Winning and losing pitchers – a fairer system

At the time of writing [October 2004], the RedSox are headed into the American League Championship series against the Yankees. To keep my mind off this I started chewing over the unfairness of who gets charged with losses and who gets the wins. Two examples stand out from the American League Division series. In the third game of the RedSox vs. the Angels, Bronson Arroyo pitched 6 innings for 2 earned runs. After he left the game the Angels caught up and so he was awarded a no decision. Derek Lowe pitched one inning for no earned runs and, because the Red Sox went ahead (and won) in the opposite inning, he was awarded the win. In the fourth game of the Twins vs. the Yankees, Rincon blew a 4 run lead without getting any outs and the Yankees pulled even. The loss, however, went to Lohse who pitched two innings but let A-Rod get the go ahead run.

It is possible to assign a win or a loss more fairly. Consider how many more earned runs the opposing team would have scored if the other pitchers had pitched instead of pitcher X, then turn that into an earned run rate by dividing by the number of innings X pitched. (If X didn’t get any outs before being taken off, still call that 1/3 inning.) [2017 addition: To be a strict earned run rate, multiply the earned run rate per inning by 9.]

The winning pitcher on the winning team is the one who has the highest “What if” value and the losing pitcher on the losing team is the one with the lowest (most negative) value.

The tables below show how this works out for the two playoff games in question.

Here’s the formula written out.

What If Value = (TER-ERx)/(TIP-IPx) – ERx/IPx, where

TER = Total earned runs

TIP   = Total innings pitched

ERx = earned runs for pitcher X

IPx   = innings pitched by pitcher X

Notice that this formula doesn’t factor in how many runs the pitcher’s team scores in the innings opposite those he pitches—after all, the pitcher has no effect on that and it is very weird that it comes into consideration under the current system for assigning wins and losses.

(October 2004 contribution to Sox News for Kids, a baseball magazine edited by a teenager I knew + Tweaks made in August 2017)

RedSox vs. Angels

IP ER What If Value
Arroyo 6 2 0.67
Myers 0 1 -2.49
Timlin 0.667 3 -4.18
Embre 0.667 0 0.64
Foulke 1.667 0 0.72
Lowe 1 0 0.67
Escobar 3.333 3 -0.45
Shields 1.33 1 -0.18
Donnelly 2.333 0 0.78
Rodriguez 2.667 1 0.31
Washburn 0 1 -2.49

Foulke gets the win, not Lowe, but Arroyo is close. Washburn gets the loss, not Rodriguez.

Twins vs. Yankees

Vasquez 5 5 -1
Loaiza 2 0 0.56
Gordon 2 0 0.56
Rivera 2 0 0.56
Santana 5 1 0.47
Balfour 2 0 0.75
Rincon 0 4 -11.79
Nathan 1.667 0 0.72
Lohse 2 1 0.125

Rincon gets the loss and Loaiza, Gordon and Rivera share the win.


About Peter J. Taylor
Peter Taylor teaches and directs programs on critical thinking, reflective practice, and science-in-society at the University of Massachusetts Boston. He studies the complexity of environmental and health sciences in their social context as well as innovation in teaching, group process, and interdisciplinary collaboration (see He is especially interested in conversations with others who are, in diverse ways, "troubled by heterogeneity" (

One Response to Winning and losing pitchers – a fairer system

  1. Two questions:
    1. How did someone who had a systematic brain invent an unfair system and get it accepted? (That is, gIven the systematic thinking, why didn’t they come up with a system like my proposal?)
    2. How to get people who are used to a certain system to buy into a higher ideal–fairness–and thence to change to a fairer system?

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