Quality of Pitchers Faced

Over the years, I’ve made several attempts to adjust both hitter and pitcher performance statistics based on the quality of their opposition, but I’ve never settled on a method that I really like. Those failures will not stop me from trying. In this attempt, I’ve opted to use a plus/minus approach similar to those used in modern defensive statistics like Defensive Runs Saved. Here’s how it works in this case. Whenever a batter records a hit, I am giving him credit of 1.0 hits minus the batting average allowed this season by the pitcher he is facing. So if that hit comes against Clayton Kershaw, that’s 1.0 minus 0.185 or 0.815 hits over what that pitcher would be expected to allow in a typical at-bat. If instead that hit comes against Alfredo Simon, that’s 1.0 minus 0.348 or just 0.652 hits. Meanwhile, if the batter fails to get a hit, he receives 0.0 minus the pitcher’s batting average allowed, which would be -0.185 hits against Kershaw and -0.348 hits against Simon.

With that method, both hitters who only faced Kershaw and hitters who only faced Simon would have 0.0 hits over their pitchers’ expectations (HOPE) if they performed exactly like every other hitter who faced those two pitchers this season. However, the former would be hitting .185 on the season while the latter would be hitting .348. Since no hitter is that cursed or that fortunate in practice, hitter HOPE totals are highly correlated with their batting averages (R² = 0.98 for hitters with at least 200 plate appearances). To demonstrate, here is the top 10 hitters in HOPE, all of whom are hitting over .325 this season.

The Kershaw-Simon hypothetical illustrates the key difference between batting average and HOPE that can help determine the quality of pitchers each hitter has faced this season. Only three batters with at least 200 plate appearances are hitting worse than Kershaw’s .185 batting average allowed this season (Ryan Howard, Chris Coghlan, and Yan Gomes), so if a hypothetical average hitter were to face Kershaw in every one of his plate appearances, he would rank 208th (out of 211 qualified hitters) in batting average despite being middle of the pack (tied for 128th) in HOPE. The inverse would be true for a hypothetical average hitter facing only Simon: he’d rank 3rd in batting average but 128th in HOPE.

In general, that means that the hitters with the biggest positive difference between their HOPE rank and their batting average rank have faced the easiest pitchers so far this season. Here is the top 15:

The first thing that stands out is that there are four Yankees on this list. I’ve been pretty paranoid about park effects during this research because hitters from the same team should logically be somewhat grouped—if one Yankee has played regularly and faced easy pitchers, then most Yankees will have also faced easy pitchers—so those team groupings are not the same clue of park effects that they would be in typical research. I believe that since both batting average and HOPE are not park adjusted, then the effect of parks should cancel out in the calculation of rank differences. As such, I take this leaderboard to mean that the Yankees have faced easier pitchers so far this season, an assumption that I believe passes the eye test since they have not faced the top six teams in team ERA this season—the Cubs, Mets, Nationals, Dodgers, Indians, or Giants.

Hunter Pence and Logan Forsythe are interesting names, too, because neither of them has played their teams’ full slate of games this season having spent time on the disabled list. Meanwhile, Pence is hitting 14 points higher and Forsythe is hitting 40 points higher than their career averages. Perhaps those averages will decline as they play more typical schedules over the second half?

Next, here are the 15 hitters who have faced the most difficult pitchers this season.

This list is full of Braves and a few other NL East and Central teams. The Braves have to contend with the Mets, Nationals, and Marlins, all three of whom are in the top 10 in team ERA this season. Even the Phillies were pitching well earlier in the season when the Braves played them. For Phillips and Votto, their biggest misfortune is that they cannot face their own team’s pitchers. The Reds’ 5.39 ERA is the worst in baseball.

This research will not become really interesting until I look at changes in expected quality of opposing pitchers for the rest of the season. If the Braves have to keep facing the likes of Jose Fernandez and Stephen Strasburg the rest of the season, then their difficult pitching matchups may not let up. However, before I get too far ahead of myself, I want to spend more time thinking through this approach. In particular, I’m concerned about contextual differences like parks, leagues, or whether pitchers themselves might have unbalanced schedules that I would need to somehow account for. If you have any thoughts, let me know in the comments.