# Pitcher Strengths of Schedule

I’ve always been interested in the contextual differences of player seasons. Take two random starters. Over the course of a season, they will have subtle differences in their frequencies of starts in pitcher-friendly parks and their frequencies of starts versus various teams and divisions. If the two starters are from different leagues, they will face a major difference in the number of designated hitters and pitcher batters that they face. Most of those factors are small on their own, but it feels like they could snowball on each other in extreme cases enough to make a noticeable difference in the difficulty of the pitchers’ strength of schedules.

It has taken me a while, but I think I’ve finally found an elegant way to test for those types of differences. It involves result frequencies and is best illustrated with a specific example. Stephen Strasburg started the season with a game against Miami. The first batter he faced was Dee Gordon. At that time, Gordon would reasonably have been expected to hit a single on 22.9 percent of his plate appearances versus a right-handed pitcher. He would have been expected to hit a double 3.2 percent, a triple 1.5 percent, and a home run 0.7 percent of the time.

I calculated each of those percentages—as well as ones for strikeouts, walks, and hit-by-pitches—for every batter that each pitcher faced in 2017 using the batter’s results against pitchers with the same handedness since 2015 regressed with 100 league-average plate appearances of the same bat-side-pitch-side matchup. Then, with those simple “projections” in place, I could apply their result rates to the specific plate appearances versus each pitcher. So Strasburg could have expected 0.229 singles from Gordon followed by 0.195 singles from J.T. Realmuto, 0.168 singles from Christian Yelich, and so on through the entire season to date.

The reason it’s helpful to treat each batter faced as an amalgamation of fractional totals of singles, doubles, strikeouts, etc. is so that the sum of those totals can then be used in the formulas for important rate stats, like FIP and wOBA. And voila, you have a simple stat to capture strength of schedule.

I was pleased with the approach I came up with, but when I actually ran the rates for qualified starters so far in 2017, the results were less inspiring. Perhaps the reason I hadn’t previously read much on this topic is that everyone but me intuitively knew that pitchers face very similar strengths of schedule even over about half of a season.

Easiest and Hardest Hitters Faced, SPs, 2017
Pitcher SOS wOBA Pitcher SOS wOBA
Patrick Corbin .324 Ricky Nolasco .337
Stephen Strasburg .325 Luis Severino .336
Drew Pomeranz .325 Ervin Santana .336
Robbie Ray .327 Chris Archer .336
Jacob deGrom .328 Gerrit Cole .336
Carlos Carrasco .328 Jason Hammel .336
Jaime Garcia .328 Jeremy Hellickson .336
Tanner Roark .328 Marco Estrada .336
Josh Tomlin .328
Matt Moore .328

Patrick Corbin can boast the easiest schedule of hitters faced to date, but his advantage over the starter with the toughest slate is a meager three points of wOBA. The differences are a bit larger for relevant relievers—which I qualified as having 20 or more innings pitched with 3 or more saves or 12 or more strikeouts per nine—but still too little to spurn meaningful fantasy considerations.

Easiest and Hardest Hitters Faced, RPs, 2017

Still, I think this type of analysis has potential. Take for example the fantasy-relevant relievers with the highest expected totals of home runs allowed based on the batters they’ve faced. Chris Devenski, Alex Claudio, and Seung Hwan Oh all have home run rates over 11.0 percent per fly ball, but Devenski and Claudio have both allowed fewer home runs than they would have been expected to based on the batters they’ve faced.

Most Expected HRs based on Quality of Batters Faced, RPs, 2017
Pitcher Actual HRs SOS HRs Diff
Chris Devenski 5.0 6.7 -1.7
Alex Colome 3.0 6.1 -3.1
Alex Claudio 4.0 5.9 -1.9
Corey Knebel 3.0 5.9 -2.9
Seung Hwan Oh 8.0 5.6 2.4

Sean Doolittle and Mark Melancon have each allowed three home runs, fewer than Devenski and Claudio, but both have allowed more home runs than their batters faced would normally hit. The peripherals alone may not suggest it, but it seems clear to me which relievers have done a better job of keeping the ball in the park this year.

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Scott Spratt is a fantasy sports writer for FanGraphs and Pro Football Focus. He is a Sloan Sports Conference Research Paper Competition and FSWA award winner. Feel free to ask him questions on Twitter – @Scott_Spratt

Member
Aaron (UK)

Surely the most meaningful SoS measure for a SP would be the identities of their opposing SPs? Obviously this only affects W/L.