Adjusting Career Home Runs Allowed Using HR-Plus

One way of normalizing pitchers' HR/9 is to leverage the HR-Plus (HR+) statistic that Diamond Mind Baseball uses to adjust for era differences. After calculating pitchers' career HR+, you can then use that to calculate adjusted career HRs and HR/9.

I tend to doubt I am the first person who has done this; however, after a fair amount of searching, I could not find a writeup on how to make this career adjustment. So this page documents how used HR+ to calculate career HRs allowed and HR/9 normalized to a given league, in case anyone else is interested.


The formula to calculate a pitcher's HR+ in a given season works as follows:

• Calculate the number of HRs a league-average pitcher would have given up in the pitcher's innings pitched. Do so by multiplying the league average HR/9 and the pitcher's innings pitched, then divide by 9. Let's call the result "Expected HRs".
• Divide Expected HRs by the pitchers actual HRs, then multiply the quotient by 100. Values indicate the pitcher is below average, values above 100 indicate above average.

For example, in 2011 Mariano gave up 3 HRs in 61-1/3 innings, and the league average HR/9 was .987. So Mariano's 2011 HR+ would be calculated as:

• Expected HRs: (.987 * 61.333)/9 = 6.726186.
• HR+ (rounded):  (6.726186/3) = 224.

The 224 HR+ indicates Mariano was 124% better than league average in preventing HRs.

To calculate career HR+ and adjusted HR/9 stats is then a matter of doing the following:

• Calculate the pitcher's Expected HRs for each season.
• Calculate career HR+: Divide the sum of the pitcher's expected HRs by the pitcher's career totals, then multiply by 100.
• Calculate adjusted HR/9 as follows:
  • Pick the target HR/9 environment to adjust to. I chose the 1953 AL, with a .715 HR/9.
  • Calculate the number of HRs the pitcher would have given up if his entire career occurred in the target league. This is done by multiplying the target league's HR/9 by the pitchers innings pitched, then dividing the product by 9. Let's call this "Expected Adjusted Career HRs."
  • Divide the Expected Adjusted Career HRs by the career HR+, then multiply the quotient by 100. These are the "Adjusted Career HRs."
  • Divide the Adjusted Career HRs by the career innings pitched, then multiply by 9.

For example, here's how Mariano's adjusted HR/9 was calculated:

• Career expected HRs: the sum of his season's Expected HRs is 148.65.
• Career HR+: (148.65/65) * 100 = 228.692.
• HR/9 = .313 (rounded), calculated as follows:
  • Expected Adjusted Career HRs: (.715 * 1211-1/3) * 9 = 96.2.
  • Adjusted Career HRs: (96.2/228.692) * 100 = 42.08.
  • Adjusted HR/9: ( 42.08/1211-1/3) * 9 = .313.