Win Expectancy by Run Differential

A few days go, Brilliant Reader (and Strasburg Express broadcaster) Kyle Gutshall asked me to look up the run differentials for the Woodstock River Bandits and Strasburg Express.

Predictably, it sent ATVL down a rabbit hole to look at all the teams’ run differential, and to connect this to win expectancy.

Let’s back up. Bill James, the godfather of Sabermetrics, created a formula many years ago to see which teams were “underperforming” or “overperforming” according to the amount of runs the team has scored and allowed. It is called “Pythagorean Expectation” because the formula is very similar to the Pythagorean Theorem (Runs scored squared divided by runs scored squared plus runs allowed squared).

It’s a fun exercise, but we should be careful not to place too much emphasis on this, especially with such a small sample size (VBL teams have played between 27 and 30 games). It’s dangerous to label a team as “lucky” or “unlucky” when one blowout in either direction could radically affect these numbers. For example, the Tom Sox won 17-0 on July 9th, 11-1 on July 6th, and 17-6 on June 12th. That, over three wins, is a run differential of 38, which will make it look that the team is underperforming overall (because they could have won those games with a run differential of 3).

Does all this make sense? If not, feel free to drop me a line to discuss it further.

So let’s look at the chart of VBL teams, their current W-L record and percentage, their runs scored and allowed, expected winning percentage, and the difference.

Actual Expected Expected
Team W L % RS RA % Wins Difference
Charlottesville 16 13 0.552 190 131 0.678 19.7 -3.7
Covington 17 11 0.607 159 148 0.536 15.0 2.0
Front Royal 19 9 0.679 192 126 0.699 19.6 -0.6
Harrisonburg 14 16 0.467 157 157 0.500 15.0 -1.0
New Market 14 14 0.500 175 175 0.500 14.0 0.0
Purcellville 16 12 0.571 154 137 0.558 15.6 0.4
Staunton 14 14 0.500 189 191 0.495 13.9 0.1
Strasburg 11 17 0.393 189 234 0.395 11.1 -0.1
Waynesboro 17 13 0.567 176 153 0.570 17.1 -0.1
Winchester 14 14 0.500 141 155 0.453 12.7 1.3
Woodstock 4 23 0.148 125 241 0.212 5.7 -1.7

A quick look at the difference line (negative means the team “should” have won more, while positive means they are “overperforming” or “lucky”) shows that the Tom Sox have the biggest difference the wrong way (the team “should” be 20-9 instead of 16-13), while Covington is the “luckiest,” as they “should” be 15-13 instead of 17-11. New Market is exactly where their differential would expect them to be- at 14-14. (Phew- a ton of quotation marks in there.)

So, again, take all this with a grain of salt (wonder where that phrase came from?), but it’s a fun exercise all the same.

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