### Quality of Batters Faced

A throwaway statement I made while trying to explain why Josh Beckett has seen such a marked increase in his home run rate prompted me to take a deeper look into how much the quality a batter faces has an impact on the pitcher's performance. Instead of looking at home run rates, though, I chose to look at pitchers' fielding-independent ERA, a measure of all the things for which a pitcher is responsible, and how highly it correlates with the batting average, on-base percentage, slugging percentage, isolated power (SLG-BA), gross product average (OBP*1.8+SLG/4), and weighted-on base average (OBP*2+SLG/3) of the batters he faces from 2002-2005. I split up the data into the American League and the National League because the AL designated hitter increases the quality of batter faced by AL pitchers. The pitchers looked at were all the five most used starters for their teams in those seasons.

For whatever reason, the American League had a higher correlation between the batters' statistics and the pitchers' fielding-independent ERAs, but I was more interested in seeing which statistic had the highest correlation.

In the American League, the correlations look as follows:

Batting Average: .137

On-Base Percentage: .259

Slugging Percentage: .244

Isolated Power: .262

Gross Product Average: .265

Weighted On-Base Average: .265

Not surprisingly, batting average has the lowest correlation. Batting average has long been exposed as not being able to paint a complete enough picture of a hitter's ability.

What may surprise you is that isolated power has a higher correlation than both on-base percentage and slugging percentage. Isolated power is rarely talked about in the main sports media, but the more true power that a player has, the more damage he will be able to inflict on a pitcher and also isolated power reflects more than slugging percentage the ability of a player to hit home runs. Home runs are heavily counted in fielding-independent ERA.

Also, the two variations of OPS (GPA and wOBA) are the most heavily correlated to fielding-independent ERA.

As mentioned above, the National League has a lower correlation between all of the statistics and fielding-independent ERA, but the correlations tell a similar story nonetheless.

Batting Average: -.100

On-Base Percentage: -.059

Slugging Percentage: -.030

Isolated Power: .014

Gross Product Average: -.047

Weighted On-Base Average: -.048

Again, isolated power, gross product average, and weighted on-base average are the highest correlated with fielding-independent ERA.

Most of the reason why the correlations are so low throughout is due to the fact pitchers basically face the same quality of batter every year. Some pitchers may face a slightly better hitters and some slightly worse, but overall they are all bunched together. Really, the difference in fielding-independent ERAs have to do with how good the pitcher is. Common sense would have led me to that conclusion and saved me a bunch of time, but I was not employing common sense at the time.

In order to compare to another pitching metric, I ran the same correlations for the flawed statistic that is ERA to see how it compares to fielding-independent ERA.

American League

Batting Average: .138

On-Base Percentage: .200

Slugging Percentage: .117

Isolated Power: .076

Gross Product Average: .170

Weighted On-Base Average: .172

The numbers are different with the highest correlation being between on-base percentage and ERA and isolated power now having the lowest correlation. Batting average is higher than slugging percentage now even though slugging percentage is by far a more important aspect to the same.

National League

Batting Average: -.008

On-Base Percentage: -.073

Slugging Percentage: .042

Isolated Power: .063

Gross Product Average: -.012

Weighted On-base Average: -.015

Now isolated power has the highest correlation and slugging percentage the second highest, but they are all almost zero so it doesn't really matter much since there is no correlation at all.

What this should prove is that good pitching is good against all hitters and bad pitching is bad against all hitters so pitching does not necessarily trump hitting or vice versa when you add it all up.

For whatever reason, the American League had a higher correlation between the batters' statistics and the pitchers' fielding-independent ERAs, but I was more interested in seeing which statistic had the highest correlation.

In the American League, the correlations look as follows:

Batting Average: .137

On-Base Percentage: .259

Slugging Percentage: .244

Isolated Power: .262

Gross Product Average: .265

Weighted On-Base Average: .265

Not surprisingly, batting average has the lowest correlation. Batting average has long been exposed as not being able to paint a complete enough picture of a hitter's ability.

What may surprise you is that isolated power has a higher correlation than both on-base percentage and slugging percentage. Isolated power is rarely talked about in the main sports media, but the more true power that a player has, the more damage he will be able to inflict on a pitcher and also isolated power reflects more than slugging percentage the ability of a player to hit home runs. Home runs are heavily counted in fielding-independent ERA.

Also, the two variations of OPS (GPA and wOBA) are the most heavily correlated to fielding-independent ERA.

As mentioned above, the National League has a lower correlation between all of the statistics and fielding-independent ERA, but the correlations tell a similar story nonetheless.

Batting Average: -.100

On-Base Percentage: -.059

Slugging Percentage: -.030

Isolated Power: .014

Gross Product Average: -.047

Weighted On-Base Average: -.048

Again, isolated power, gross product average, and weighted on-base average are the highest correlated with fielding-independent ERA.

Most of the reason why the correlations are so low throughout is due to the fact pitchers basically face the same quality of batter every year. Some pitchers may face a slightly better hitters and some slightly worse, but overall they are all bunched together. Really, the difference in fielding-independent ERAs have to do with how good the pitcher is. Common sense would have led me to that conclusion and saved me a bunch of time, but I was not employing common sense at the time.

In order to compare to another pitching metric, I ran the same correlations for the flawed statistic that is ERA to see how it compares to fielding-independent ERA.

American League

Batting Average: .138

On-Base Percentage: .200

Slugging Percentage: .117

Isolated Power: .076

Gross Product Average: .170

Weighted On-Base Average: .172

The numbers are different with the highest correlation being between on-base percentage and ERA and isolated power now having the lowest correlation. Batting average is higher than slugging percentage now even though slugging percentage is by far a more important aspect to the same.

National League

Batting Average: -.008

On-Base Percentage: -.073

Slugging Percentage: .042

Isolated Power: .063

Gross Product Average: -.012

Weighted On-base Average: -.015

Now isolated power has the highest correlation and slugging percentage the second highest, but they are all almost zero so it doesn't really matter much since there is no correlation at all.

What this should prove is that good pitching is good against all hitters and bad pitching is bad against all hitters so pitching does not necessarily trump hitting or vice versa when you add it all up.

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