Yesterday, Jason Collette penned an article about infield flies that ties in with a discussion I’ve been having over the past few weeks with one of my former writers at The Hardball Times Fantasy, Jeff Gross, and one of his readers, Alex Hambrick. Additionally, BP readers JoshC77 and kcshankd wondered in the comments section of Jason’s article whether the ability to induce infield flies was a repeatable skill for pitchers. Today, I thought I’d try to answer that question and present some of the research I’ve conducted in my conversations with Jeff and Alex.
Earlier this year, I wrote an article entitled “When Pitchers' Stats Stabilize,” in which I looked at how “stable” (or how “repeatable,” in terms of being a “skill”) a number of stats were—infield flies among them. In the article, I found that infield fly balls, as a rate of total batted balls, took roughly 0.6 years to “stabilize.” In other words, this initial research suggested that infield flyball rate was indeed a very repeatable skill. But in my discussions with Alex, I’ve come to suspect this may not necessarily be true—or at least not in the way my previous research suggests.
In one email, Alex wrote:
I have known for quite some time that IFFB is a strong function of FB, much like HR is a strong function of FB for pitchers. (The league average IFFB/FB hovers around 10%). In other words, you can, with reasonable accuracy, predict IFFB by simply multiplying FB by .10. (.10*FB correlates to IFFB with an r^2 of .70).
While we’ve certainly known that there is a correlation between total fly balls and infield fly balls (due in large part to the vertical location and movement of a pitcher’s pitches, forcing batters to put the ball in the air), this presented an interesting question: “Is infield fly rate a skill above and beyond a pitcher’s skill in simply allowing fly balls in general?”
To help answer this question, I decided to pull out my old friend, the splithalf correlation (if you’re interested, you can read all about the methodology in the “When Pitchers' Stats Stabilize” article). What I’ve done is run two separate analyses. In the first, I’ve run a splithalf correlation using infield flies per contacted balls (henceforth referred to as IF FB%) in both halves. In the second, I put IF FB% in one half and put all flies multiplied by .07 (roughly seven percent of flies are of the infield variety) per contacted balls (henceforth referred to as FB*.07) in the other half. So essentially, I’m first correlating IF FB% with itself and then correlating it with flyball rate. This gives us the following results:
Stat 
Denominator 
Correlated With 
Stabilizes 
Years 
IF FB 
GB+OF+IF+LD 
IF FB% 
288 
0.6 
FB*.07 
GB+OF+IF+LD 
IF FB% 
216 
0.5 
That’s very interesting. While the differences are small, IF FB% actually seems to be less stable than simply using a leagueaverage percentage of infield flies per total flies. Since multiplying by .07 doesn’t affect the correlation (I’ve just included it to better illustrated the point that this is an estimate of infield flies), what this essentially tells us is that flyball percentage better predicts infieldfly percentage than it can predict itself.
Let’s check out one more way of looking at infield flies. We know that total flies stabilize very quickly, so perhaps infield flies per total flies (henceforth referred to as IF/FB) will prove useful.
Stat 
Denominator 
Stabilizes 
Years 
OF+IF 
GB+OF+IF+LD 
109 
0.2 
IF FB 
OF+IF 
414 
2.5 
Nope. While the percentage of total flies (FB%) stabilizes extremely quickly (as quickly as groundballs do, for what it’s worth), it takes the average pitcher two and a half years for his IF/FB rate to stabilize. That means we can throw IF/FB rate out the window entirely—we’d be far better off using either IF% or FB*.07.
We could stop here and have learned something useful, but we can do a little better yet. What these splithalf correlation tests give us is the point at which the stat produces an R of 0.50. Using this data, we can create a regression to the mean equation and estimate a player’s true talent level. While the easiest mean to regress to is always the league average, it’s rarely the best. As Alex posited, and as has been known for a while now, flyball rate and infieldfly rate are correlated. As such, we can reexamine this relationship and then use our results as the mean we regress to.
(The above graph includes all pitcher seasons with at least 100 innings pitched in a year from 2005 to 2010)
As you can see, the relationship is very strong (rsquared of 0.68). Pitchers who give up a lot of total flies also manage to induce a lot of infield flies. The most extreme flyball pitchers actually manage to convert nearly 10 percent of all contacted balls into popups. So instead of regressing each pitcher to leagueaverage flyball rate, we can regress each pitcher to his own unique rate based upon this relationship.
Now we get to the fun part: applying all of this to actual players. Ideally, we’d use multiple years, incorporate aging, weighting, etc., but I’m just going to do it simply. What I’ve done is used a pitcher’s actual, unregressed 2011 flyball rate to create his personal mean based on the formula above. I’ve then regressed his 2011 infieldfly rate onto this mean based upon the splithalf correlation tests we ran at the beginning of the article. When I do this and focus on all pitchers who made at least 10 starts this season, here are the pitchers with the best infield fly ball “true talent” levels (rIF%):
FB% 
rIF% 

58% 
15.0% 

50% 
14.8% 

47% 
13.2% 

48% 
12.5% 

54% 
12.4% 

44% 
12.1% 

49% 
11.8% 

48% 
11.6% 

46% 
11.3% 

50% 
11.2% 

46% 
11.0% 

44% 
11.0% 

43% 
10.9% 

44% 
10.6% 

46% 
10.5% 

39% 
10.3% 

43% 
10.2% 
That’s an interesting name at the top of the list. When we think about top pitchers, Guillermo Moscoso isn’t the first guy that comes to mind. While his strikeout and walk rates are underwhelming, he’s an extreme flyball pitcher, which will allow him to induce a lot of popups. There are some other notsoterrific players on this list (Collmenter, Matusz, Tillman, Cecil, Hughes), but since they all have posted high fly rates, they’ll at least be useful in terms of inducing popups and keeping a lowerthannormal BABIP. Jered Weaver—sort of the poster boy for using infield flies to beat his FIP—ranks second on the list, and longtime popup artist Clayton Kershaw also ranks highly.
Now let’s take a look at our trailers:
FB% 
rIF% 

22% 
2.7% 

19% 
3.2% 

26% 
3.5% 

22% 
3.6% 

25% 
3.7% 

25% 
3.9% 

28% 
4.1% 

28% 
4.1% 

24% 
4.2% 

24% 
4.2% 

30% 
4.3% 

29% 
4.3% 

24% 
4.3% 

27% 
4.3% 

29% 
4.5% 

26% 
4.6% 

24% 
4.7% 

32% 
4.7% 
Extreme groundball pitchers rule this list. Notorious sinkerballer Derek Lowe trails everyone in terms of regressed infieldfly rate, followed by 2011 breakout pitcher Charlie Morton. Romero and Greinke have been excellent this season in terms of strikeouts and walks, but as groundball pitchers, they shouldn’t be expected to induce many popups. They remain elite pitchers, though, since these kinds of pitchers can afford to give up a few more hits as they allow fewer homers.
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But as you showed, that alone does not have much predictable value. Would it not be more effective if you combined it with HR/FB? A pitcher with a low HR/FB and high IFF/FB should indicate a pitcher with a skill for minimizing flyball distance therefore to be underestimated by xFIP. Whereas a pitcher a with a high HR/FB and low IFF/FB should indicate a pitcher with the reverse skill and therefore likely to be overestimated by xFIP. And for the pitchers in between FB% is good enough.
"just looking at the list, the better pitchers have better IFF/FB rates than just IFF rates." I can check this. Since 2003, pitchers with xFIPs better than 3.5 have an aggregate 10.3% IF/FB. Everyone else is 10.4%.
"A pitcher with a low HR/FB and high IFF/FB should indicate a pitcher with a skill for minimizing flyball distance therefore to be underestimated by xFIP." I agree in principle that minimizing the distance of fly balls would be an important skill for a pitcher (if it's something they can control to any reasonable degree), but the problem here is that HR/FB is highly unstable. Over a long period of time it will be able to serve as a fair proxy for fly ball distance, but for the kind of samples we usually deal with, it just isn't going to be useful for that purpose. My previous article showed that it takes 10 years worth of data before we can account for just half of the variation in the stat. And that ignores issues of weighting and aging which are huge over a period that long.
I can, however, see your reasoning that a pitcher who induces a lot of infield flies may also induce shorter outfield flies and, therefore, allow fewer homers. As one way of checking this, if I look at pitchers since 2003 with an IF/FB greater than 15%, they post a HR/OF of 11.7 percent. League average over that time has been 11.5 percent. A good thought, but a cursory glance shows there to be no relationship.
Actually, I wasn't exactly sure, so I asked Mike Fast. He wasn't 100% sure either, but said that any ball classified as a popup and was caught was fielded by an infielder. So basically any ball fielded by an infielder, it becomes a subjective judgment about how high the ball went. There were a few popup singles to outfielders, though. So I guess we're not entirely sure what directions, if any, stringers are given. Maybe a good question for someone at MLBAM, like a Cory Schwartz. Or a stringer.
Don't know if that would affect your analysis at alljust an observation.
The MLBAM definition is not really about who caught it, it's about distance from the plate, and 160180 feet or so from the plate makes more sense to me as a popup boundary than the varying 127.6155.5 feet boundary that BIS uses.
Ultimately, of course, I think a lot of things about the GBLDFBPU division are screwy, but the MLBAM definition just seems a little less screwy here than the BIS definition.
What I see is that, leaving line drives aside here, MLBAM basically codes anything in the air that is of a depth that could be reasonably caught by an infielder at some position to be a popup. It's not about whether the infielder actually catches it or lets it fall (ideally). My impression is that MLBAM drew a line that was basically along the boundary where an outfielder racing in and an infielder racing back would meet.
On the other hand, I have seen balls just on the outfield grass be coded by BIS as outfield flies. Because I have much less BIS data to go on, I don't have as firm of an impression as to where or how they drew the boundary. I had thought it was at the edge of the outfield grass (or the equivalent line painted on the turf), but you seem to indicate that's not the case, so I don't know.
They mark infield flies based on distance from home plate. The latest I heard is 140 to 150 feet.
League average is about 21%, the most extreme are 28%, the less extreme are 15%.
I have to admit that I'm still a fan of IF/OF, though I can't adequately explain why. It feels like it captures a nuance that IF/Contact misses.
"Wouldn't the rate (the 7% you used in your first table) go up as the overall flyball rate goes up." Yes, it does go up. The graph shows that relationship. Those with a 15% FB% will have about a 2% IF% and those with a 60% FB% will have about a 15% IF%.
Also, is correlating something the only point? How about having a better handle on what makes pitchers unique and interesting?
Not sure where the rsquared confusion comes from. If we're testing for accuracy, the rsquareds provide evidence that one way is more accurate than the other.
For instance, you say that your rsquared of .68 is "much more significant." But than what? The .21? But those were two different regressionsone regressing IF/FB rate vs FB/Contact rate and the other comparing the IF/Contact rate in two halves. Why compare them?
So, could you improve your model by varying the 7%, according to the pitcher's FB%? Or would that not be worth it?
Yes, this is what I did in the second half of the article. Based upon the correlation I ran between IF% and FB% (the equation for which is shown in the graph), I created each pitcher's own, unique, flyballbased IF% mean. That's what I regressed their actual IF% to.
So, how quickly does this formula stabilize? Is it an improvement over the straight 7%?
Should I just give up on this stuff?
The HR/FB thing was just mentioned as a point of reference, to say that the "stabilization point" for IF/FB is pretty modest, that IF/FB does have a fair amount of predictive value in terms of predicting IF FBs. Everyone knows that HR/FB is incredibly unstable, so I listed that to show that IF/FB isn't anywhere near that and does have some utility.
"Yes, it does go up. The graph shows that relationship."
...are you saying that you didn't use a standard 7% of flyballs in your first table? You increased it as the pitcher's flyball rate increased?
Were you referring to something different?
FB/BIP "stabilizes" in about 100 BIP, while IF/BIP "stabilizes" in 288 BIP. I assume this is almost entirely due to the fact that there are many less FB than IF in a group of BIP.
0.07*FB/BIP "stabilizes" against IF/BIP more quickly than IF/BIP itself does (216 BIP). I assume it has something to do with the relative frequency of FB and the tight relationship between FB and IF. If you take anything that has a strong relationship with another thingand that second thing happens a lot more often than the firstyou will naturally have an equation that "stabilizes" more quickly. This is probably natural mathematics.
IF/FB takes longer to stabilize (414 flyballs). I assume this is due to two things. One is again the low rate of infield flies, but exacerbated by the fact that we don't know the pitcher's flyball rate. The rate at which flyballs are actually infield flies will partially depend on how many flyballs that pitcher gives up per ball in play. I wonder how quickly IF/FB would stabilize if you included the pitcher's flyball tendencies?
So, if you want to predict future flyballs, you need to base your calculations off something that includes "information" about his contact rate and his flyball rate. Due to the correlation between infield flies and all flies, previous IF rate does that, but previous FB rate stabilizes more quickly because there are a lot more of them.
Does this make sense to people?
FB/BIP "stabilizes" in about 100 BIP, while IF/BIP "stabilizes" in 288 BIP. I assume this is almost entirely due to the fact that there are many less FB than IF in a group of BIP.
should say this...
FB/BIP "stabilizes" in about 100 BIP, while IF/BIP "stabilizes" in 288 BIP. I assume this is almost entirely due to the fact that there are many less IF than FB in a group of BIP.