THE BOOK--Playing The Percentages In Baseball

It is a really good article.  I just asked Andy (by e-mail) why he thinks the managers outperformed the expected performance for same- side pinch hitters and how signifciant the 13 point difference was in 2005 PA.

I was hoping you guys would link to this.  Here’s the main thing that came to my mind when reading it - was any adjustment done for quality of pitcher faced? It doesn’t sound like it, but maybe I misinterpreted his model. 

It would seem to me that most pinch hitting (not for the pitcher, of course) is done late in ballgames, and so pinch hitters will be facing relievers a vast majority of the time.  Additionally, teams usually pinch hit only in high leverage situations, so they’re going to be facing a premium subset of relievers. 

By comparing the average lines for the hitters versus their performance in situations where they would be expected to be facing premium pitchers in a high majority of the sample, you would naturally expect the hitters performance to be lower, simply due to the quality of the pitcher, and not due to a disadvantage in pinch hitting.

It would seem like Andy would have needed to develop an expected baseline performance for those hitters versus the pitchers they faced, rather than versus the aggregate of MLB pitchers, to have this comparison work.  Maybe he did and I just missed it, but I’m not sure.

I think Andy did:

Nor have I considered the identity of the opposing pitcher, whether he is a starter or reliever, the ballpark, platoon effects, groundball/flyball tendencies, or home field advantage.

To create a more thorough analysis, I’ve created a baseball model that includes all of these variables…

So, his initial analysis was just straight numbers.  For the balance of the article, he uses a whole bunch of factors, and tries to correct for them.

I had this question while reading the book also.  What causes this effect?  Would we expect to see this effect for defensive replacements who play an inning or two in the field before batting?  Is this effect also present the first time through the lineup?  Is the effect also present in DHs (Giambi and Thomas are famous for batting much better when playing 1B than DH, but is that just two guys)?

I believe Andy noted in the book that the DH penalty was half that of the PH.

In the batting order chapter, I did show the effect as gaining 8 points of wOBA each time through the order.

So, let’s work it out.  A league average hitter would do the folllowing in the starting lineup the first three times up:
.332, .340, .348, for an overall average of .340
A league average PH starts off at:
.316
Just guessing, but the average DH would be:
.320, .328, .336, for an overall average of .328

(All more or less)

You make a good point that the PH penalty and DH penalty should be compared against the first-time up numbers.

So, the true PH penalty is not 24 points or so, but 16 points.  The true DH penalty would be 12 points.

So, it’s not that the DH penalty is half as much, but pretty much 75% as much. 

Good point.

Tom, I think your numbers are all wrong.

Suppose that the average hitter sees four pitchers in a game—a starter three times, and a reliever.  Assuming the starter and reliever are equally good, and that the starter/reliever difference is 28 points of wOBA (I don’t recall the exact difference), a .341 overall hitter should hit:
.340 first time
.348 second time
.356 third time
.320 vs reliever
This gives an average of .341—348 vs the starter and 320 vs the reliever.

Now, let’s pick an extreme case.  A pinch hitter only comes in during the second half of the game, and thus will only see a starter the third time through the order or the reliever.  Naturally, he’ll REALLY hit 36 points better against the starter than the reliever.  But, the model is expecting an average starter, meaning that it’s modeled as if he hits 28 points different.  Since the model reports a 21-point penalty, here is the model breakdown:
.327 vs starter
.299 vs reliever,
i.e. 21 points worse against both starter and reliever.  In reality, since all the “vs starter” ABs come against tired starters, he is hitting 36 points different:
.331 vs starter third time
.295 vs reliever,
which means 25 points worse against both starter and reliever than if the same player were starting.

In other words, a more correct version (albeit, in the extreme case in which a large number of ABs come against tired starters) increases the PH penalty to 25 points (from 21 points).  More likely, it’s probably only 2 points more than reported.

I have new numbers for the DH penalty as well.  I think it increased a little, but don’t recall offhand.  To answer Jim’s original question, though, players do suffer drops in performance when DHing.  We couldn’t look into it more because of the correlation between DHing and being injured.

Interesting. 

I wish I would have done the following work, as a way to figure out if it’s the tiring pitcher, or the familiarity aspect: look at the PH against SP and RP, and that same PH as a starting hitters against SP and RP (controlling for quality and handedness), each time through the order.

This would better answer if it’s the tiring pitcher, or the familiarity factor.

Let’s see.  If we look at the PH versus the starting pitcher, and there is a substantial tiring factor that accounts for the “times through order decrease in pitching performance” we should see a pinch hitter penalty plus a tiring factor.  Let’s say that the pinch hitting penalty is 6% due to the pinch hitter not being “warmed up.” We should see a 6% decrease in the pinch hitter’s performance plus an X% increase due to the pitcher being tired, for a total of 6+X% decrease in performance, where X (the tiring factor for the pitcher) is presumably less than the 6%.

If there is no substantial tiring factor and it is the familiarity thing, we should see a 6% decrease for the PH notbeing warmed up plus an X% penalty for not facing the pitcher yet in the game.  But how do we know the independent 6%?

As Tango says, if we look at PH facing relievers only, we know that there is no tiring factor for the pitcher, but a familiarity factor for the PH, which is the same familiarity factor that ALL batters face versus this reliever, assuming that he is a short reliever.  So we can isolate the PH not being warm factor by simply looking at the batter’s overall stats adjusted for the reliever’s overall stats and compare this to the PH’s actual stats versus these relievers.  The net result is the PH not being warm factor only.

For example, let’s say that our PH’s overall wOBA when facing everyone is .350.  Let’s say that when they pinch hit versus relievers only, the overall wOBA of the relievers is exactly league average.  If these PH actually hit .330 against these (short only) relievers, then we know that the PH not being warm penalty is 20 points or 5.7%.

Now, if we look at any (if it is the same, even better) PH versus a starting pitcher late in the game and we find that they hit more than 5.7% worse, adjusted for these starting pitchers, then we know that starters are tired.  If we find that they hit worse than 5.7%, then we know that there is a familiarity penalty at work in addition to the not being warm factor.

Another way to figure out the same thing (whether starters get tired or the batters get more familiar with them, as the game goes on) is to compare the difference between starters and PH late in the game versus starting pitchers and then again, versus relievers.  If there is a greater difference versus starters, then we know that there is a familiarity factor.  If there is a lesser difference, then we know that there is a tiredness factor.  It could, of coourse, be both, which would result in around the same difference between starting batters and PH versus starting pitchers, and then again versus relievers.

Tango or Andy.  Any data you guys can whip up on this?  All you would need to do is present PH data versus starters and then again versus short relievers, and present the batting wOBA adjusted for pitching strength faced.  Something like the following:

PH’s v rel.  Pitchers faced “Adjusted” batting

.310 .330 .330

PH’s when not pinch hitting

.350

Implies a PH not being warm penalty of 20 points.

If this:

PH’s v start.  Pitchers faced “Adjusted” batting

.330 .360 .321

This is a decrease of 29 points which implies a familiarity penalty of 9 points to go along with the PH not being warm penalty of 20 points.

However, if this:

PH’s v start.  Pitchers faced “Adjusted” batting

.350 .360 .340

This is a decrease of only 10 points, which implies a 10 point increase due to the starter being tired plus a 20 point penalty for being a PH and not being warmed up, for a net penalty of only 10 points.

I hope I got this right.  It is a little tricky.

I think you can test the “warmed up” factor by looking at defensive replacements (or pinch-runners who later bat), and by looking at visiting teams in the top of the first.  And maybe by looking at players after rain delays, although I can’t imagine this is recorded anywhere.

(OTOH, don’t pinch-hitters and DHs warm up in the batting cages during the game?)