Win Probability Added and the bunt

Studes has started a regular column on The Hardball Times where he tracks the flow of Win Probability for each team. In these articles, the bunt usually comes off badly. Even in late innings in a tie game, sac bunting a man from 1st to 2nd with no outs decreases the team’s win probability (though it increases the chances that the team scores one run – how this is possible is beyond me [actually, it isn’t, it’s just a little paradox when you first hear it]).
Still, I think a bunt is useful (in late innings at least). Maybe just bunting someone over from 1st to 2nd with no outs is not. You still need a hit to score (and maybe even a single isn’t enough), but you have only two chances left instead of three.
Instinctively, I’d say that bunting a man from second to third with no outs instead is much more useful. Now, the runner can score on every hit, sac fly, squeeze bunt, a wild pitch…
Happy with my new “theory”, I tried it out with the “win expectancy finder” on walkoffbalk.com. Today, the Chicago White Sox played the Tigers in Detroit. With Jeremy Bonderman pitching, the Sox trailed 2-3 and had runners on 1st and 2nd (Pierzynski and Crede). Then Uribe bunted them over. The move paid of when Podsednik drove them both in. So, was the bunt a good decision or were the Sox just lucky?
Win probability before the bunt: 0.451
Win probability after the bunt: 0.426
Hm, so looks like it was just luck after all, or what?
I wasn’t satisfied with the result, obviously, so I wanted to check something else. When Crede scored from 2nd on the single, the Tigers nearly had a play at the plate. Considering that Crede is a faster runner than Pierzynski, one might assume that Pierzynski wouldn’t have been able to score had he still been on 2nd base, so had Uribe hadn’t bunt and singles instead of Podsednik, that might have just loaded the bases.
Win probability after the bunt and the 2-RBI single: 0.671
Win probability without the bunt and a single by Uribe loading the bases: 0.529
So, if you look at the bunt from this angle, it might actually have been a good choice.
On the other hand, had Pierzynski been able to score, we look at this:
Win probability without the bunt and a single by Uribe scoring one and putting runners at the corners: 0.706

All in all, I think the question “to bunt or not to bunt” won’t be settled here (obviously) and probably won’t be settled by looking at win probabily alone. The runners’ speed and the hitter in the on deck circle also have a large impact on the outcome, I’d guess. Also, as much as I like the idea of win probability, the data sample just is a little bit too small. For example, there have only been 51 games with the score tied in the 6th, visiting team batting and runners on the corners and no outs.

Conclusion: I would still bunt with no outs to get a runner to 3rd, though I wouldn’t do it with a runner on 1st. Then, I would pinchrun Dave Roberts and let him steal 2nd.