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Home-field advantage is one of the greatest puzzles of baseball (and other sports) analysis. Indeed, my colleague Matt Swartz wrote a Burns-esque five-part inquisition into the topic a few months ago. Home-field advantage unquestionably exists. In 2009, the home team won 54.9 percent of all regular season games, and that general range (53-55 percent) has remained remarkably consistent over the years. Seeing that teams play an equal number of home and road games, and that who hosts a regular season game is not determined by the overall quality of the team (as in the NFL playoffs), then the home team should win at a rate close to 50 percent. But HFA persists. Why?

On an intuitive level, it doesn’t seem strange that there’s a home-field advantage. The crowd generally root, root, roots for the home team and, in certain cities, hurls objects at the visitors. The visitors have to stay in a hotel for the duration of the series, while the home team’s players get to stay in their own houses/apartments and eat home cooking with their friends/spouses/significant others/kids/pets. Is home cooking really that good for hitting a fastball?

The Gory Methodological Details

Here I’ll investigate what role “home cooking” plays in HFA. I created a database of everything that happened in MLB between 1997 and 2008, and calculated the overall seasonal OBP for each batter and pitcher during that season. I restricted the sample to plate appearances in which a batter with a minimum of 250 PA for the season in question squared off against a pitcher with 250 batters faced.

I calculated the probability of that each plate appearance should end in an on-base event, given who the batter and pitcher are, using the odds ratio method. Since OBP is a probability number (.330 means he got on base 33% of the time), it can be turned into an odds ratio (prob / (1 – prob)). Then the formula for the expected odd ratio (hereafter OR) is (batter OR / league OR) * (pitcher OR / league OR) = (expected OR / league OR). The rest is simple algebra and the expected OR can be re-converted into a probability (OR / (OR + 1)). Of course, the number of on-base events registered in a plate appearance is either 1 or 0. But the actual number of on-base events in a given series of plate appearances should match up pretty closely with the summed probabilities. That is unless another factor is getting in the way. But if there is, it will be independent of the quality of the batter and pitcher.

I looked at all plate appearances for the home team (some 200,000+) from 1997-2008. Sure enough, the home team registered 101.8 percent of the on-base events that they would be expected to based on batter and pitcher quality. Road teams checked in at 98.4 percent of expectations. It’s not a massive difference, but one that could certainly throw a few games here and there. There’s our home-field advantage effect at the at-bat level.

Is Home Cooking Really That Good?

Now the problem with looking into “home cooking” variables is how to run a controlled study. There are plenty of situations in which the home team has home cooking on its side. Are there situations where the visiting team has a home cooking advantage? Thanks to interleague play, there are! (Who said that interleague play was only good for producing gimmicky games based on bad geographical puns? Oh wait, that was me.) Every year now since 1997, the Cubs have played the White Sox, the Angels have played the Dodgers, the Mets have played the Yankees, and the A’s have played the Giants. Voila, a “road” game in the same city!

It’s likely that the Cubs players all stay in their Wrigleyville apartments the night before playing the White Sox. Maybe they all even congregate at the Addison Red Line stop and ride together to 35th Street, but when they show up to U.S. Cellular Field, they put on their gray unis. I found about 6000 plate appearances from these same-city interleague games in which the “road” team was at bat. Will these players behave like they are at home or on the road? It turns out that they behave like they are on the road, registering about 98.3 percent of the on-base events expected of them.

What about the other side of the coin? Can we find a time when a player is likely to be living in a hotel, but gets to be part of the home team? Consider the player who is traded in mid-season. If he’s dealt from Boston to LA, he won’t have time to set up an apartment in LA, and for a few weeks will probably be living out of a suitcase, just like he is on the road. I looked at players who played with more than one team in a season (whether by reason of a trade or being released and signed elsewhere), over their first 50 plate appearances with the team. (Obviously, only the ones which involved the player being at his new home ballpark.) Again, this netted me about 6000 PA‘s. The results: 106.2 percent of the expected on-base events!

There’s probably some effect in that latter group for the fact that most trades happen mid-summer when the pitchers are little bit more tired and the air is a little warmer. Still, it looks like players don’t mind living out of a suitcase. And why should they? They do it all the time! Big leaguers spend five or six weeks in spring training, then spend the next six months taking extended road trips and do this year after year. It’s likely that most players have simply adapted to these demands. There must be another factor other than home cooking at work here.

Have You Been Here Before?

In Matt Swartz’s series, one of the particularly interesting things he found was that HFA was less when the game was amongst two teams from the same division. He hypothesized that perhaps, because intra-division rivals play each other more (thanks, unbalanced schedule!), players are more familiar with the other ballparks within their division. Of course, they would be most familiar with their own home ballpark, and as such have a home-field advantage. Does familiarity with a ballpark make things easier? And if so, can we isolate this effect?

Where to find players who would be intimately familiar with a ballpark, but who would be in the visiting dugout? I found all players from 1997-2008 who had amassed more than 1000 PA with one team, and then in the next year, moved on to another team. For example, Roberto Alomar played with the Orioles in 1997 and 1998. The next year, he signed with the Indians. What happened when he went back to visit Camden Yards during the ’99 season as a visitor? Players who fit this filter got 102.9 percent of the on-base events expected of them. Suddenly, we’ve turned road players to hitting like they are home players, but only in parks where they’ve had extensive prior experience.

On the other side, what about teams who are playing at home in a brand-new, just-opened ballpark? They are wearing their white uniforms, but have no familiarity with the ballpark itself. No one does. I looked at what these home teams did during the month of April when opening a new park. The results: 96.4 percent of the expected on-base events. It looks like the driving factor here is familiarity with the park itself.

What Pot-Smoking 19-year-olds Can Teach Us About HFA

I’d argue that we have a case of state-dependent learning. Hitting a baseball is a skill, and players are constantly learning to develop that skill through experience. In psychology, we know that learning isn’t simply a matter of remembering facts in isolation. Indeed, when you learn or experience something, it’s encoded in association with other stimuli that are going on around it. Ever hear a song and have it trigger a memory?

We recall information best when we do so in a situation that closely matches the circumstances where we learned it to begin with. There’s a famous 1973 study in which UCLA students were recruited to perform a standard memory task, to learn various pairs of nonsense syllables (goff goes with jum). Only there was a catch. Half of the students did so after smoking marijuana. The other half were sober. (Note: How this got past an ethics board, I have no idea.) Ten days later, they returned and were randomized again. Half smoked, half did not. All were asked to recall as many pseudo-word pairs as they could. The randomization created four different possible combinations: sober/sober, high/sober, sober/high, and high/high. The group that recalled the most (not surprisingly) was the sober/sober group. The surprising second-place finishers though were the group that had smoked prior to both learning and recall. The researchers took this as evidence that what mattered most was the match of states for the two tasks (learning and recall). Thus was born the theory of state-dependent learning.

There are a thousand little differences between stadia. That’s what makes going to another city to watch a game so much fun. They may not be very different in the grand scheme and all have the same rough anatomy, but as anyone who’s decorated an apartment knows, it’s the little things that make it yours. Hitters spend most of their time in one ballpark learning to hit, and probably pick up on and learn things of which they aren’t even aware. It’s not that the lessons learned don’t carry over to other ballparks-they do. It’s just that the full richness of those lessons only comes out when the batter is standing in the place where he learned them in the first place. You can probably remember a lot of stories from high school. But go back and actually stand in those hallways again, and you’ll suddenly remember details that you’d forgotten about for a long time. Home-field advantage is likely made, in part, of these context effects.

Epilogue

The careful reader will note that there’s a small hole in my logic. Our “recently traded” players hit well above their expectations (and as such, like “home team” players), yet it’s likely that they’re moving to a stadium which they haven’t spent much time in. Perhaps they’ve never set foot in the new place. How to reconcile this?

I don’t think that state-dependent learning explains all of HFA, although it surely explains part of it. In this case, I think that there are some other confounding variables in the “recently traded” group. For one, I mentioned the timing issue. Being traded at the deadline means that the plate appearance which I am measuring likely come in August when it’s warmer and the pitchers are more tired. But there’s another issue. By August, a baseball season can become very monotonous for the players. A new beginning is worth something. If you don’t believe me, go down to the local gym on January 10th right after those New Year’s resolutions kick in. You’ll see a bunch of people there working out who had given up going to the gym five years ago. Go again on March 15th, and you’ll see a few listless survivors. It’s hard to sustain motivation for anything for a long time, but a change in things can re-focus attention. In addition, an August tradee is likely to be a veteran going from a bad team to a good one, or a young player going from the bench to a chance to play every day. Perhaps I don’t have a perfect theory, but if nothing else, I hope you might understand that context matters in understanding baseball (and everything else).

Russell A. Carleton, the writer formerly known as ‘Pizza Cutter,’ is a contributor to Baseball Prospectus. He can be reached here.

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xenolith
12/15
This is a really interesting piece. One thing I wonder though, wouldn't most of the HFA for a team be tied up in the fact that they get to bat last? Or is that not as big of a benefit as most people assume?
Wereslug
12/15
I think people agreed (in the comments of Matt's pieces) that batting last accounted for half of HFA at most.
pizzacutter
12/15
I agree that batting last plays a huge part. In fact, it's on my to-do list to look into some of the mechanisms of why exactly that happens.
ssimon
12/15
I thought HFA was simply due to the fact that home players have a small advantage in terms of the strike zone. That led to slightly fewer strikeouts, slightly more walks, and slightly better contact.
pizzacutter
12/15
I'd personally like to see that one in Pitch F/X. (Has someone done this study?) The effect could be that road pitchers pitch a little more tentatively.
fireal20
12/15
Concerning the logic "hole", couldn't a lot of it be explained by selection bias in that typically those getting moved at the deadline are above-average (at least slightly) players? At least anecdotaly, I can't think of too many bad players who go to a new team and get lots of ABs.
pizzacutter
12/15
That's actually the exact reason that I used the odds ratio correction method. I'm measuring outcomes relative to expectancies. So, if the player traded was an overall .400 OBP guy, the model knows that and expects him to be on base 40% of the time.
fireal20
12/15
Ah, that part must have left my head by the time I got to the end. =)
hiredgoon1
12/15
Interesting piece, Russell. I've always found it odd that HFA is more pronounced in other sports, even though these sports have standardized fields of play. Do you think context-dependent learning can be a factor when the context (i.e. court, field, ice) is nearly identical?
pizzacutter
12/16
Thanks. Actually, I'd argue the other way. HFA would still be as strong. The differences between stadia are more than just outfield dimensions and foul territory. In basketball, the acoustics are a little different everywhere you go, I'm sure the floor is slightly different in consistency... little things like that. It's not that they directly interfere with play, but they do impart a slightly different feel to the arena/stadium. I think that's part of what's being responded to.
swartzm
12/16
Dan, I think the reason that HFA is bigger in other sports is that the team that is "supposed to win" wins more often in other sports. The Nats will take 1 game out of 3 from the Yankees on average, but there's not really a point in watching the Lions try to play the Colts. It's certainly not 1 in 3. Baseball games are frequently decide by a dozen or two pitches on the borderline, a few bloop hits, or home run just inside the foul pole. My theory is that's why HFA is smaller in baseball-- more luck, less other stuff.

Russell, I loved this article. I hope the new Ken Burns inning follows Burns' own Burns-esque nine innings as well as this followed up on mine. Great insight, great results.
lichtman
12/16
"That's actually the exact reason that I used the odds ratio correction method. I'm measuring outcomes relative to expectancies. So, if the player traded was an overall .400 OBP guy, the model knows that and expects him to be on base 40% of the time."

Pizza, if the players who are traded tend to be good, they also tend to be lucky, so any post-trade performance will regress, whether you use the odds ratio method of matchup expectancy or not.

Good stuff, BTW!

I too am waiting for a pitch f/x analysis of home and away. Mostly I want to know if umpires have a different K zone for home and away teams or make some occasionally biased calls.
dkirchg
12/16
Motivation I think is another factor. If you are playing like a bum at home the local papers and radio let you know it. If you go 0-4 on the road with three Kâ€™s you were just a victim of the home town pitchers great performance. When you get traded you have something to prove (your not a bum). When you play in the high media town a bum turns into a super bum. I wonder if high media towns have a higher HTA then a town with a small media? Nice article.
nosybrian
12/16
I wonder if the difference in HFA between MLB and other sports isn't partly due to the number of games played, and further whether some of the "randomness" of baseball game predictions isn't also due to the same factor.

Illustration in point: I took a young Brazilian kid to a baseball game a year or so ago, and he kept asking me questions like, "Why is everybody so quiet?" And "Why isn't the hitter running hard to first base?" I think part of the answer is that the guys play a whole lot of games every year, and both the fans and the players realize that it's a long season and they conserve their psychic and physical energy.

But in a sport in which there are relative few matches, each game is more important players spend time preparing for each opponent and fans build up expectations (and tickets are harder to get) for the next game. In that situation, the potential "fan" part of the HFA may come more into play than in a typical regular-season baseball game.

The above is a predicate for asking: Does the HFA differ between "important" games and "regular games," such as between playoff and regular season games, or if you apply some other definition of the importance of a given game -- e.g., the strength of the rivalry, standings, even-ness of the talent or records of the two teams, date in the season, or some other criterion? I would hypothesize that when games are critical and the fans in particular become very intense (one simple operational indicator: is it a sellout?), the crowd matters.

nosybrian
12/16
In this connection, the length of the NBA season makes it hard to hype up the intensity of the crowd for many of the games, but the one impression I have when comparing games in recent years from those in the old days -- say at MSG, where I used to attend Knicks games in the heyday of Earl Monroe, Walt Frazier, et al -- is that everything is ear-splittingly loud these days, and court-side and time-outs have become a circus of dances and music. The announcer who in the old days would just matter-of-factly call out the name of the player who just scored ("Bradley," "deBusschere") now screams in heavily miked-up excitement, while players thump their chests, etc. Baseball isn't nearly so intense in tha way.

Again my question is, is there something other than familiarity with the stadium/field that accounts for differences in HFA -- that perhaps enhances or deadens the effect? In particular, the stakes involved in a given game or the immediate and active engagement of the crowd.
YaoPau
12/17
Is "being cheered for" taken out of the equation only because it can't be quantified? Because that would explain just as much as your state-dependent learning theory.

Home team overall registers 101.8% of expected OBP. Check.
Cubs registering 98.3% in Sox park. Check.
Player living in hotel on new team at 106.2%. Check.
Robby Alomar in Camden Yards at 102.9%. Check.
Home team in new ballpark at 96.4%. Nope.

"Being cheered for" works in 4 of the 5 instances, same as the state-dependent learning idea. And I'm guessing there have been plenty of studies showing that people improve when those around them support them.

Another issue with the state-dependent learning idea is that home field advantage exists in other sports too where the stadia nuances are more controlled. Take basketball for instance. The courts might have different colors, with stadium lights shining through the hoop at different angles, but they are mostly identical. There are no lips on the grass, extra room in left center, or hills in center field, but the home field advantage is still there.
pizzacutter
12/18
I don't know that the theory holds. Obviously, the home team will be cheered for in their own park, and the new acquisition will be cheered in his new home park. But the crowd at a Cubs-Sox game is decidedly mixed, and the response to a returning veteran might be "you betrayed us in free agency!" or more likely, "Oh yeah, didn't you used to play here last year?"

I've actually heard MLB players interviewed saying that they take the cheering for the other team and pretend that the crowd is cheering for them.

I'd also contend that HFA isn't just a function of the actual field of play. Even if ballparks were completely uniform, I think we'd still see these effects. Consider your high school for a moment. It has the same basic anatomy as all the other high schools in America. But you could tell your high school immediately when you walked in, even if it has changed a lot (like mine!) The nuances at a ballpark can be in the ambient noise in the background (is the park in the middle of downtown with a bunch of traffic around? By a river?)
TheRealNeal
12/19
It could be that you're looking at it incorrectly by lumping all players into one homogeneous mass.

Say you have two teams consisting of players who perform at these percentages at home:
A B
100 95
101 106
101 106
102 110
100 95
99 95
101 95
101 105
101 95

Much like lumping the good hitters at the top of the lineup tends to help them score runs, lumping home field hitters onto one lineup may yield bigger benefits than a bunch of average home-field hitters.