# What’s the Point of DIPS, Anyway?

In the last piece I wrote, I mentioned that I have some concerns about the way that people tend to think about defense independent pitching statistics (DIPS), especially FIP. (Refresher: Fielding Independent Pitching is a metric commonly used as an ERA estimator based on a pitcher’s walk, strikeout, and HR numbers.) I’m writing this piece in part as a way for me to sort some of my thoughts on the complexities of defense and park adjustments, not necessarily to make a single point (and none of these thoughts are terribly original).

All of this analysis starts with this equation, which is no less foundational for being almost tautological: Runs Allowed = Fielding Independent Pitching + Fielding Dependent Pitching. (Quick aside: Fielding Independent Pitching refers both to a concept and a metric; in this article, I’m mostly going to be talking about the concept.) In other words, there are certain ways of preventing runs that don’t rely on getting substantial aid from the defense (strike outs, for instance), and certain ways that do (allowing soft contact on balls in play).

In general, most baseball analysts tend to focus on the fielding independent part of the equation. There are a number of good reasons for this, the primary two being that it’s much simpler to assess and more consistent than its counterpart. There’s probably also a belief that, because it’s more clearly intrinsic to the pitcher, it’s more worthwhile to understand the FI portion of pitching. There are pitchers for whom we shy away from using the FI stats (like knuckleballers), but if you look at the sort of posts you see on FanGraphs, they’ll mostly be talking about performance in those terms.

That’s not always (or necessarily ever) a problem, but it often omits an essential portion of context. To see how, look at these three overlapping ways of framing the question “how good has this pitcher been?”:

1) If their spot on their team were given to an arbitrary (replacement-level or average) pitcher, how much better or worse would the team be?

2) If we took this pitcher and put them on a hypothetically average team (average in terms of defense and park, at least), how much better or worse would that team be?

3) If we took this pitcher and put them on a specific other team, how much better or worse would that team be?

Roughly speaking, #2 is how I think of FanGraphs’ pitcher WAR. #1 is Baseball Reference’s WAR. I don’t know of anywhere that specifically computes #3, but in theory that’s what you should get out of a projection system like Baseball Prospectus’s PECOTA or the ZiPS numbers found at FanGraphs’. (In practice, my understanding is that the projections aren’t necessarily nuanced enough to work that out precisely.)

The thing, though, is that pitchers don’t work with an average park and defense behind them. You should expect a fly ball pitcher to post better numbers with the Royals and their good outfield defense and a ground ball pitcher to do worse in front the butchers playing in the Cleveland infield. From a team’s perspective, though, a run saved is a run saved, and who cares whether it’s credited to the defense, the pitcher, or split between the two? If Jarrod Dyson catches the balls sent his way, it’s good to have a pitcher who’s liable to have balls hit to him. In a nutshell, a player’s value to his team (or another team) is derived from the FIP and the FDP, and focusing on the FIP misses some of that. Put your players in the best position for them to succeed, as the philosophy often attributed to Earl Weaver goes.

There are a number of other ways to frame this issue, which, though I’ve been talking in terms of pitching, clearly extends beyond that into nearly all of the skills baseball players demonstrate. Those other frames are all basically a restatement of that last paragraph, so I’ll try to avoid belaboring the point, but I’ll add one more example. Let’s say you have two batters who are the same except for 5% of their at-bats, which are fly balls to left field for batter A and to right field for batter B. By construction, they are players of identical quality, but player B is going to be worth more in Cleveland, where those fly balls are much more likely to go out of the park. Simply looking at his wRC+ won’t give you that information. (My limited knowledge of fantasy baseball suggests to me that fantasy players, because they use raw stats, are more attuned to this.)

Doing more nuanced contextual analysis of the sort I’m advocating is quite tricky and is beyond my (or most people’s) ability to do quickly with the numbers we currently have available. I’d still love, though, to see more of it, with two things in particular crossing my mind.

One is in transaction analysis. I read a few pieces discussing the big Samardzija trade, for instance, and in none did they mention (even in passing) how his stuff is likely to play in Oakland given their defense and park situation. This isn’t an ideal example because it’s a trade with a lot of other interesting aspects to it, but in general, it’s something I wish I saw a bit more of—considering the amount of value a team is going out of a player after adjusting for park and defense factors. The standard way of doing this is to adjust things from his raw numbers to a neutral context, but bringing things one step further, though challenging, should add another layer of nuance. (I will say that in my experience you see such analyses a bit more with free agency analyses, especially of pitchers.)

The second is basically expanding what we think of as being park and defensive adjustments. This is likely impossible to do precisely without more data, but I’d love to see batted ball data used to get a bit more granular in the adjustments; for instance, dead pull hitters should be adjusted differently from guys who use the whole field. This isn’t anything new—it’s in the FanGraphs page explaining park factors—but it’s something that occasionally gets swept under the rug.

One last note, as this post gets ever less specific: I wonder how big the opportunity is for teams to optimize their lineups and rotations based on factors such as these—left-handed power hitters go against the Yankees, ground ball hitters against the Indians, etc. We already see this to some extent, but I’d be curious to see what the impact is. (If you can quantify how big an edge you’re getting on a batter-by-batter basis—a big if—you could run some simulations to quantify the gain from all these adjustments. It’s a complex optimization problem, but I doubt it’s impossible to estimate.)

One thing I haven’t seen that I’d love for someone to try is for teams with roughly interchangeable fourth, fifth, and sixth starters to juggle their pitching assignments each time through the order to get the best possible matchups with respect to park, opponent, and defense. Ground ball pitchers pitch at Comiskey, for instance, and fly ball pitchers start on days when your best outfield is out there. I don’t know how big the impact is, so I don’t want to linger on this point too much, but it seems odd that in the era of shifting we don’t discuss day-to-day adjustments very much.

And that’s all that I’m talking about with this. Defense- and park-adjusted statistics are incredibly valuable tools, but they don’t get you all the way there, and that’s an important thing to keep in mind when you start doing nuanced analyses.

# A Little Bit on FIP-ERA Differential

Brief Summary:

Fielding Independent Pitching (FIP) is a popular alternative to ERA predicated on a pitcher’s strikeout, walk, and home run rates. The extent to which pitchers deserve credit for having FIPs better or worse than ERAs is something that’s poorly understood, though it’s usually acknowledged that certain pitchers do deserve that credit. Given that some of the non-random difference can be attributed to where a pitcher plays because of defense and park effects, I look at pitchers who change teams and consider the year-over-year correlation between their ERA-FIP differentials. I find that the correlation remains and is not meaningfully different from the year-over-year correlation for pitchers that stay on the same team. However, this effect is (confusingly) confounded with innings pitched.

After reading this Lewie Pollis article on Baseball Prospectus, I started thinking more about how to look at FIP and other ERA estimators. In particular, he talks about trying to assess how likely it is that a pitcher’s “outperforming his peripherals” (scare quotes mine) is skill or luck. (I plan to run a more conceptual piece on that FIP and other general issues soon.) That also led me to this FanGraphs community post on FIP, which I don’t think is all that great (I think it’s arguing against a straw man) but raises useful points about FIP regardless.

After chewing on all of that, I had an idea that’s simple enough that I was surprised nobody else (that I could find) had studied it before. Do pitchers preserve their FIP-ERA differential when they change teams? My initial hypothesis is that they shouldn’t, at least not to the same extent as pitchers who don’t change teams. After all, in theory (just to make it clear: in theory) most or much of the difference between FIP and ERA should be related to park and defensive effects, which will change dramatically from team to team. (To see an intuitive demonstration of this, look at the range of ERA-FIP values by team over the last decade, where each team has a sample of thousands of innings. The range is half a run, which is substantial.)

Now, this is dramatically oversimplifying things—for one, FIP, despite its name, is going to be affected by defense and park effects, as the FanGraphs post linked above discusses, meaning there are multiple moving parts in this analysis. There’s also the possibility that there’s either selection bias (pitchers who change teams are different from those who remain) or some treatment effect (changing teams alter’s a pitcher’s underlying talent). Overall, though, I still think it’s an interesting question, though you should feel free to disagree.

First, we should frame the question statistically. In this case, the question is: does knowing that a pitcher changed teams give us meaningful new information about his ERA-FIP difference in year 2 above and beyond his ERA-FIP difference in year 1. (From here on out, ERA-FIP difference is going to be E-F, as it is on FanGraphs.)

I used as data all consecutive pitching seasons of at least 80 IP since 1976. I’ll have more about the inning cutoff in a little bit, but I chose 1976 because it’s the beginning of the free agency era. I said that a pitcher changed teams if they played for one team for all of season 1 and another team for all of season 2; if they changed teams midseason in either season, they were removed from the data for most analyses. I had 621 season pairs in the changed group and 3389 in the same team group.

I then looked at the correlation between year 1 and year 2 E-F for the two different groups. For pitchers that didn’t change teams, the correlation is 0.157, which ain’t nothing but isn’t practically useful. In a regression framework, this means that the fraction of variation in year 2 E-F explained by year 1 E-F is about 2.5%, which is almost negligible. For pitchers who changed teams, the correlation is 0.111, which is smaller but I don’t think meaningfully so. (The two correlations are also not statistically significantly different, if you’re curious.)

Looking at year-to-year correlations without adjusting for anything else is a very blunt way of approaching this problem, so I don’t want to read too much into a null result, but I’m still surprised—I would have thought there would be some visible effect. This still highlights one of the problems with the term Fielding Independent Pitching—the fielders changed, but there was still an (extremely noisy) persistent pitcher effect, putting a bit of a lie to the term “independent” (though as before, there are a lot of confounding factors so I don’t want to overstate this). At some point, I’d like to thoroughly examine how much of this result is driven by lucky pitchers getting more opportunities to keep pitching than unlucky ones, so that’s one for the “further research” pile.

I had two other small results that I ran across while crunching these numbers that are tangentially related to the main point:

1. As I suspected above, there’s something different about pitchers who change teams compared to those who don’t. The average pitcher who didn’t change teams had an E-F of -0.10, meaning they had a better ERA than FIP. The average pitcher who did change teams had an E-F of 0.05, meaning their FIP was better than their ERA. The swing between the two groups is thus 0.15 runs, which over a few thousand pitchers is pretty big. There’s going to be some survivorship bias in this, because having a positive ERA-FIP might be related to having a high ERA, which makes one less likely to pitch 80 innings in the second season and thus more likely to drop out of my data. Regardless, though, that’s a pretty big difference and suggests something odd is happening in the trade and free agency markets.
2. There’s a strong correlation between innings pitched in both year 1 and year 2 and E-F in year two for both groups of pitchers. Specifically, each 100 innings pitched in year 1 is associated with a 0.1 increase in E-F in year 2, and each 100 innings pitched in year 2 is associated with a 0.2 decrease in E-F in year 2. I can guess that the second one is happening because lower/negative E-F is going to be related to low ERAs, which get you more playing time, but I find the first part pretty confusing. Anyone who has a suggestion for what that means, please let me know.

So, what does this all signify? As I said before, the result isn’t what I expected, but when working with connections that are this tenuous, I don’t think there’s a clear upshot. This research has, however, given me some renewed skepticism about the way FIP is often employed in baseball commentary. I think it’s quite useful in its broad strokes, but it’s such a blunt instrument that I would advise being wary of people who try to draw strong conclusions about its subtleties. The process of writing the article has also churned up some preexisting ideas I had about FIP and the way we talk about baseball stats in general, so stay tuned for those thoughts as well.

# More on Stealing with Runners on the Corners

A few people kicked around some suggestions about my last piece on Tom Tango’s blog, so I’m following up with a couple more pieces of analysis that will hopefully shed some light on things. As a quick refresher, I looked at steal attempts with runners on the corners and found that the success rate is much larger than the break even point, especially with two outs. My research suggests teams are too conservative, i.e. they should send the runners more. For more about methods and data, look at the prior piece.

One initial correction from Tango is that I was treating one class of events improperly; that’s since been corrected. (Specifically, two out events where one runner is out and the other scores are now counted as successes, not failures.) Another point made by Peter Jensen is that I should consider what happens when the runners are moving and contact is made; that’s going to require a bit more grinding with the data, but it’s now on my list of things to look at.

Next, there were some questions about how much of the success rate is due to having abnormally good or bad runners. Here are two plots showing all successes and failures by the stolen base percentages of the runners on first and third. The first is for all situations, the second for two out situations only.

Quick data note: to compute attempts and stolen base percentage, I used a centered three-year average, meaning that if an attempt took place in 2010 the SB% fed in would be the aggregate figure from 2009–2011. These charts only include situations where both runners have at least 20 attempts.

To simplify the charts a bit, I put the attempts into one of 36 buckets based on the SB% of the runners and then computed the success rates for those buckets; you can see the results in the tables below. The bucket boundaries are based on the distribution of SB%, so the 17th, 33rd, 50th, 67th, and 83rd percentiles. Sample sizes are roughly 55 for two outs (minimum 40) and 100-110 overall (minimum 73).

Outcomes of 1st/3rd Steal Attempts by SB% of Runners on Base, All Situations
Third Base SB% Bucket
1st Base SB% Bucket 27.3%—61.4% 61.4%—68% 68%—72.5% 72.5%—75.8% 75.8%—80% 80%—95.5%
33.3%—64.9% 72.6 79.1 83.0 77.1 83.3 81.0
64.9%—70.6% 80.3 85.6 80.8 88.2 86.8 87.1
70.6%—74.4% 86.4 84.0 83.7 87.3 85.3 86.3
74.4%—77.6% 85.6 85.9 91.4 86.4 92.7 89.8
77.6%—81.2% 91.3 90.5 83.3 90.3 95.2 90.6
81.2%—96.2% 90.8 84.9 89.4 90.8 93.6 89.1
Outcomes of 1st/3rd Steal Attempts by SB% of Runners on Base, Two Outs
Third Base SB% Bucket
1st Base SB% Bucket 27.3%—60.9% 60.9%—67.6% 67.6%—72.1% 72.1%—75.5% 75.5%—80% 80%—93.9%
35%—64.1% 86.9 89.2 87.7 84.6 92.5 89.4
64.1%—70.1% 89.6 93.2 89.1 89.1 87.8 91.5
70.1%—74% 92.7 85.7 91.7 96.6 93.3 91.5
74%—77.5% 94.1 93.3 92.9 94.6 100.0 93.5
77.5%—81.1% 95.0 87.7 94.4 93.5 98.2 97.1
81.1%—95.5% 95.8 89.3 90.7 91.2 95.7 95.5

As you can see, even with noticeably below-average runners at both bases (average SB% is 70%), teams are successful so often that they should be trying it more often—all buckets but one in the two tables have a success rate above break-even. (BE rates are 75.5% overall and 69% for 2 outs.) There’s still a little bit of selection bias, which is pertinent, though I don’t think it accounts for most of the effect—see the note below. However, the fact that every single bucket comes in well above the break-even rate suggests to me that even accounting for the selection bias, this is still an area where managers should be more aggressive. At the very least, it seems that if there are two average base thieves on and two out, the runner on first should be going much more frequently than the current sub-10% attempt rate.

Note: One important thing to consider is that putting the attempts minimum in place noticeably increases the success rate—from 83% to 86% overall, and from 90% to 92% for two out situations. (The explanation for that is that really slow players don’t necessarily have poor SB%, they just have next to no stolen base attempts, so they are falling out of the data.) However, if you stick to the attempts where one or both runners have few attempts, the success rate only drops about 2 percentage points, which is still pretty far above the breakeven point overall and with two outs.

# Stealing an Advantage from First and Third

(Note: Inspired by this post from Jeff Fogle, I decided to change the format up a bit for this post, specifically by putting an abstract at the beginning. We’ll see if it sticks.) This post looks at baserunning strategy with runners on first and third, specifically having to do with when to have the runner on first attempt to steal. My research suggests that teams may be currently employing this strategy in a non-optimal manner. While they start the runner as often as they should with one out, they should probably run more frequently with zero and two outs with runners on first and third than they currently. The gain from this aggressiveness is likely to be small, on the order of a few runs a season. Read on if you want to know how I came to this conclusion.

Back when I used to play a lot of the Triple Play series, I loved calling for a steal with runners on first and third. It seemed like you could basically always get the runner to second, and if he drew a throw then the runner on third would score. It’s one of those fun plays that introduced a bit of chaos and works disproportionately frequently in videogames. Is that last statement true? Well, I don’t know how frequently it worked in Triple Play 99, but I can look at how frequently it works in the majors. And it appears to work pretty darn frequently.*

* I haven’t found any prior research directly addressing this, but this old post by current Pirates analytics honcho Dan Fox obliquely touches on it. I’m pretty confident that his conclusions are different because he’s omitting an important case and focusing directly on double steals, and not because either one of us is wrong.

The data I looked at were Retrosheet play-by-play data from 1989–2013, looking at events classified as caught stealing, stolen bases, balks, and pickoffs with runners at first and third. I then removed caught stealing and steals where the runner on first remained on first at the end of the play, leaving 8500 events or so. That selection of events is similar to what Tom Tango et al. do in The Book and control for the secondary effects of base stealing, but I added the restriction about the runner on first to remove failed squeezes, straight steals of home, and other things that aren’t related to what we’re looking at. This isn’t going to perfectly capture the events we want, but modulo the limitations of play-by-play data it’s the best cut of the data I could think of. (It’s missing two big things: the impact of running on batter performance and what happens when the runners go and the ball is put in play. The first would take a lot of digging to guess at, and the second is impossible to get from my data, so I’m going to postulate they have a small effect and leave it at that.)

So, let’s say we define an outcome to be successful if it leads to an increased run expectancy. (Run expectancy is computed empirically and is essentially the average number of runs scored in the remainder of an inning given where the baserunners are and how many outs there are.) In this particular scenario, increased run expectancy is equivalent to an outcome where both runners are safe, which occurs 82.7% of the time. For reference, league average stolen base percentage over this period is 69.9% (via the Lahman database), so that’s a sizeable difference in success rates (though the latter figure doesn’t account for pickoffs, errors, and balks). (For what it’s worth, both of those numbers have gone up between 4 and 6 percentage points in the last five years.)

How much of that is due to self-selection and how much is intrinsic to the situation itself? In other words, is this just a function of teams picking their spots? It’s hard to check every aspect of this (catcher, pitcher, leverage, etc.), so I chose to focus on one, which is the stolen base percentage of the runner on first. I used a three year centered average for the players (meaning if the attempt took place in 1999, I used their combined stolen base figures from 1998–2000), and it turns out that on aggregate runners on first during 1st and 3rd steal attempts are about one percentage point better than the league average. That’s noticeable and not meaningless, but given how large the gap in success rate is the increased runner quality can’t explain the whole thing.

Now, what if we want to look at the outcomes more granularly? The results are in the table below. (The zeros are actually zero, not rounded.)

Outcomes of 1st/3rd Steal Attempts (Percentage)
Runner on First’s Destination
Runner on Third’s Destination Out 1st Base 2nd Base 3rd Base Run
Out 0.20 0.97 2.78 0.23 0.00
3rd Base 12.06 0.00 69.89 0.00 0.00
Run 1.07 0.36 9.31 2.98 0.15

This doesn’t directly address run expectancy, which is what we need if we’re going to actually determine the utility of this tactic. If you take into account the number of outs, balks, and pickoffs and combine the historical probabilities seen in that table with Baseball Prospectus’s 2013 run expectancy tables*, you get that each attempt is worth about 0.07 runs. (Restricting to the last five years, it’s 0.09.) That’s something, but it’s not much—you’d need to have 144 attempts a year at that success rate to get an extra win, which isn’t likely to happen given that there only about 200 1st and 3rd situations per team per year according to my quick count. Overall, the data suggest the break even success rate is on the order of 76%.**

* I used 2013 tables a) to simplify things and b) to make these historical rates more directly applicable to the current run environment.

** That’s computed using a slight simplification—I averaged the run values of all successful and unsuccessful outcomes separately, then calculated the break even point for that constructed binary process. Take the exact values with a grain of salt given the noise in the low-probability, high-impact outcomes (e.g. both runners score, both runners are out).

There’s a wrinkle to this, though, which is that the stakes and decision making processes are going to be different with zero, one, or two outs.  In the past, the expected value of running with first and third is actually negative with one out (-0.04), whereas the EV for running with two outs is about twice the overall figure. (The one out EV is almost exactly 0 over the last five years, but I don’t want to draw too many conclusions from that if it’s a blip and not a structural change.) That’s a big difference, probably driven by the fact that the penalty for taking the out is substantially less with two outs, and it’s not due to a small sample—two out attempts make up more than half the data. (For what it’s worth, there aren’t substantive discrepancies in the SB% of the runners involved between the different out states.) The table below breaks it down more clearly:

Success and Break Even Rates for 1st/3rd Steal Attempts by Outs
Number of Outs Historical Success Percentage Break Even Percentage
0 81.64 74.61
1 73.65 78.00
2 88.71 69.03
Overall 82.69 75.52

That third row is where I think there’s a lot of hay to be made, and I think the table makes a pretty clear case: managers should be quite aggressive about starting the runner if there’s a first and third with two outs, even if there’s a slightly below average runner at first. They should probably be a bit more aggressive than they currently are with no outs, and more conservative with one out.

There’s also plenty of room for this to happen more frequently; with two outs, the steal attempt rate last year was about 6.6% (it’s 5% with one out, and 4% with no outs). The number of possible attempts per team last year was roughly 200, split 100/70/30 between 2/1/0 outs, so there are some reasonable gains to be made. It’s not going to make a gigantic impact, but if a team sends the runner twice as often as they have been with two outs (about one extra time per 25 games), that’s a run gained, which is small but still an edge worth taking. Maybe my impulses when playing Triple Play had something to them after all.

# A Look at Pitcher Defense

Like most White Sox fans, I was disappointed when Mark Buehrle left the team. I didn’t necessarily think they made a bad decision, but Buehrle is one of those guys that makes me really appreciate baseball on a sentimental level. He’s never seemed like a real ace, but he’s more interesting: he worked at a quicker pace than any other pitcher, was among the very best fielding pitchers, and held runners on like few others (it’s a bit out of date, but this post has him picking off two batters for each one that steals, which is astonishing).

In my experience, these traits are usually discussed as though they’re unrelated to his value as a pitcher, and the same could probably be said of the fielding skills possessed by guys like Jim Kaat and Greg Maddux. However, that’s covering up a non-negligible portion of what Buehrle has brought to his teams over the year; using a crude calculation of 10 runs per win, his 87 Defensive Runs Saved are equal to about 20% of his 41 WAR during the era for which have DRS numbers. (Roughly half of that 20% is from fielding his position, with the other half coming from his excellent work in inhibiting base thieves. Defensive Runs Saved are a commonly used, all-encompassing defensive metric from Baseball Info Solutions. All numbers in this piece are from Fangraphs. ) Buehrle’s extreme, but he’s not the only pitcher like this; Jake Westbrook had 62 DRS and only 18 WAR or so in the DRS era, which means the DRS equate to more than 30% of the WAR.

So fielding can make up a substantial portion of a pitcher’s value, but it seems like we rarely discuss it. That makes a fair amount of sense; single season fielding metrics are considered to be highly variable for position players who will be on the field for six times as many innings as a typical starting pitcher, and pitcher defensive metrics are less trustworthy even beyond that limitation. Still, though, I figured it’d be interesting to look at which sorts of pitchers tend to be better defensively.

For purposes of this study, I only looked at what I’ll think of as “fielding runs saved,” which is total Defensive Runs Saved less runs saved from stolen bases (rSB). (If you’re curious, there is a modest but noticeable 0.31 correlation between saving runs on stolen bases and fielding runs saved.) I also converted it into a rate stat by dividing by the number of innings pitched and then multiplying by 150 to give a full season rate. Finally, I restricted to aggregate data from the 331 pitchers who threw at least 300 innings (2 full seasons by standard reckoning) between 2007 and 2013; 2007 was chosen because it’s the beginning of the PitchF/X era, which I’ll get to in a little bit. My thought is that a sample size of 330 is pretty reasonable, and while players will have changed over the full time frame it also provides enough innings that the estimates will be a bit more stable.

One aside is that DRS, as a counting stat, doesn’t adjust for how many opportunities a given fielder has, so a pitcher who induces lots of strikeouts and fly balls will necessarily have DRS values smaller in magnitude than another pitcher of the same fielding ability but different pitching style.

Below is a histogram of pitcher fielding runs/150 IP for the population in question:

If you’re curious, the extreme positive values are Greg Maddux and Jake Westbrook, and the extreme negative values are Philip Humber, Brandon League, and Daniel Cabrera.

This raises another set of questions: what sort of pitchers tend to be better fielders? To test this, I decided to use linear regression—not because I want to make particularly nuanced predictions using the estimates, but because it is a way to examine how much of a correlation remains between fielding and a given variable after controlling for other factors. Most of the rest of the post will deal with the regression methods, so feel free to skip to the bold text at the end to see what my conclusions were.

What jumped out to me initially, is that Buehrle, R.A. Dickey, Westbrook, and Maddux are all extremely good fielding pitchers that aren’t hard throwers; to that end, I included their average velocity as one of the independent variables in the regression. (Hence the restriction to the PitchF/X era.) To control for the fact that harder throwers also strike out more batters and thus don’t have as many opportunities to make plays, I included the pitcher’s strikeouts per nine IP as a control as well.

It also seems plausible to me that there might be a handedness effect or a starter/reliever gap, so I added indicator variables for those to the model as well. (Given that righties and relievers throw harder than lefties and starters, controlling for velocity is key. Relievers are defined as those with at least half their innings in relief.) I also added in ground ball rate, with the thought that having more plays to make could have a substantial effect on the demonstrated fielding ability.

There turns out to be a noticeable negative correlation between velocity and fielding ability. This doesn’t surprise me, as it’s consistent with harder throwers having a longer, more intense delivery that makes it harder for them to react quickly to a line drive or ground ball. According to the model, we’d associate each mile per hour increase with a 0.2 fielding run per season decrease; however, I’d shy away from doing anything with that estimate given how poor the model is. (The R-squared values on the models discussed here are all less than 0.2, which is not very good.) Even if we take that estimate at face value, though, it’s a pretty small effect, and one that’s hard to read much into.

We don’t see any statistically significant results for K/9, handedness, or starter/reliever status. (Remember that this doesn’t take into account runs saved through stolen base prevention; in that case, it’s likely that left handers will rate as superior and hard throwers will do better due to having a faster time to the plate, but I’ll save that for another post.) In fact, of the non-velocity factors considered, only ground ball rate has a significant connection to fielding; it’s positively related, with a rough estimate that a percentage point increase in groundball rate will have a pitcher snag 0.06 extra fielding runs per 150 innings. That is statistically significant, but it’s a very small amount in practice and I suspect it’s contaminated by the fact that an increase in ground ball rate is related to an increase in fielding opportunities.

To attempt to control for that contamination, I changed the model so that the dependent (i.e. predicted) variable was [fielding runs / (IP/150 * GB%)]. That stat is hard to interpret intuitively (if you elide the batters faced vs. IP difference, it’s fielding runs per groundball), so I’m not thrilled about using it, but for this single purpose it should be useful to help figure out if ground ball pitchers tend to be better fielders even after adjusting for additional opportunities.

As it turns out, the same variables are significant in the new model, meaning that even after controlling for the number of opportunities GB pitchers and soft tossers are generally stronger fielders. The impact of one extra point of GB% is approximately equivalent to losing 0.25 mph off the average pitch speed; however, since pitch speed has a pretty small coefficient we wouldn’t expect either of these things to have a large impact on pitcher fielding.

This was a lot of math to not a huge effect, so here’s a quick summary of what I found in case I lost you:

• Harder throwers contribute less on defense even after controlling for having fewer defensive opportunities due to strikeouts. Ground ball pitchers contribute more than other pitchers even if you control for having more balls they can make plays on.
• The differences here are likely to be very small and fairly noisy (especially if you remember that the DRS numbers themselves are a bit wonky), meaning that, while they apply in broad terms, there will be lots and lots of exceptions to the rule.
• Handedness and role (i.e. starter/reliever) have no significant impact on fielding contribution.

All told, then, we shouldn’t be too surprised Buehrle is a great fielder, given that he doesn’t throw very hard. On the other hand, though, there are plenty of other soft tossers who are minus fielders (Freddy Garcia, for instance), so it’s not as though Buehrle was bound to be good at this. To me, that just makes him a little bit quirkier and reminds me of why I’ll have a soft spot for him above-and-beyond what he got just for being a great hurler for the Sox.

# Picking a Pitch and the Pace of the Game

Here’s a short post to answer a straight-forward question: do pitchers that throw more pitches pitch more slowly? If it’s not clear, the idea is that a pitcher who throws several pitches frequently will take longer because the catcher has to spend more time calling the pitch, perhaps with a corresponding increase in how often the pitcher shakes off the catcher.

To make a quick pass at this, I pulled FanGraphs data on how often each pitcher threw fastballs, sliders, curveballs, changeups, cutters, splitters, and knucklers, using data from 2009–13 on all pitches with at least 200 innings. (See the data here. There are well-documented issues with the categorizations, but for a small question like this they are good enough.) The statistic used for how quickly the pitcher worked was the appropriately named Pace, which measures the number of seconds between pitches thrown.

To easily test the hypothesis, we need a single number to measure how even the pitcher’s pitch mix is, which we believe to be linked to the complexity of the decision they need to make. There are many ways to do this, but I decided to go with the Herfindahl-Hirschman Index, which is usually used to measure market concentration in economics. It’s computed by squaring the percentage share of each pitch and adding them together, so higher values mean things are more concentrated. (The theoretical max is 10,000.) As an example, Mariano Rivera threw 88.9% cutters and 11.1% fastballs over the time period we’re examining, so his HHI was $88.9^{2} + 11.1^{2} = 8026$. David Price threw 66.7% fastballs, 5.8% sliders, 6.6% cutters, 10.6% curveballs, and 10.4% changeups, leading to an HHI of 4746. (See additional discussion below.) If you’re curious, the most and least concentrated repertoires split by role are in a table at the bottom of the post.

As an aside, I find two people on those leader/trailer lists most interesting. The first is Yu Darvish, who’s surrounded by junkballers—it’s pretty cool that he has such amazing stuff and still throws 4.5 pitches with some regularity. The second is that Bartolo Colon has, according to this metric, less variety in his pitch selection over the last five years than the two knuckleballers in the sample. He’s somehow a junkballer but with only one pitch, which is a pretty #Mets thing to be.

Back to business: after computing HHIs, I split the sample into 99 relievers and 208 starters, defined as pitchers who had at least 80% of their innings come in the respective role. I enforced the starter/reliever split because a) relievers have substantially less pitch diversity (unweighted mean HHI of 4928 vs. 4154 for starters, highly significant) and b) they pitch substantially slower, possibly due to pitching more with men on base and in higher leverage situations (unweighted mean Pace of 23.75 vs. 21.24, a 12% difference that’s also highly significant).

So, how does this HHI match up with pitching pace for these two groups? Pretty poorly. The correlation for starters is -0.11, which is the direction we’d expect but a very small correlation (and one that’s not statistically significant at p = 0.1, to the limit extent that statistical significance matters here). For relievers, it’s actually 0.11, which runs against our expectation but is also statistically and practically no different from 0. Overall, there doesn’t seem to be any real link, but if you want to gaze at the entrails, I’ve put scatterplots at the bottom as well.

One important note: a couple weeks back, Chris Teeter at Beyond the Box Score took a crack at the same question, though using a slightly different method. Unsurprisingly, he found the same thing. If I’d seen the article before I’d had this mostly typed up, I might not have gone through with it, but as it stands, it’s always nice to find corroboration for a result.

Relief Pitchers with Most Diverse Stuff, 2009–13
Name FB% SL% CT% CB% CH% SF% KN% HHI
1 Sean Marshall 25.6 18.3 17.7 38.0 0.5 0.0 0.0 2748
2 Brandon Lyon 43.8 18.3 14.8 18.7 4.4 0.0 0.0 2841
3 D.J. Carrasco 32.5 11.2 39.6 14.8 2.0 0.0 0.0 2973
4 Alfredo Aceves 46.5 0.0 17.9 19.8 13.5 2.3 0.0 3062
5 Logan Ondrusek 41.5 2.0 30.7 20.0 0.0 5.8 0.0 3102
Relief Pitchers with Least Diverse Stuff, 2009–13
Name FB% SL% CT% CB% CH% SF% KN% HHI
1 Kenley Jansen 91.4 7.8 0.0 0.2 0.6 0.0 0.0 8415
2 Mariano Rivera 11.1 0.0 88.9 0.0 0.0 0.0 0.0 8026
3 Ronald Belisario 85.4 12.7 0.0 0.0 0.0 1.9 0.0 7458
4 Matt Thornton 84.1 12.5 3.3 0.0 0.1 0.0 0.0 7240
5 Ernesto Frieri 82.9 5.6 0.0 10.4 1.1 0.0 0.0 7013
Starting Pitchers with Most Diverse Stuff, 2009–13
Name FB% SL% CT% CB% CH% SF% KN% HHI
1 Shaun Marcum 36.6 9.3 17.6 12.4 24.1 0.0 0.0 2470
2 Freddy Garcia 35.4 26.6 0.0 7.9 13.0 17.1 0.0 2485
3 Bronson Arroyo 42.6 20.6 5.1 14.2 17.6 0.0 0.0 2777
4 Yu Darvish 42.6 23.3 16.5 11.2 1.2 5.1 0.0 2783
5 Mike Leake 43.5 11.8 23.4 9.9 11.6 0.0 0.0 2812
Starting Pitchers with Least Diverse Stuff, 2009–13
Name FB% SL% CT% CB% CH% SF% KN% HHI
1 Bartolo Colon 86.2 9.1 0.2 0.0 4.6 0.0 0.0 7534
2 Tim Wakefield 10.5 0.0 0.0 3.7 0.0 0.0 85.8 7486
3 R.A. Dickey 16.8 0.0 0.0 0.2 1.5 0.0 81.5 6927
4 Justin Masterson 78.4 20.3 0.0 0.0 1.3 0.0 0.0 6560
5 Aaron Cook 79.7 9.7 2.8 7.6 0.4 0.0 0.0 6512

Boring methodological footnote: There’s one primary conceptual problem with using HHI, and that’s that in certain situations it gives a counterintuitive result for this application. For instance, under our line of reasoning we would think that, ceteris paribus, a pitcher who throws a fastball 90% of a time and a change 10% of the time would have an easier decision to make than one who throws a fastball 90% of the time and a change and slider 5% each. However, the HHI is higher for the latter pitcher—which makes sense in the context of market concentration, but not in this scenario. (The same issue holds for the Gini coefficient, for that matter.) There’s a very high correlation between HHI and the frequency of a pitcher’s most common pitch, though, and using the latter doesn’t change any of the conclusions of the post.

# Is There a Hit-by-Pitch Hangover?

One of the things I’ve been curious about recently and have on my list of research questions is what the ramifications of a hit-by-pitch are in terms of injury risk—basically, how much of the value of an HBP does the batter give back through the increased injury risk? Today, though, I’m going to look at something vaguely similar but much simpler: Is an HBP associated with an immediate decrease in player productivity?

To assess this, I looked at how players performed in the plate appearance immediately following their HBP in the same game. (This obviously ignores players who are injured by their HBP and leave the game, but I’m looking for something subtler here.) To evaluate performance, I used wOBA, a rate stat that encapsulates a batter’s overall offensive contributions. There are, however, two obvious effects (and probably other more subtle ones) that mean we can’t only look at the post-HBP wOBA and compare it to league average.

The first is that, ceteris paribus, we expect that a pitcher will do worse the more times he sees a given batter (the so-called “trips through the order penalty”). Since in this context we will never include a batter’s first PA of a game because it couldn’t be preceded by an HBP, we need to adjust for this. The second adjustment is simple selection bias—not every batter has the same likelihood of being hit by a pitch, and if the average batter getting hit by a pitch is better or worse than the overall average batter, we will get a biased estimate of the effect of the HBP. If you don’t care about how I adjusted for this, skip to the next bold text.

I attempted to take those factors into account by computing the expected wOBA as follows. Using Retrosheet play-by-play data for 2004–2012 (the last year I had on hand), for each player with at least 350 PA in a season, I computed their wOBA over all PA that were not that player’s first PA in a given game. (I put the 350 PA condition in to make sure my average wasn’t swayed by low PA players with extreme wOBA values.) I then computed the average wOBA of those players weighted by the number of HBP they had and compared it to the actual post-HBP wOBA put up by this sample of players.

To get a sense of how likely or unlikely any discrepancy would be, I also ran a simulation where I chose random HBPs and then pulled a random plate appearance from the hit batter until I had the same number of post-HBP PA as actually occurred in my nine year sample, then computed the post-HBP wOBA in that simulated world. I ran 1000 simulations and so have some sense of how unlikely the observed post-HBP performance is under the null hypothesis that there’s no difference between post-HBP performance and other performance.

To be honest, though, those adjustments don’t make me super confident that I’ve covered all the necessary bases to find a clean effect—the numbers are still a bit wonky, and this is not such a simple thing to examine that I’m confident I’ve gotten all the noise out. For instance, it doesn’t filter out park or pitcher effects (i.e. selection bias due to facing a worse pitcher, or a pitcher having an off day), both of which play a meaningful role in these performance and probably lead to additional selection biases I don’t control for.

With all those caveats out of the way, what do we see? In the data, we have an expected post-HBP wOBA of .3464 and an actual post-HBP wOBA of .3423, for an observed difference of about 4 points of wOBA, which is a small but non-negligible difference. However, it’s in the 24th percentile of outcomes according to the simulation, which indicates there’s a hefty chance that it’s randomness. (Though league average wOBA changed noticeably over the time period I examined, I did some sensitivities and am fairly confident those changes aren’t covering up a real result.)

The main thing (beyond the aforementioned haziness in this analysis) that makes me believe there might be an effect is that the post-walk effect is actually a 2.7 point (i.e. 0.0027) increase in wOBA. If we think that boost is due to pitcher wildness then we would expect the same thing to pop up for the post-HBP plate appearances, and the absence of such an increase suggests that there is a hangover effect. However, to conclude from that that there is a post-HBP swoon seems to be an unreasonably baroque chain of logic given the rest of the evidence, so I’m content to let it go for now.

The main takeaway from all of this is that there’s an observed decrease in expected performance after an HBP, but it’s not particularly large and doesn’t seem likely to have any predictive value. I’m open to the idea that a more sophisticated simulator that includes pitcher and park effects could help detect this effect, but I expect that even if the post-HBP hangover is a real thing, it doesn’t have a major impact.