Ah, so we meet again…
November 24, 2008 11 Comments
A trivia question: Over the last 25ish years (since 1981), what batter/pitcher combo has faced each other the most? As you might expect, these are two gentlemen who played more than 20 years each (and both premiered in the same year), both spent their entire careers in the same league, but were never teammates. The names are at the end, but if this is any hint, they faced each other 154 times over their careers.
So after the 35th time, who really had the advantage? Is it the pitcher who now “knows how to get the batter out?” After all, he’s had the experience to see what a batter will swing at and what he won’t. Then again, maybe the batter has the advantage. He’s had the experience to see what the pitcher throws and can figure out his patterns. Indeed, there’s always talk that when a player is traded to/signs in a new league, he will have a period of adjustment, owing to the fact that he likely hasn’t faced many of the batters/pitchers that he will now be facing. I’ve actually heard it all four ways, that a batter will benefit from/suffer for his first foray into a new league (because the pitchers haven’t seen him/he hasn’t seen the pitchers before) and that a pitcher will benefit from/suffer for his foray into a new league (same logic). What gives?
Well, let’s look at what really happens. I took all the Retrosheet play by play files from 1980 to 2007 and put them into one big file. (My computer currently hates me.) I sorted them into chronological order and then numbered the different confrontations between batter and pitcher. I dumped everyone who appeared in the 1980 season from the data set. Johnny Bench faced Tom Seaver in 1980, but certainly, that wasn’t the first time that they’d seen each other (although my data set would have considered them to be just introduced). In order to maintain the intergrity of the sample, they had to go.
Then I coded for whether the plate appearance ended in the batter being on base (even if that meant an ROE). My first thought was to run a simple OBP broken down by the number of times that the two had faced each other. But then in order to get to a point where a player had been around long enough to face a pitcher 20 times, he was probably a different class of hitter than the guy who only only got marginally introduced to a couple pitchers. Same logic goes for pitchers who stick around. So, I had to calculate what the expected OBP of the plate appearances in question might be. I calculated both the player’s yearly OBP and the pitcher’s OBP given up (plus the league OBP for the year). To make sure I wasn’t getting any .500 OBPs from someone going 1-for-2, the pitcher and batter had to have logged 250 PAs in the year in question. This had the nice side effect of getting rid of pitchers hitting.
You can calculate what the expected OBP of a particular batter/pitcher matchup is by converting OBPs into odds ratios (OBP / 1-OBP), and then using the formula.
(batter OR / lg OR) * (pitcher OR / lg OR) = (expected OR / lg OR)
Once you have the expectation, you can turn it back into an OBP rather easily (OR / (OR + 1)).
Then, it was simply a matter of watching what happened when I compared what would have been expected to what actually happened. I fumbled around with some binary logit models to see what happened, and they generally showed that as a pitcher and batter faced each other more often, the advantage slowly worked its way in the batter’s favor, but I think that the graph shows the effect a little better. On this graph, numbers above zero mean that the pitcher has the edge. Below, the batter has the edge.
In the first meeting between batter and pitcher, the pitcher had a 7 point advantage in OBP. By the time of the second meeting, that advantage was almost entirely gone (down to 1.5 points), and then by the third meeting, the outcome was most likely to be even-up to expectations. Following that, you can see that the graph jumps around a little, but the general trend-line is downward until about 35 PA’s. After that, the graph just gets really unstable. My interpretation is that means that we have something of a real effect, although not a very coherent one, and the fluctuations may have to do with selective sampling and a decreasing number of pitcher-batter pairs that have met 30-something times.
There’s certainly a trend line to be had, and it certainly looks like it points toward the batter having the edge as he faces a pitcher more often, and by meeting #35, the magnitude is 13 points worth of OBP. At first, the pitcher has the element of surprise, but the pitcher must strategize on how to remove the batter from the batter’s box with a new strategy each time, while the batter himself must simply react to what’s thrown at him. At first, the batter has nothing to go on, but if he can learn the pattern (and it looks like he does) he can react better.
So for a short period of time, an exotic pitcher does have the advantage. But not for long. That advantage wears off pretty much the second time through the lineup.
Trivia answer: Greg Maddux has faced Barry Bonds* 154 times over their careers. Second place on the list, incidentally, also belongs to Greg Maddux, this time paired with Craig Biggio (140).