December 15, 2009

Baseball Therapy

Home-Field Advantage

by Russell A. Carleton

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 10^th 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.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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