THE BOOK--Playing The Percentages In Baseball

MGL, what are your projected UZR’s for both Gross and Fernando Perez? I’m not entirely sure who’s the better outfielder (or at least right fielder) between the two, but just using my eyes, Perez looks better to me, and if that’s correct, then I guess Maddon made a mistake (aside from the bullpen mismanagement) by not bringing in the superior defender when trying to protect the lead. I would not, however, be surprised to see my own eyes in disagreement with UZR.

I don’t have nearly enough data on either player, especially Perez, to make any meaningful statement.

I would go with Perez.  There may be little data to go on, but he is obviously a lot faster.  After Gross’s gross throw in the 8th I don’t think I would have wanted him in the outfield for any reason.  If the game had gone into extra you’d still have Baldelli to pinch hit for Perez.

Gross’s numbers this year and last year according to the fans are ok.  Average arm.  This might simply have been a bad throw from a decent to good fielder.

While positioning shallower decreases the value of a single, it may reduce the probability of an out and increase the probability of a double or triple.

E(runs) = p(1b)*E(runs|1b) + p(2b)*E(runs|2b) + p(3b)*E(runs|3b) + p(out)* E(Runs|out).

A similar equation could be generated to compare the win values of each event. Reducing the E(runs|1b) doesn’t self-evidently improve the chances of winning, even in this case. Law’s point about “getting the out” hasn’t been tackled adequately because you haven’t addressed the relevant trade offs. The burden of proof is still on you to show why average positioning is wrong.

I am afraid that it is tautological that as the relative values of the single and extra base hit changes, so does the optimal positioning of the OF’ers. Whether you are anyone else understands that or not is not my problem.  I’ve tried to explain it as best as I can.

What the hell does the “burden of proof” have anything to do with anything?  Law made a statement.  I refuted it and explained how and why quite extensively. As I said, if someone does not understand my explanation, I can’t help that.  Not understanding something is not the same as arguing against it.

It CANNOT be correct to have the same positioning as the game situation changes literally batter by batter.  Optimal positioning of the outfield is a function of the win values of the out, single, and extra base hit, and as a function of the probabilities of keeping runners on base from advancing extra bases on hits (or outs on a tag play) and throwing them out.

There are only 3 positions without getting more specific than that: An “average” one, a deeper one, and a shallower one.  It is trivial to determine whether optimal positioning is shallower or deeper than average under extreme conditions.  Absolutely trivial.  For conditions that are near average, it is not so easy, because first you would have to define “average position” based on all possible game situations and how often they occur.

The situation we are talking about, bottom of the 9th, tying run on second, 2 outs, is an extreme situation.  As I have now said about 4 or 5 times,it is easy, without doing the calculations to know which one of only three possible scenarios is optimal - a “normal” positioning, somewhat closer, or somewhat deeper.

I COULD go through the calculations, but I am not going to.

However, if anyone disagrees even a little, with my conclusion, I will be happy to wager money on it and give that person 2-1 and we can let an independent analyst do the calculations.

I am 99% certain that it is a trivial conclusion that the outfielder plays more shallow than say, a tie game with no one on, in the first or second inning (given the same batter and pitcher, weather and park, etc.).  When the extra base hit has around the same win value as the single, AND you absolutely must throw out the runner on a single otherwise you lose the game, it is MORTALLY OBVIOUS that you must play considerably shallower than “average.”

And by the way, it is definitely true that maximizing the probability of the out is mostly the consideration in that bottom of the 9th situation.  You and Law are correct about that (you might have to give up a slight amount of that because you need to give yourself a better chance of throwing out the runner on a single). 

However, your flaw is thinking that normal positioning maximizes that chance.  It does NOT!  It can’t.  You would only maximize your chances of getting an out in a normal situation if the value of the single were the same as the extra base hit. If the extra base hit is worth more than the single, which it usually is, then it is 100% correct to play a little deeper than what would maximize your likelihood of getting an out.  That is obvious.

Now, once the single and extra base hit have the same value (as they almost do in our bottom of the 9th, runner on second, 2 out, tie game situation), THEN we do want to maximize the chances of getting an out.  That necessarily means that we must move in a little closer than we would when the extra base hit is worth more than the single, which is most of the time.  Why do you think that a team plays a “no doubles (and triples) defense (deeper than usual) in certain situations late in a game?  Because the extra base hit is worth MORE (in win expectancy) in relation to the single than is the case in a typical or average situation!

I don’t know how to explain it any clearer or better than that.  If anyone does not understand it, I suggest they ask someone else for help or give up the argument.

So, mgl, if I don’t understand your logic here (which I don’t, although I think it’s because it’s faulty, not because I’m stupid), should I just assume you don’t want to hear about it? I don’t understand why you’re so upset about J’s point, since his main criticism (that you didn’t address Law’s point about the likelihood of getting an out) was valid. Nor do I understand why you guys have a comment section if you’re so upset when people use the format to engage your work in substantive crticial discussion. Nor do I understand why you spend so much time and space arguing with J after you state that you’ve already explained it to your best ability and that it’s not your problem if people don’t understand it. Your condescension is extremely irritating. I know that you are way, way smarter and more knowledgeable than me in matters relating to baseball, but I do not want to feel like I can’t ask you questions or argue with you about things just because you’re smarter. It doesn’t help anyone if you get so upset when people question you. You’ve now taken the position that anyone who disagrees with you is merely stupider than you are and shouldn’t waste your time. What exactly are you trying to accomplish if your default position on the issues is not to explain or persuade, but simply to shut down discussion under an air of superiority? I think you would be a better blogger if you exercised a little patience and humility, but that’s my opinion and your blog, so take it for what it’s worth.

Yes, I apologize for my petulance, often called “impetulance,” a word which does not exist.

What exactly are you trying to accomplish if your default position on the issues is not to explain or persuade

Clearly that is NOT one of my faults, among many.  I have “explained and persuaded” to the tune of 2 very long posts.  Honestly, I can do no more on this issue other than essentially repeat myself.  If someone “disagrees,” so be it.  (And I never, in this thread at least, even remotely called anyone “stupid,” although I am sure you think I implied that, which is also your prerogative.)

Glad to see a post from someone I did not know was around, whoever you may be!  Sometimes I think there are only 10 or 20 readers of this blog.

Hope you stay around despite by despicable disposition.

I don’t like arguing. I stand by what I wrote. You can decide for yourself the value of it.

I see no confusion in MGL’s explanation twice over. The process in position the OF (play shallower to give the OF a higher chance to throw out the runner at or prevent the runner from advancing to home plate) on that particular situation is correct (bottom of the 9th, winning run on second, 2 outs). Just because the outcome was negative doesn’t mean the process was flawed. This is coming from a regular fan who knows very little of the advanced metrics.

I thought MGL explained it fairly well originally, and then exhaustively the second time, and he’s certainly right. Due to the game situation, the fielder needs to shift his coverage inward to restore the optimal balance of being beaten in front of himself or behind himself.  The extreme game situation actually does make this whole thing easier - with fewer outs or other innings to come, you have to worry about what happens next, but here you don’t.

J suggested that MGL didn’t address the probability of outs, but if you’re talking about the probability of a single dropping in, and the probability of extra base hits over the top, outs is all that is left.

MGL, I think you’re clear here.  Pretty typical stuff (excellent insight, mildly prickly) from my perspective as a long-time reader and occasional poster…

Thanks guys.  Yes, definitely unnecessarily prickly, but I really thought that the reasoning, especially in that situation, is a no-brainer.

On ESPN, Keith responded that he meant “normal” position for all hitters.  I responded cordially but implied that that made no sense, since every batter/hitter (and park, weather, etc.) has a different position (across all game situations) of course and that I thought it was pretty obvious that we were talking about “normal” for Coco/Wheeler.  No big deal though.  Again, I don’t know whether Gross was playing correctly or not.  I only know that whatever his “normal” (and hopefully correct) position is with Wheeler versus Crisp, that he needs to play considerably closer in that situation, which he seemed to be.

BTW, I have talked about fielder positioning before.  I don’t think that teams understand the dynamics and I don’t think that they properly move their fielders in and out (and for first and third basemen away from or towards the line) as the game progresses and the relative values of the single and extra base hit changes.  It is probably no big deal though, as they do understand the extreme and important ones.