Toward valuing a hit kept in the infield

Sunday night I was playing with my newly populated Retrosheet Database (thanks a lot Colin Wyers!) and watching Japan vs Cuba.

As I finished calculating run values for various events, Johjima was on second with one out; Iwamura hit a groundball that looked headed to centerfield. Instead second baseman Yulieski Gourriel made a diving grab, turned his body and tried to get the runner at first. Akinori was safe, but the play by Gourriel prevented Johjima from scoring (he would undoubtely have, had the ball gone through).

Fielding metrics that compare outs made vs expected outs treat such a play as a failure for the infielder; maybe Gourriel wouldn't be charged with a great negative contribution, since the ball was in a zone where not many outs are expected to be made. Anyway I believe the Cuban second baseman might deserve more than a mild negative score on that play.

Using data from the last five years, I calculated that a single that goes to the outfield has a run value of 0.477, while a single that stays in the infield is worth 0.409 runs.

Those are values averaged across all the possible base/outs situation. In the specific enviroment in which the play occurred the difference would be between 0.681 and 0.482.

Let's stick with the average values for singles. This implies that infielders tries with same effort to keep the ball in the infield when the bases are empty (can we consider this to be true?).

Let's assume that the ball hit by Iwamura, on average, goes to the outfield 80% of the times, ends as an infield hit 15% of the times and is converted in an out the remainig 5% of the times (numbers entirely made up on the spot). The expected run value is 0.8 x 0.477 + 0.15 x 0.409 + 0.05 x (-0.288) = 0.429 (-0.288 is the value for the out I got from the 2004-08 data).

Gourriel kept the ball in the infield, for a run value of 0.409, thus we should credit him for preventing 0.02 runs.

I haven't read the second edition of the Fielding Bible, but I suspect that the plus/minus system doesn't properly value a play like this.

I'm pretty sure that David Pinto's PMR (that I prefer to +/-) doesn't deal with this either (PMR is outs made vs expected outs).

It's been a long time since I've read MGL's work on UZR at Baseball Primer, so I don't remember if UZR addresses similar events.

I don't know if factoring this kind of play into a fielder's evaluation has a significant impact on his contribution, but I believe it's worth to investigate into the matter.

Note: the percentages I made up have been chosen by design to give a positive value for Gourriel's play. If we delve into real data and find real probabilities, infield singles will give the fielder negative contribution most of the time (less negative than outfield singles, anyway).