road differential and age is .0884, and the correlation between ERA home-road differential and age is only -.0294. The former is statistically significant, while the latter is not. Perhaps pitchers (in this study, starting pitchers generally, since relievers rarely get 40 innings both at home and on the road) are better able to adjust their bodies on the road to be ready to play, while everyday players may struggle a little more with travel as they age.

This is the fifth and final article in this home-field advantage series. We have learned many surprising but also a few unsurprising things throughout this series. We have learned that teams do not have very persistent home-field advantages, with the exception of the Rockies, and that home-field advantage affects nearly every aspect of a player’s game, especially in exhibiting skills in which they are particularly strong. We have learned that travel and distance both play important parts as far as home-field advantage, and we have learned that not only is home-field advantage not especially large in the first game of a series, it is actually more prevalent in the penultimate game of the series by a statistically significant amount.

I will certainly revisit various ideas to test them later, and I may write those up in an article at a later date or an unfiltered post. There certainly are a lot of other possible ways of looking at home-field advantage, and I can see from reader comments and emails that this is a topic that interests many of you. Please feel free to contact me if you have ideas of your own about home-field advantage that you would like to work on, or if you would like to test my conclusions further. I think that I took a pretty big bite out of home-field advantage in this series, but I’m sure that I missed some things. After all, I did most of this research in transit-while on the road. Perhaps you can do better at home.

Thank you for reading

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Matt, what if all of these offensive rates, like OPS, HR/PA, etc. are multiplicative, or at least partially multiplicative and partially additive, rather than just additive, which I think they might be?

Or what if you use an odds ratio method, which I think might be the correct thing to do?

If home road difference is a fixed ratio rather than a fixed difference, and you correlate H/R differences from one year to the next, guess what? You are going to get a strong correlation. You will also get a stronger correlation for players with higher numbers, for the same reason.

Plus, to be honest, the park factor thing is really going to throw a monkey wrench into the equation. Even if you try and park adjust, I think. Using one year park factors is going to create a lot of noise and if you arbitrarily regress 50%, if that regression is not enough, you have a lot of noise, and if it is too much, you will get correlations just from the park factors alone. Plus, again, I would NOT be using Rockie players at all. Including them, whether you use park factors or not, is going to give you a positive correlation overall.

Anyway, we'll start with the assumption that what we consider to be a "fixed" HFA is that all teams have the same difference between their home and road WP (and it is not a given that we can't define a "fixed" HFA as a fixed ratio between home and road WP). We'll call that .08 (.54 -.46). So, for example, a good team with a .600 overall WP will be .640 at home and .560 on the road. The assumption is that that will also be true regardless of the level of offense or defense at home or on the road (I don't know if that is true or not either).

Now, what do we have to do with runs scored and allowed in order for that to be true? Let's say that we have a team that scores 4.5 runs and allows 4.5 runs. In order for them to have a .540 WP at home and .460 on the road, we would have to add .18 runs to their runs scored and subtract .18 from their runs allowed OR we would have to multiply their runs scored by 1.04 and divide their runs allowed by 1.04. Which way works better?

Let's say that we have a team that scores 6 and allows 6 overall. Their overall WP is still .500. If we add .18 runs to their home score and subtract that from their runs allowed, we get a WP of only .530. If we multiply their runs scored by 1.04 and divide their runs allowed buy 1.04, we get .539, which is near what we want.

So for level of offense and defense, it looks like we have to multiply runs by a fixed amount. What about for the strength of a team. Say a team scored 5 and allows 4 overall. They are a .610 team. We expect them to be .650 at home and .570 on the road. Let's do the same thing - try adding or subtracting a fixed number of runs and let's try multiplying home and road runs by a fixed number. Adding and subtracting .18 runs gives us 5.18 RS and 3.82 RA at home, which is a WP of .648 and on the road, it is 4.82 and 4.18, or .571 on the road, pretty close to what we want. What about multiplying and dividing by 1.04? At home, we get .646, and on the road, we get .572, so adding and subtracting seems to be better.

So, it is not real clear to me which is the correct way to do it.

To be honest, I think you have to do some sort of odds ratio rather than assuming a fixed difference or a fixed ratio. If you do that, you have to re-run your correlations. I am not exactly sure how to do that, but I'm sure someone can help...
I did the 50% regressed park factors just to get a ballpark approximation (no pun intended, but discovered and not deleted upon editing my comment). I'm sure there would be a better way to do it, but I only had 1-year park factors accessible.

The odds ratio may be better than the difference. I'm not 100% sure which way is better, but I ran the numbers and found, using the regressed park factors, the ratio of the home number to the away number would be, with and without Colorado (left, right):

OPS: +.1031, +.1068
HR/AB: -.0608, -.0638
BB/PA: -.0589, -.0600
K/PA: +.0341, +.0285
BABIP: +.0848, +.0954
OBP: +.1009, +.1139
SLG: +.0671, +.0698
ISO: -.0420, -.0429
AVG: +.0753, +.0823

So it seems that it probably still is true for hitting, but only with respect to BABIP skills, and what it affects. I'm not sure I have a beat yet on the negative correlations for power and patience related stats.

For pitchers:

ERA: -.0986
K/9: -.0130
BB/9: -.0139
HR/9: -.0448

So it seems weaker than in the article, but still indicating that better pitchers can excel especially well at home.

For year-to-year correlations:

OPS: +.1732, +.1771
HR/AB: +.0788, +.0758
BB/PA: +.0411, +.0539
K/PA: +.0831, +.0735
BABIP: +.0812, +.0956
OBP: +.1741, +.1814
SLG: +.1419, +.1449

ERA: +.0217, +.0216
BB/9: +.0659, +.0752
K/9: +.0828, +.0847
HR/9: -.0311, -.0249

So, it seems that HFA ability is persistent especially for hitters and somewhat for pitchers, regardless of whether you do differences or odds ratios. Interesting; I'm happy that worked out.

I'm curious if anybody else has any thoughts on which way to do this. Thanks for your comment, MGL.
If the skills which appear to be most affected by home-field advantage are those relating to strike zone management, does that suggest a home-team bias on the part of umpires?