January 4, 2005

Blocking the Uppercut

Tackling the Jeromy Burnitz Problem

by Seth Samuels

How many times have you heard an announcer say about a player, "He uses an uppercut swing to get more out of his power?" Or, conversely, "He tries to keep the ball on the ground to get the most out of his speed?" But then, you look at the player's numbers, and the first guy has a .230 batting average to go with all his homers, and the second guy leads the world in singles and little else. These are what I like to call, respectively, the Jeromy Burnitz Problem and the Luis Castillo Problem. Both have swings that deviate from the standard line drive swing. They use extreme swings, intended to hit flyballs or grounders, respectively, in order to get the most out of their natural abilities. What I wanted to know was, are they actually succeeding?

To answer this question, I had to begin by setting up a model of projected player performance to accurately determine what a player's numbers would look like based on changes in GB/FB/LD rates. This model was inspired by the one used by John Burnson in the 2004 Baseball Forecaster, in order to predict batting average. We use a linear regression of the form: Outcome Type = (Batted Ball Type)*(a + b*(Power) + c*(Speed)). Using Retrosheet--the greatest thing in the world--data from 1990-92, we can obtain all outcomes for groundballs, flyballs, line drives, and pop-ups, as well as bunts. Possible outcomes for which I derived the equation were singles, doubles, triples, home runs, one out, double plays, and triple plays. Of course, there is some overlap, as hits sometimes still lead to outs, but that's not a big problem.

The next step was to create values for raw power and raw speed. Neither one is close to perfect, but both work well enough. For power I used HR/(.092*FB+.026*LD). This is a measure of how many home runs the player hit compared to how many a league average player would be expected to hit given the same number of flyballs and line drives. A value such as 1.22 would then mean his power was about 22% above league average. The equation for raw speed is of the form (3B/(2B+3B))/.11. I chose this measure instead of one involving stolen bases because stolen bases involve baserunning skills, which are a separate talent from raw speed. The average player gets triples on about 11% of non-HR extra-base hits, generally due to odd bounces and average speed. This equation, like the other, measures the player's raw speed relative to league average.

At this point, I chose to normalize both values, so that the constant value in the regression equation would be the league average, and the result would then be adjusted up or down based on above or below-average power and speed. Power was normalized with 1 and .688, while speed was normalized with 1.084 and .775, to account for skewness. Again, these values are not perfect, but they more than adequately represent a player's raw power and speed in terms of projecting the results of balls put into play.

At this point, using players with a minimum of 250 balls after contact, I was able to calculate various expected values:

x1B = GB * (.216 + .008*Pwr + .002*Spd) + FB * (.038 - .002*Pwr) + LD *
(.522 - .008*Pwr + .003*Spd) + Pop * (.034 - .003*Pwr - .003*Spd) + Bunt *
(.273 + .034*Spd)

x2B = GB * (.020 + .001*Pwr - .001*Spd) + FB * (.057 - .004*Pwr - .005*Spd)
+ LD * (.158 + .012*Pwr - .015*Spd) + Pop * (.010 - .001*Pwr + .002*Spd)

x3B = GB * (.001 + .002*Spd) + FB * (.013 + .010*Spd) + LD * (.019 +
.001*Pwr + .012*Spd)

xHR = FB * (.088 + .057*Pwr + .001*Spd) + LD * (.027 + .023*Pwr - .001*Spd)

x1P = GB * (.678 - .018*Pwr + .004*Spd) + FB * (.798 - .050*Pwr - .008*Spd)
+ LD * (.273 - .025*Pwr + .001*Spd) + Pop * (.952 + .005*Pwr + .002*Spd) +
Bunt * (.681 - .032*Spd)

x2P = GB * (.057 + .005*Pwr - .006*Spd) + .004*FB + LD * (.014 - .002*Pwr
+ .001*Spd) + .001*Pop + .003*Bunt

*Note: All coefficients are significant at the 99.99% level except for
LD*Spd in x1P, which has a p-value of .03.

Triple plays are so infrequent that we cannot actually expect them as an outcome. Double plays are calculated separately from one-out plays for the same reason that singles are calculated differently from doubles: one double play is more damaging to a team than two plays on which one out is made, just as one double is not equal to two singles. So now, the next step is to determine what the true value of each outcome is, along with strikeouts and total walks (including HBP). For this, I ran all team data for the same three seasons, and attempted to determine the number of runs created by each possible outcome, in the style of Jim Furtado's XR model. This equation, using only coefficients significant at the 99% level, came out as follows:

XR = -.114*SO + .330 *TBB + .365*1B + .712*2B + 1.104*3B + 1.494*HR -
.037*1P - .394*2P

With all of that done, we can get to the meat and potatoes. We can input the expected results from various batted ball types into the XR equation. Once we simplify it, we come up with the following:

XR = .330*BB - .114*SO 

+ GB * (.047 + .003*Pwr + .004*Spd) 

+ FB * (.170 + .084*Pwr + .010*Spd) 

+ LD * (.349 + .043*Pwr - .001*Spd) 

+ Pop * (-.016 - .002*Pwr) 

+ Bunt * (.073 + .021*Spd)

This is the number of runs we can expect from each possible outcome of an at-bat. So, we can tackle the Jeromy Burnitz Problem head-on by looking at this part of the equation: FB * (.170 + .084*Pwr + .010*Spd) + LD * (.349 + .043*Pwr-.001*Spd). It is clear that the initial value of a line drive (.349) is far greater than that of a flyball (.170). While a line drive leads to fewer home runs, it also leads to substantially fewer outs, and many more singles, doubles, and triples. But it is also evident that power has a stronger effect on flyballs than it does on line drives. So, is there a point at which a player can have enough power to make a flyball more valuable than a line drive? The answer, it would seem, is no.

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