Swinging at first pitch and game theory

I’ve been looking at some of the changing trends involving the first pitch of the batter-pitcher match-up for Beyond the Box Score over the past few weeks, with far more enthusiasm than I probably should. It’s a part of the game that I find fascinating, and the more I look into it the more oddities seem to be revealed.

For instance, I’ve noticed that BABIP on the first pitch has been mysteriously on the rise over the last two decades, and that only once-in-a-lifetime pitchers like Greg Maddux were particularly adept at inducing outs in 0-0 counts.

Until today, though, I’ve mostly dealt with first pitch trends from the pitchers’ perspective. This morning I want to look at first pitch balls in play for unique types of hitters, trying to determine which types tend to succeed more often when putting the ball in play early in the count.

Taking advantage of a patient hitter

We are aware that certain ballplayers have reputations as unusually patient hitters and will rarely swing on the first pitch. In my years as a baseball fan, Joe Mauer or Kevin Youkilis as having a similar type of approach at the plate.

We might suspect, then, that opposing teams travel with scouting data on how seldom these batters hack in 0-0 counts and would apply this information to their advantage on the mound. If we’re fairly certain Youkilis and Mauer are going to balk at the first pitch, why bother throwing anything off the plate? After all, the differences between the outcomes of an 0-1 count and a 1-0 count are enormous. In 2012 alone, it was ultimately the difference between an .822 OPS and a .612 OPS for major league hitters on average. That first strike is critical.

This is where the power of game theory comes in. If, for instance, Mauer and Youkilis know that they are far more likely to get a meatball to begin their plate appearance, how well do they fare on that rare occasion when they do swing at that first pitch?

To answer this, I looked at wOBA on first pitch balls in play including home runs (or wOBA/CON for “wOBA on contact”) for all hitters with at least 2,500 plate appearances since 2002. I then compared their wOBA/CON on first pitch against their wOBA/CON in all counts.

The hitters who put the ball in play least often on the first pitch are mostly players you would probably expect, that is, players with prominent reputations for having a patient approach at the plate:

Batters with lowest first pitch BIP% since 2002

# Name Year PA wOBA/CON FP_BIP% FP_BIP PA FP_wOBA/CON
1 Joe Mauer 2004 4592 0.383 1.6 254 0.410
2 Jack Cust 2002 2577 0.468 2.6 214 0.524
3 Nick Swisher 2004 5193 0.402 2.8 386 0.400
4 Kevin Youkilis 2004 4348 0.413 2.8 215 0.412
5 Franklin Gutierrez 2006 2680 0.353 3.5 119 0.440
6 Jayson Werth 2002 4138 0.432 3.8 207 0.487
7 David Murphy 2006 2601 0.382 3.8 237 0.330
8 Chad Tracy 2004 2856 0.368 3.9 207 0.374
9 Shin-Soo Choo 2005 2965 0.427 4.8 290 0.471
10 Bill Hall 2002 3683 0.405 5.1 363 0.427

For the most part, this is a group of above-average hitters who are well-known for their ability to work counts and wait for “their pitch.” We can see that, as a whole, their wOBA/CON on first pitch was significantly higher than their overall rates. In fact, the difference between the weighted average of their first pitch wOBA/CON and their overall wOBA/CON was a healthy .024. That may seem impressive, but we have to remember that the league as a whole generally has an advantage when putting the ball into play on the first pitch.

These are the league rates during that same time period, 2002-2012:

image

On average since 2002, major league hitters have enjoyed a .013 spike in their wOBA/CON when putting the ball in play on the first pitch. So Mauer, Youkilis and Co. seem to gain an advantage of .09 wOBA/CON over the rest of the league when ambushing a pitcher on 0-0.

This advantage for the more patient hitters seems to hold true for onlythe most elite members of their kind, however. Hitters with the top 50 fewest first pitch balls in play percentage did not seem to hold much of an advantage over the league and actually scored a hair below league average with just a .010 delta in their weighted average.

In fact, the some of the most aggressive hitters over the last 10 years actually seemed to fare far better than some of their patient counterparts when swinging on 0-0 counts:

Batters with highest first pitch BIP% since 2002

# Name Year PA wOBA/CON FP_BIP% FP_BIP PA FP_wOBA/CON
1 Melky Cabrera 2005 3945 0.344 36.8 520 0.359
2 Delmon Young 2006 3690 0.374 27.5 644 0.387
3 Michael Bourn 2006 3372 0.355 27.3 320 0.381
4 Juan Rivera 2002 3897 0.346 26.0 528 0.343
5 Vinny Castilla 2002 2682 0.342 24.6 539 0.388
6 Nomar Garciaparra 2002 3423 0.361 24.4 729 0.383
7 Miguel Olivo 2002 3889 0.386 23.8 528 0.452
8 Ty Wigginton 2002 4886 0.369 23.6 705 0.370
9 A.J. Pierzynski 2002 5803 0.345 22.6 1014 0.343
10 Marco Scutaro 2002 5023 0.324 21.1 546 0.250

So we have some strange things going on here. Certain notoriously patient hitters like Mauer, Jack Cust, and Jayson Werth appear to be demonstrating some ability to catch pitchers by surprise by swinging on 0-0. But for others, like Nick Swisher and Youkilis, there doesn’t seem to be much of an effect. Furthermore, some of the players from our group of 10 highly-aggressive hitters were just as fortunate in first pitch BIP situations, while the group as a whole improved exatly the same amount as the league (.010):

Group Change in wOBA/CON
Top 10 lowest FP_BIP% 0.022
Top 50 lowest FP_BIP% 0.010
Top 50 highest FP_BIP% 0.012
Top 10 highest FP_BIP% 0.010
LG-AVG 0.010

It would seem, then, that success with balls in play on first pitch is mostly random, perhaps with a few outliers where game theory might come in to play. But if the effect exists, it exists only on that extreme end of the spectrum. For example, If we look at all 302 hitters from 2002-2012 with at least 2,500 plate appearances, we can see that their success in putting the ball in play in 0-0 counts is not at all dependent on the frequency with which they occur. The relationship between first pitch balls-in-play percentage and wOBA on contact for all 302 hitters was a non-existent r = .0004:

image

Unfortunately, there is no overwhelming evidence that hitters who swing less often at the first pitch gain an advantage by occasionally shocking the opposition and jumping on an 0-0 meatball. But there may be enough to suggest that for certain hitters whose first-pitch habits are extremely conservative, the occasional ambush may produce a small, marginal advantage over the rest of the league. We may just need more ways to test the issue.

I’d appreciate your comments on any way this line of inquiry might be improved, or what possible explanations you might have as to why game theory in 0-0 counts doesn’t seem to pay off with the significant dividends one might expect. Are hitters simply too uncomfortable departing from their well-defined, finely-tuned approach at the plate? Does jumping on the first pitch just feel too unnatural to them?

I’d like to hear your thoughts.

References & Resources
All data includes post-season PA.
Thanks to retrosheet and Fangraphs “GUTS” for providing data used in this article.

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Comments

  1. MGL said...

    James, you know that there is a utility, bevent.exe, that automatically extracts almost any field (including pitch sequence) in the retrosheet data files, right?

    If you like, I can send you a file of the data you are interested in (first pitch swing percentages and outcome on the swing). And of course you want to compare that outcome to their overall outcome on “a swing”, although I’m not sure what metric to use on a swing, since you can’t really use wOBA, although you can use some form of it, which includes strikes I suppose.) Let me know.

  2. MGL said...

    James,

    I am not sure why you are using contact numbers (e.g. FP contact %) rather than swing percentage (including strikes – misses and fouls).

    If you do that, you might find a correlation between first pitch SWING percentage and wOBA (including misses and fouls) differential.

    The reason you are getting no correlation may be this:

    Regarless of whether a batter is patient or impatient on the FP, if he is a power hitter, he may miss a lot, which would make his first pitch contact rate a lot lower, making it look like he is not a patient hitter. If he is a contact, slap hitter, he will have a higher first pitch contact rate, making him look like an impatient hitter, regardless of how often he actually swings at the first pitch.

    So what you may be getting in your correlation is actually two offsetting correlations: One, where the the correlation between FP SWING (not just contact) percentage and wOBA differential is indeed positive (and perhaps fairly large), and the other, where the correlation between FP contact % (the percentage of contact per swing) and wOBA correlation is negative, because weaker hitters are making more contact regardless of how often they swing.

    In any case, you are looking at patience versus impatience on the first pitch. Use swing percentage on NOT contact percentage on the first pitch!

  3. James Gentile said...

    Thanks for your thoughts MGL,

    As far as using Contact% instead of swing%, it was simply a matter of what data was available to me. Extracting pitch sequence info from the retrosheet files was proving a bit troublesome. I’ve been dabbling with pitch f/x over the last few days in order to find that very same measurement you’re asking for(swing rate on first pitch), but my code still needs a few tweaks.

    I’ll be sure to revisit the correlation when I have the new data! Thanks for your comments!

  4. Brian Cartwright said...

    The logical fallacy, which has been committed almost everyone who has done first pitch analysis, is to equate swinging at a first pitch to putting the ball in play. As mgl has pointed out, swinging also includes misses and fouls.

    Each pitched can be grouped into three outcomes – a called ball, a called strike, or a swing. Then simply measure the final outcome of each plate appearance that begins with each of these first pitch results.

    High contact hitters can afford to take a strike, as with one or even two strikes their odds of striking out are not crippling. Low contact hitters do not have that luxury, they cannot afford to give away any strikes and should be swinging at most pitches in the zone.

    Here are a few of the batters from the first table, plus Bobby Abreu. Joe Mauer likely should swing at more first strikes (those in the zone!) as the difference between his called strike and swing wOBA is very large, while his first fitch swing rate is very low. Bobby Abreu’s strength is getting ahead in the count, and has very little difference between taking a striking and swing, so he is likely correct to swing at only 9.3% of first pitches.

    Luis Castillo actually did worse swinging at the first pitch than taking a strike

    First Pitch, final wOBA for PA
    (2005-2012, from Gameday)
    Sw% Called B Called S Swing
    094 451 308 426 -118 Mauser
    097 409 301 327 -026 Abreu
    106 342 276 274 +002 Gutierrez
    109 452 331 378 -047 Youkilis
    117 360 278 257 +023 Castillo
    150 325 288 293 -005 Pierre
    207 427 277 343 -066 Swisher
    289 413 264 371 -107 Cust

  5. Brian Cartwright said...

    The prerequisite point is that to measure the utility of swinging at the first pitch, one must look at the results of all plate appearances, not just the times when a ball is put in play. Jack Cust WALKED 9.4% of the time he swung at the first pitch, a higher rate than the majority of players in all situations. That has to be considered in the analysis.

    At a minimum, plate appearances will be divided into swing/no swing. In deciding to swing, the batter must factor fastball/off speed, in zone/out of zone, on the edge/down the middle, how many strikes remaining, the cost of a strike to that particular batter – so yes, pitch f/x will be extremely helpful in an in depth study.

    Batters have better than average results on their balls in play on the first pitch because there is a higher percentage of fastballs and balls near the middle of the plate. Pitchers want to throw a first pitch strike. The best BIP numbers are on 2-0 counts. Pitchers do not want to go 3-0, resulting in the highest percentage of fastballs down the middle.

  6. MGL said...

    Brian, the question is what would have happened if player X did not swing at the first pitches that he swung at. We know what did happen when he swung. To answer what would have happened if he did not swing, we need pitch F/X to tell us where the pitches were. Presumably they were closer to strikes than the pitches he did not swing at. How much, we don’t know without pitch F/X. So in order to estimate whether particular batters are swinging too much or too little (or just right), we need to use pitch F/X. Also, the sample sizes are so small when batters swing at first pitches, there is really too much random fluctuation on the outcome to be able to use that to estimate whether an individual batter swings too much or too little.  We can, however, use conglomerate data of different types of batters to get some idea as to whether certain individual batters swing too much or too little at first pitch pitches, again, using pitch F/X data.

    Also, how often each batter should swing at first pitches highly depends on the pitcher, so without controlling for pitcher (I assume that batters face fairly different pools of pitchers), you also are not going to get very reliable results.

  7. philosofool said...

    Brian,

    You said that the best BIP numbers are in 2-0, but it looks like 3-0 is best. Are you just throwing those out because some much of swinging in a 3-0 count is situational?

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