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# Effects of Defense on ERA and WHIP

Pitchers can’t control every aspect of the game around them including the the defense behind them. A team’s defense can effect a pitcher’s WHIP and ERA by letting more batted balls turn into hits (increasing WHIP) therefore leading to more runs allowed (increasing ERA). The following is a look at how much a team’s defense could effect a pitcher’s ERA or WHIP.

ERA

This study started when I noticed that about all of the Royal’s starters had higher ERA than their FIP or xFIP. The Royals defense the past few years has been statistically one of the league’s worst. I decided to see if the trend was true for all teams. Then an adjustment could be added to a pitcher’s true talent value (FIP, xFIP, tEA, SIERA) to get their projected ERA. FIP is used as the true talent value in this study.

FIP was subtracted from ERA to get the number of extra runs possibly allowed or prevented by the defense. Then, the ERA-FIP value is compared to the team UZR/150 (this number is calculate as the season goes on here and could be used to determine the good and bad defensive teams) and the total UZR for every team over the past 5 years. I stayed at the team level to try to eliminate some statistical noise when looking at individual pitchers. Here are the graphs of the numbers, trend line, equation and r-squared values:

Though the r-squared is not close to ideal, there is a general trend of higher ERA-FIPS for bad defensive teams. With that knowledge, here are some general rules of thumb for ERA adjustment when used with a best guesstimate of a team’s defense:

ERA Adjustment for UZR/150 values = -0.027(UZR/150)
ERA Adjustment for Total UZR values = -0.00426(Total UZR)

The range works out that the worst defensive teams(-10 UZR/150, -80 UZR) add ~ 0.30 points to a pitcher’s ERA while the best teams (-10 UZR/150, -80 UZR) take off ~0.30 points. Most teams (78%) fall in the -5 to 5 UZR/150 range or -40 to 40 UZR range, so most pitcher’s FIP will be adjusted by an average of +/- 0.15 points to get their ERA.

WHIP

A pitcher has control over the walk portion of WHIP (Walks and Hits per inning pitched), but very little control over the hit portion. A porous defense will allow a few more balls to get through, thereby increasing the number of hits allowed.

To compare team defensive values to WHIP, the walks allowed by the teams were removed and only HIP is left. Here are the graphs of the values, trend line, equation and r-squared when comparing HIP to team UZR/150 and total team UZR over the past 5 years:

Again the correlation is not perfect, but there is a definite trend of bad defensive teams allowing more hits than the better defending teams. With this information, here are the adjustments for a pitcher’s (W)HIP knowing the defense played behind the pitcher:

WHIP Adjustment for UZR/150 team values = -.00392(UZR/150)
WHIP Adjustment for UZR total team values = -0.000736(Total UZR)

The swing from the worst to best defensive teams is ~ 0.1 WHIP. In most fantasy leagues, WHIP totals are fairly close together, so a swing of 0.1 could be significant.

Conclusions

The changes in a pitcher’s ERA and WHIP due to the defense behind him are somewhat measurable. If you have a pitcher ranked above another one, they should probably not be switched just because of their team’s defense. If two pitchers are to close to tell apart though, the one with a better defense playing behind him should get the nod.