In talking about how we calculate pitcher win values, we’ve covered FIP, differences in replacement level for each league and role, run environments, the dynamic runs-to-wins conversion, and park factors. What we haven’t done is walked through an example, from scratch, of how the pitcher win values are calculated. That’s what we’re going to do today.
We’ll use Felix Hernandez as our guinea pig. In 2008, he threw 200 2/3 innings with a 3.80 FIP as a starting pitcher in the American League. Remember, we noted earlier that the league average runs per game in the AL was 4.78 last year, so we rescaled Felix’s FIP to make 4.78 equal league average. Adding in a park adjustment for a half season in Safeco Field (with a park factor of .96), we get a 4.28 neutral park FIP scaled to RA for Felix’s 2008 season.
Now, we have to figure out the runs to wins conversion based on Felix affecting the run environment he pitches in. To do so, find his innings pitched per start (6.5), subtract that from 18, and multiply that by the league average runs per game. Then, we add to that those 6.5 innings multiplied by his park adjusted FIP, and divide that by 18, and then use Tango’s +2*1.5 runs to wins converter. So, the formula for Felix would be ((11.5 * 4.78 + 6.5 * 4.28)/18)+2)*1.5, which would give us a run environment of 9.90 runs per win. So, for every 9.9 runs he saves, he gets credit for one win.
His 4.28 FIP is 0.50 runs per nine innings better than league average. What does Felix’s 4.28 FIP translate into in terms of win%? 0.50 divided by 9.90 equals .050. Add that to .500 and we get .550, making Felix a .550 win% pitcher. Remember, an average pitcher would post a .500 win%, and a replacement level starting pitcher would post a .380 win%. So now we subtract .380 from .550, and we get Felix as .17 wins better than a replacement level starter every nine innings.
Factoring in his actual innings pitched, we get .170 * 200.67 / 9, which comes out to 3.8 wins. That’s his wins above a replacement level starting pitcher, or what we call his win value for 2008. Remember, though, these are context neutral win values. Actual wins contributed to a team’s ledger will also be affected by how each pitcher performed with runners on base, as well as the performance of the defenders behind the pitcher. There are going to be cases where a pitcher has a much better (or worse) context neutral win value than you might expect if you’re used to looking at his W-L record or his ERA.
That does not mean these win values are “wrong”. We’ve removed the situational context of the pitcher’s performance, just as we do for hitters. Pitchers can either underperform or outperform their win values with extreme performances in “clutch” situations. We can measure the differences in these situational performances by looking at a pitcher’s WPA or WPA/LI and comparing it to his Win Value. For too long, we’ve lacked a resource for context neutral win values for pitchers, having to settle for situational win values that include a lot of variables. These pitcher win values offer us a great opportunity to explore more of what is in a pitcher’s control and what is not.