No, no, no, no, no, no, no, no.

Well, sometimes yes, but not always.

I was discussing bunting with Jack Moore on Twitter the other day. (Which eventually prompted this post.) It went like this:

Jack Moore @jh_moore (This is Jack talking to me)

@BadgerNoonan But that’s like the whole point of WPA — it introduces the context of the bunt which is key in the evaluation.

@BadgerNoonan (This is me talking to Jack)

@jh_moore WPA in a vacuum isn’t great for this. Need to compare to other potential outcomes and odds of them occurring.

Jack Moore @jh_moore (This is Jack talking to me)

@BadgerNoonan Yes. A bunt is bad if it makes you less likely to win. It’s good if it makes you more likely to win.

To some extent we were talking past each other here which is one of the curses of being limited to 140 characters. I won’t pretend to speak for Jack, though I think he was just stating the basic truth of WPA, that it can be higher or lower based on the given situation, which is true.

I was saying something different. Back in the day I used to read William Krasker’s football strategy site which explained optimal strategic decisions in certain situations using William’s Dynamic Programming model, which relies heavily on win probability charts. This was probably my first big exposure to win probability as a concept, at least as far as sports analysis goes.

The conclusion of any given post by Williams is almost always “So the Xers should go for it if they will be successful Y% of the time. If you read the Tango/Lightman/Dolphin Book you’ll often see something very similar.**

Let’s quickly talk about WPA. WPA is “Win Probability Added.” WPA is “the difference between the win probability when the player came to bat and the win probability when the play ended.”*** Let’s say that the win probability when he starts his at-bat is exactly .50. Something is going to happen during his at-bat that raises or lowers that probability. He might hit into a DP, or make an out, or make an out that advances a runner, or walk, or hit a single, double, triple, HR, or various other outcomes. When he is finished it is very unlikely that his team’s win probability will still be .50. Some outcomes will add to the team’s win probability and some will subtract from it. The important point, and the point I was trying to make, is that there are *different levels* of positive and negative outcomes (and different risks associated with those outcomes), and simply saying that WPA increased is at best an incomplete analysis. If there is a 70% chance of getting down a bunt that increases your WPA by a small amount, and a 40% chance that swinging away will increase your WPA by a far greater amount, the bunt can still be the wrong call *even though it increases your WPA*.

The analogy I like to use is blackjack. Say the dealer has a 6 showing. He’s going to bust over 40% of the time in this situation. Now let’s say you have a total of 9. Your options are to stand, hit, or double down. The correct play**** is to double down. The odds of the dealer busting are overwhelming, and even if he doesn’t you still may end up with 20, 19, 18, or 17 and win or push and win double your original bet. But doubling down has a cost in that you only get one more card. From the perspective of trying to win *this hand*, doubling down is riskier. If you just hit you have the opportunity to cure a bad situation with a subsequent hit. If you flip a 2 to make 11, you may then hit that into a 21 and beat the dealer even if he makes 20. Your odds of winning the hand are better if you hit rather than double, and assuming you win, you will have more money than you started with. Your “win probability” will have increased even though you made the wrong call.

This analogy is a little unfair since any decent players knows that in the long run hitting in this situation (versus doubling) is a losing strategy, and in deciding whether to bunt or hit it’s often a closer call, but the point still holds that if you have two situations, both of which will leave you better off than you were before, one is still a superior choice to the other.

This is pretty clear if you look at all of the outcomes I have listed above. Going from having no outs and a man on first to one out and a man on second may, in certain circumstances increase your win probability, but having two on and no out will increase it more. Having two additional runs and none out will increase it even more. There is a cost to going for a hit in that it’s far less likely, but the payoff is undoubtedly greater, and you need to factor in the likelihood and payoff of all outcomes. (And how many runs are necessary to win. The bottom of the 9th is sometimes a different animal.) A bunt *may* still be the superior option if the odds of a hit, an extra base hit, or a walk are low, and/or if the odds of a double play are high, but you have to factor in all of those outcomes.

So Jack is wrong when he says that a bunt that increases your win probability is automatically good. A bunt is not necessarily good even if it makes you more likely to win if you forego an action that would make you still more likely to win.*****

*Yup, that’s an interrobang.

**I disagree with some of MGL’s game theory analysis with regards to bunting in that I think the situations where it’s useful are far less prevalent, but that’s for another time.

***Wikipedia. Very concise here.

****Yes, yes, assuming neutral count.

*****Jack is nothing if not diligent. He ran 5000 Monte Carlo Machine simulations of bunting in the 9^{th} inning. He concluded that bunting is worse than swinging away, though not by very much.

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Bunting is also not a 100% guaranteed outcome, which is my strongest argument against it.

It’s successful, what, 80% of the time? If you’re not gaining at least 1/4 the WPA you would lose with an unsuccessful bunt with a good bunt, then it’s a losing proposition, even if a successful bunt gains WPA.

It’s basically the same way that poker works.