In which Nate Silver invents Three True Outcome Percentage right before our very eyes. In which Nate Silver provides us a way of ranking Vin Mazzaro ahead of Aroldis Chapman in something.

The Grand Experiment
March 12, 2003

Abstract: With two newsy examples as his hook, Nate looks at which types of pitcher have had disproportionate success converting from the bullpen to a rotation, and which types have struggled. Helpfully for his premise, Danny Graves and Byung-Hyun Kim (both, at the time, converting from the ninth inning to the first) were nothing alike. Graves was a finesser; Kim struck out a quarter of the batters he faced; Graves had a very moderate platoon split, Kim’s was giant. His findings: the pitchers who transitioned the best, relative to their talent level, were those who struck out few batters, walked few batters, and allowed few home runs.

Table 2: Correlations between RA Delta and peripheral statistics

        Strikeout rate:   -.46
        Walk rate:        -.20
        Home run rate:    -.39

The higher a pitcher ranked on a Three True Outcomes leaderboard, the better he was suited for the bullpen instead of the rotation.

Key Quote: "It's always easier to follow statistical evidence with intuition than the other way around, but this result, if it's real, makes plenty of sense. It simply isn't possible to pitch like Calvin Schiraldi for seven innings at a time; the pitch counts rise too quickly, and the strain on the arm is too great. A pitcher like Schiraldi needs to change his approach when pitching for extended stretches in a way that a pitcher like Billy Swift does not. Inevitably, that means allowing a few more runners to reach base. If the pitcher is also vulnerable to the long ball, as Schiraldi was, his RA can rise very quickly as solo shots turn into three-run jobs."

If It’s Real: If it’s real, we can apply it to the current crop of pitchers who are either going to convert or will be part of a convert-or-not-convert controversy. (And, as long as starters pitch three times as many innings, there will always be convert-or-not-convert controversies.) Did a quick poll of names to throw into the mix, and here they all are, sorted by TTO% as relievers over the past two seasons.

Pitcher Innings TTO%
Vin Mazzaro 91 23
Carlos Martinez 23.67 28
Robbie Ross 127.33 29
Justin Wilson 78.33 31
Alex Wood 21.67 34
Drew Smyly 80.33 35
Neftali Feliz 131.67 35
Aaron Crow 113 35
Joba Chamberlain 62.67 35
Dustin McGowan 25.67 35
Brett Cecil 71.67 36
Alex Torres 66 37
Trevor Rosenthal 98 42
Aroldis Chapman 135.33 56

(I went further back for Feliz. Some pitchers have only relieved for one inning.)

To be very clear: This isn’t saying Mazzaro would be a better starter than Rosenthal. Just that he would show the smallest delta between his relief work and his rotation work. That Rosenthal is more better in relief than Mazzaro is more better in relief. This, as a quick eyeballing of the list shows, is the central dilemma for teams: If Nate’s right, then the most benefit comes from converting the worst pitchers into the biggest roles. Which raises a whole secondary math problem.

But We Said IF It’s Real: Ben wrote about a group of convertees in spring 2012, and Colin Wyers’ research assistance turned up very different results.



K Rate


BB Rate








The walk rate was less helpful to a reliever converting to the rotation, but still helpful; the power rate was much less helpful, but still helpful; and the strikeout rate flipped entirely, from being a negative indicator for a relief pitcher to a positive indicator. By this prescription, Rosenthal likely flips to the best bet for converting.

Graves and Kim, incidentally, both flopped as starters.

Tables: 3
Graphs: 0
Equations: 0

On the Nate Silver Must-Read Scale: 1