I'm sure if you've watched much baseball you've heard it said that with the infield in a hitter's average goes up 100 points...or 75 points...or something like that. In any case the conventional wisdom is that batting average goes up significantly when the defense is attempting to prevent a critical run from scoring by positioning their infielders close.
John Walsh's excellent articles on THT prompted me to take a quick look at just how true the conventional wisdom is using play by play data for 2003-2005. The problem is that PBP data does not contain indicators that say "infield was in" on this or that particular play. So we'll have to make some guesses as to when the infield is likely to be in. This too is fraught with difficulty since when you think about it, teams play their defenses in a variety of configurations from double play depth, to in at the corners and DP depth up the middle, in at the corners and half-way up the middle, to all the way in. In fact, in thinking about it I don't have a good feel for how often managers actually bring their infields in - a case of not actually observing what it is you're seeing I suppose.
In any case I took at stab at identifying those situations where the infield was likely to be in. They were:
In other words I'm assuming that teams don't play the infield in when they have a lead, when they're down by a number of runs, or before the fifth inning, and that they would go for the double play before the 6th inning. In both cases I'm looking at all balls that were put in play excluding bunts.
So to make the comparison I looked at batted ball outcomes by trajectory in these situations and when these situations didn't apply. First, let's take a look at the non infield-in situations.
traj tot pct out s d t hr h sf e
F 113815 28.3% 73.2% 5.6% 8.1% 1.2% 11.9% 26.8% 3.0% 0.2%
G 179978 44.7% 76.5% 21.4% 2.0% 0.1% 0.0% 23.5% 0.0% 2.5%
L 76351 19.0% 26.5% 51.8% 17.6% 1.5% 2.5% 73.5% 0.0% 0.1%
P 32670 8.1% 98.1% 1.5% 0.4% 0.0% 0.0% 1.9% 0.0% 0.3%
402814 67.9% 21.1% 6.5% 0.7% 3.8% 32.1% 1.0% 1.2%
As you can see out of 400,000 batted balls 67.9% were turned into outs. The highest percentage turned into outs were popups and the lowest was line drives.
Now let's take a look at the outcomes in infield-in situations.
traj tot pct out s d t hr h sf e
F 953 28.4% 76.4% 8.3% 6.4% 1.0% 7.9% 23.6% 60.1% 0.1%
G 1555 46.4% 73.6% 24.1% 2.2% 0.1% 0.0% 26.4% 0.0% 3.2%
L 551 16.4% 16.7% 60.4% 18.5% 1.6% 2.7% 83.3% 0.2% 0.0%
P 295 8.8% 98.0% 2.0% 0.0% 0.0% 0.0% 2.0% 0.7% 0.0%
3354 67.2% 23.6% 5.9% 0.6% 2.7% 32.8% 17.2% 1.5%
What's interesting is that the percentage of balls turned into outs is essentially the same, just .7% lower at 67.2%. Interestingly, the line drive hit rate climbs from 73.5% in other situations to 83.3% in infield-in situations. This indicates that the advantage for the hitter with the infield in lies in poking line drives through the drawn in infield. You can also see that the hit rate for ground balls goes up three percent to 26.4% as more hard hit grounders scoot between infielders. This is what you would expect.
The most surprising aspect of this analysis is that fly balls are converted into outs over 3% more often in infield-in situations than in others. That difference can be explained by the 4% drop in homeruns that accompany the infield-in situations. As Walsh pointed out in his article what is likely going on here is that hitters knowingly sacrifice power in these situations in order to put the ball in play since simply hitting a fly ball gives them over an 80% chance of scoring the runner from third. You can also see this to a lesser degree with line drives where hitters hit fewer line drives with the infield drawn in and more ground balls. Another factor to be considered is that pitchers pitch more carefully with runners on base and so are less likely to challenge hitters with pitches, that when they miss, are driven out of the yard.
So what about our question? Well, let's take fly balls out of the picture since they are likely governed both by hitter intent and pitcher reticence. When totalling the balls in play on the ground and line drives outcomes, hitters have a .384 chance of getting a hit in other situations and a .413 chance with the infield in - a 30 point difference. That's not as much of a bump as you might suppose.
However, that assumes that all fly balls are counted against the hitter. In infield-in situations 60% of those flyballs are counted as sacrifice flies and therefore don't count against the hitter's average. This quirk of the rule book that many would like to see eliminated means that a hitter's actual batting average goes up much more significantly. A second factor is that batters do indeed strike out less frequently with the infield-in which raises their batting average as well. Walsh ran the numbers for me and found that overall the batting average is .265 and that in the infield-in situations it's .348, an 83 point difference. When sac flies are counted as outs the average is .300. So over half the 83 point increase is due to the sac fly rule while half is due to the combination of defense alignment (more balls getting through the infield) and batters putting the ball in play more often.
And that's about what you would expect. Teams play the infield in not because it affords a better chance of getting the batter out, but because it raises the probability that the runner on third will have to remain on third or get thrown out at the plate.
So the conventional wisdom is superficially correct in that batting average does go up with the infield in. But when you dig a litter deeper you find that hitters don't stand a significantly better overall chance of getting a hit with the infield in.