If you read these pages you are familiar with the notion that pitchers have little control over the outcome of balls hit into play (and not leaving the park). That’s why our writers always warn you when a pitcher has an eye-catching ERA, but an extremely low batting average on balls in play: They usually hint to a likely decline due to luck turning around.

So pitchers have little control (but they do have some) on allowed BABIP, which influences scoreboard stats, such as ERA. But pitchers are not created equal relative to how much their performance is at the mercy of BABIP fluctuations: Simply, if one allows few balls in play, his performance (and his ERA) is mostly influenced by strikeouts, walks and home runs allowed—he is said to be a Three True Outcomes pitcher.

This article will show how to detect the effect that a variation in BABIP will have on a given pitcher’s ERA. What’s the use in knowing that? A fantasy owner, for example, might want to know which of two pitchers with similar ERAs is expected to be more consistent and, conversely which is the riskier choice (but also the one with the highest upside). It can sort of help put confidence bands around an ERA forecast.

### A brief digression

I’m currently reading *Wizardry: Baseball’s All-Time Greatest Fielders Revealed*, by Michael A. Humphreys. I have just finished the first part, which is dense with formulas defining the foundations of his defense evaluation system.

The formulas might appear scary at a first look, but they are actually extremely simple, and that’s what I’m loving about the book. The paragraph titled “A neat coincidence” is the perfect example of this simplicity. Combining his defensive equations, Humphreys comes up with this formula for run prevention:

(1) *Defensive Runs = -.28 x SO + .34 x BB + .47 x HA + 1.49 x HR* where HA are hits allowed minus home runs allowed*

which he shows to mirror the widely accepted offensive run creation formula:

(2) *Offensive Runs = -.27 x BO + .33 x BB + .55 x H + 1.40 x HR* where BO denotes batting outs and H is hits minus home runs**.

* Note: here signs appear inverted since Runs Allowed are the goal, while Humphreys presents them as Runs Saved

** Note: actually we are more used to Runs Created formulas like RC = a x 1B + b x 2B + c x 3B + d x HR + f x BB – g x SO …; in order to show the symmetry between offensive runs created and defensive runs prevented, Humphreys blended all the non-HR base hits in a single bucket and devised an appropriate coefficient, based on the relative frequencies of singles, doubles and triples.

Simplicty was also in **Voros McCracken**‘s world shocker. In case you are not keeping score, more than a decade has passed since he exposed how little control pitchers have on balls put into play by opponent batters.

The article you are currently reading is a back-of-the-envelope calculation combining McCracken’s work and the Humphreys formula above.

### Just a little bit of algebra

Let’s calculate the right hand of equation (1) above for every major league pitcher in every season from 2000 to 2010 and plot the results against the earned runs on the pitchers’ stats line.

It looks like Humphreys’ formula does a good job in predicting the ER (though it’s built to predict total runs), starting from hits, home runs, strikeouts and walks. The Pearson’s correlation coefficient is over .95. Obviously, since earned runs are a subset of the total runs allowed by a pitcher, the estimated runs are systematically higher than the observed ER.

Let’s work a little algebra around equation (1). Since BABIP is defined as (H-HR)/(AB-SO-HR)*, the HA term in (1) can be rewritten as (AB-SO-HR) x BABIP and the whole equations as (3) *Runs = -.28 x SO + .34 x BB + .47 x (AB – SO – HR) x BABIP + 1.49 x HR*

*Note: The actual formula adds SF to the denominator; here Sac Flies have been removed because they are hardly found in forecasts.

Having rewritten (1) as (3), we now have BABIP as a predictor of ER, thus we can estimate the effect of a given variation in BABIP has on a pitcher’s ER. Assuming everything else remaining constant, the numbers of extra runs allowed due to an increase of 10 points of BABIP can be estimated as:

(4) *extra runs = a x (AB – SO – HR) x .01*

*a* was .47 in equation (3), but should be decreased a bit if Earned Runs are of interest instead than total runs (it will be .4 for the rest of this article).

To get the effect of 10 BABIP points on ERA, one should also consider the reduced number of innings pitched because of the extra hits allowed. One can be conservative and assume that the pitcher faces the same number of batters and the difference in innings is simply one for every three outs lost (this is what we’ll do here). However it’s likely that a pitcher experiencing a high BABIP is removed earlier, thus the effect should be greater.

### Some examples

Let’s take Randy Wolf‘s career numbers and plug them into equation (4).

*.4 x (AB – SO – HR) x .01 = .4 x (7390 – 1567 – 249) * .01 = 22.30*

Had Wolf’s BABIP throughout his career been 10 points higher, his ER total would roughly be 56 units higher. Taking into account the deflated number of innings he would have pitched due to higher number of hitters reaching base, his ERA would be 0.15 points higher in this scenario.

Mike Magnante pitched from 1991 to 2002 for the Royals, the Astros, the Angels and the Athletics. His career ERA (4.08) is quite similar to Wolf’s (4.13). In his case 10 more BABIP points would have signified an ERA increased by 0.18. Though 0.18 versus 0.15 might not seem a big deal, remember it’s the estimated effect on an increase of 10 BABIP points. BABIP year-to-year fluctuations for a pitcher are usually of a higher magnitude (Magnante and Wolf experienced on average a yearly 30 BABIP jump in either direction).

In fact, Magnante, with his 0.18 estimated increase, is in the top 25 percent among pitchers playing since 1990, while Wolf ranks in the bottom 25 percent with his 0.15.

Since we have calculated Magnante’s ERA to be at the mercy of BABIP fluctuations more than Wolf’s, we should expect the ERA of the latter to be more consistent througout his career. That’s exactly what we see comparing the charts below.

*Charts courtesy of FanGraphs.*

Wolf’s ERA has never approached either the 3.00 or the 6.00 marks, while Magnante’s has gone as low as 2.45 and as high as 5.97.

Look back to equation (4) for a moment: the part that varies from pitcher to pitcher is the one in parentheses; in particular, it decreases as strikeouts and home runs allowed increase. Thus it’s not a surprise that Wolf, who sports a 7.23 strikeout per nine innings rate and gives up 1.15 dingers per nine frames, is less BABIP-affected than Magnante, who used to strike out fewer batters (5.06 K/9) but also allowed fewer round trippers (0.66 HR/9).

The Wolf-Magnante comparison is obviously a cherry-picking example. Looking at all the major league pitchers since the 1990s, those whose BABIP effect on ERA is in the bottom 25 percent (Wolf’s pals) have experienced a 0.49 correlation between their seasonal BABIP and ERA, while those in the top 25 percent (Magnante’s buddies) scored a 0.57 value.

### Putting boundaries to the future

Let’s see how a fantasy owner can make use of what we have been talking about.

One neat feature of THT Forecasts is that you can specify your *Price Guide* (i.e. your league rules) and our system converts Oliver forecasts to dollar value in your league environment. For example, setting up a basic 5×5 league (Batting stats: AVG, R, RBI, HR, SB, pitching stats: W, S, ERA, WHIP, K), and specifying other important parameters, such as budget, minimum bid, qualifiers and position constraints, you get the amount of dollars you should pay for each player.

Let’s now pause for a few minutes while those who hadn’t done it yet make their subscription to THT Forecasts.

In the set example, Joakim Soria and Carlos Marmol are valued the same amount of dollars. The expected BABIP influence over ERA, given their Oliver forecast for 2011, is 0.10 ERA points for every 10 points of BABIP for Marmol, versus 0.14 for Soria. Thus, the latter is expected to be more sensitive to BABIP variations.

Coming out of an impressive 15.99 K/9 season, Marmol is predicted to score over 12 in that stat. On the other hand Soria, who also has a good record of striking people out, set a career-low 6.05 K/9 last year, which makes his 2011 projection just over 7.

The difference in strikeouts explains the lower influence of BABIP on Marmol’s ERA.

Who should you trade for if you need a closer for the stretch? Personally I would go with the most consistent performer if I had to maintain a lead, while rolling the dice if I was behind in the standings. But that’s your choice; the important part is you know the “boundaries.”

Also, remember BABIP is mostly beyond the pitcher’s control, but that doesn’t mean it is all luck: The fielders behind the mound have something to say on the rate at which batted balls are converted into outs. Thus a team change, being it either the pitcher moving to another ballclub or a new fielder arriving in town, would have a greater impact (for better or worse) on Soria’s numbers than on Marmol’s.

### From fantasy to reality

The Giants’ starting rotation (defined as the five starters with the highest number of starts so far) have the following BABIP-influence values, calculated on their respective career stat lines:

Player BABIP effectVogelsong 0.19 Cain 0.14 Bumgarner 0.15 Lincecum 0.12 Sanchez 0.14

Those numbers are quite different from the ones pertaining to the Royals’ starters.

Player BABIP effectChen 0.16 Davies 0.19 Francis 0.18 Hochevar 0.19 O'Sullivan 0.20

The values above tell us the Giants’ pitchers should be less impacted by the BABIP vagaries, while the Royals should pay more attention to defense when considering possible roster movements.

**References & Resources**

Data from Fangraphs.

Projections from THT Forecasts.

Tom said...

Very interesting stuff, Max. Nice to see how much BABIP can effect different types of pitchers. I traded for Chris Carpenter yesterday in hopes that he had experienced some poor BABIP luck this year. With his somewhat low K/9 (6.75) and reasonable HR/9 (1.02), I’m guessing he’s been effected more than most would be by his .333 BABIP.