We all know the story: Yoenis Cespedes is a bad defensive center fielder. In 912 career innings in center field, Cespedes has rated miserably in both Ultimate Zone Rating (UZR), with a -17.6 UZR/150, and Defensive Runs Saved (DRS), with a prorated -23.7 DRS/150. Based on those metrics, he should continue to be an awful defensive center fielder in 2016, right?
Not necessarily. Let’s use a few different methods to estimate Cespedes’ defensive value as a center fielder and determine how effective he will be in the future.
Method 1: Regress past defensive data in CF
This is the simplest (and crudest) method of all. If we average Cespedes’ center field contributions per 150 games by UZR (-17.6) and DRS (-23.7), we find that Cespedes is a -20.85 run defender per 150 games. Because of the small 900-inning sample, we’ll regress that by 50% and estimate that Cespedes is a -10.4 runs per 150 games defender in center. This is what many people in the analytical community roughly believe Cespedes’ defensive value in center field to be. Methods 2 and 3, shown below, illustrate why I disagree with this valuation.
Method 2: Combine Cespedes’ Range in CF with his Arm Throughout the Outfield
One thing everyone can agree on with Cespedes: he has a cannon of an arm. Whether he’s playing center field or left field, we should expect his arm to be significantly above average, right?
Well, in his 912 career innings in center field, UZR and DRS seems to disagree. They rate his arm at -0.8 runs and +2 runs, respectively. Decent, no doubt, but not the arm that most of us are accustomed to with Cespedes.
Yet, if we look at his entire career in the outfield, including time in both center field and left field, his arm has been worth +28 runs by DRS and +26.5 runs by UZR in roughly 4300 innings. When averaged and scaled to 150 games, the value of his arm comes out to roughly +9.5 runs per 150 games over a very large sample, much more in line with what we would expect.
Next, we must factor Cespedes’ center-field range into the equation. In 912 innings, DRS pegs his range (they term it rPM) at -17, while UZR estimates his range (they use RngR) at -12.2. When averaged and scaled to 150 games, his range comes out to -20.4 runs per 150 games. Because of the small 900-inning sample, we’ll once again regress his range by 50%, getting us to -10.2 runs per 150 games.
Factor in his arm, worth +9.5 runs per 150 games, and suddenly our estimate of Cespedes comes to -0.7 runs per 150 games in center field. In other words: his excellent arm makes up for his poor range, making him a roughly league-average defensive center fielder.
Method 3: Isolate the Value of Cespedes’ Arm, Then Use Positional Adjustments to Estimate Cespedes’ Range in CF
This is the most complicated of the three methods. First, we must become comfortable with the idea of positional adjustments. Essentially, the purpose of positional adjustments is to provide a run value for each position, using past data of players switching positions to estimate the defensive difficulty of each position. For example, while shortstop is a difficult position to play — and hence has a +7.5 run positional adjustment (per 162 games) — first base is not, with a -12.5 run positional adjustment. Theoretically, if a shortstop was to switch to first base, the theory of positional adjustments would estimate a 20-run improvement in defense per 162 games.
Of course, positional adjustments don’t always work so conveniently, a reality the Red Sox discovered the hard way after moving Hanley Ramirez from shortstop to left field backfired tremendously. Indeed, the difficulty of learning a new position oftentimes overshadows the theoretical improvement that should come from moving down the defensive spectrum.
In the outfield, however, things work much smoother, simply because each outfield position requires roughly the same skill-set: speed, first-step quickness, and efficient route running. Using the positional adjustments from FanGraphs, we’d expect a left fielder (-7.5 run positional adjustment) to be approximately 10 runs worse in center field (+2.5).
For this exercise, we’ll isolate Cespedes’ arm from his range, using the +9.5 runs per 150 game figure we got from Method 2 to estimate the value of his arm (or +10.3 runs per 162 games). Why? For the most part, throwing arm strength is something we don’t expect to change too much shifting from left field to center. The main difference between playing center field and left field is the range required for each position.
Estimating Cespedes’ range in center field using positional adjustments requires some tricky math. First, let’s examine Cespedes’ range throughout his entire outfield career. In 4295.33 innings combined between the two positions, Cespedes’ range is estimated at -13 runs by DRS (rPM) and -4.3 runs by UZR (RngR), or an average of -2.9 runs per 162 games (FanGraphs’ positional adjustments are scaled to 1458 innings, or 162 games).
Next, let’s calculate the percentage of his innings in left and center. 3383/4295.33 shows us that 78.76% of his innings came in left field, and, by extension, that 21.24% of his innings came in center.
Now, the tricky part: algebra. If “x” is his range in CF, “x+10” is his range in LF, and +10 is the positional adjustment per 162 games from LF to CF, we solve for x with the following formula:
0.2124 * x + 0.7876 * (x+10) = -2.9
Wolfram Alpha, what say you?
x = -10.8, or -10.8 range runs per 162 games in CF.
Now, factor in Cespedes’ +10.3 runs per 162 games from his arm, and you arrive at his defense being worth -0.5 runs per 162 games. Just as in Method 2, it appears that the value of Cespedes’ throwing arm essentially counteracts his poor range, making him once again a roughly league-average defender in center
Method 4: Use Positional Adjustments to Estimate Cespedes’ Total Value in CF
While Methods 2 and 3 are certainly improvements over Method 1, there are some minor flaws in the methodology for each of the two methods. In Method 2, we arbitrarily regressed Cespedes’ range in CF by 50%, when in truth we don’t know exactly how much his range needs to be regressed. In both Methods 2 and 3, we assumed that the value of Cespedes’ arm wouldn’t change significantly by moving from LF to CF, when in reality it may be more difficult to accumulate value via throwing as a center fielder.
To address these concerns, let’s do the same Method 3 Calculation except instead of attempting to find Cespedes’ range in CF, we’ll try and estimate Cespedes’ total value in CF, using nothing other than positional adjustments, UZR, and DRS. Rather than breaking down those metrics into their individual components, we’ll simply use the positional adjustments on the metrics themselves, a more traditional calculation.
First, let’s average Cespedes’ total DRS (15 runs) and UZR (20.7 runs) and scale it to 162 games, arriving at +6.1 runs per 162 games between left and center. Then, let’s do the same algebra we did in Method 3, with “x” representing his UZR/DRS in CF and “x+10” representing his UZR/DRS in LF.
0.2124 * x + .7876 * (x+10) = 6.06
We’ll head over to Wolfram Alpha one last time, with x = -1.8 runs per 162 games.
This might be the most accurate estimation of his value in CF of all, as it doesn’t rely on the raw value of his arm (like in methods 2 and 3) or a regressed version of his range in center (like methods 1 and 2).
Don’t believe the skeptics. While Cespedes has rated terribly in roughly 900 innings of data in center field, it’s silly to limit yourself to such a small center field sample size when we have more than 4000 innings of data, separate range and arm ratings, and positional adjustments at our disposal. Using some basic arithmetic, we’ve proven that Cespedes should probably be no worse than a hair below average defensively in center field, as his extremely valuable arm (+10.3 runs per 162 games) makes up for his below-average range.
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