THE BOOK--Playing The Percentages In Baseball

To me, there is no such thing as an “opinion” on which of two strategies yields the highest win expectancy. ...

Nowhere does my opinion matter…

In a Platonic sense I agree: there exists some exact values of the requisite variables which, if known, could lead to a precise computation.

Where opinion matters, though, is in how people may estimate the requisite variables. How likely Craig is to successfully steal matters, or how likely I think Pujols is to make contact, etc. Given some set of assumptions, then yes, you can say the decision is either good, bad, or close.

Not all sets of assumptions are created equal, but where the play falls may depend on what set of assumptions you use, and that is ultimately a matter of opinion.

What we can say is that down 2 runs, the value in running is almost entirely to avoid a double play, while the risk is the double play that happened, or that Pujols’s batting is somehow negatively impacted by having Craig run. Helping Craig himself score by taking an extra base is irrelevant because someone after Craig needs to score as well.

I do find it ironic that after being the hero early in the series (two game winning pinch hits, and a game 3 HR in his first at-bat), Craig now could be cast as the goat for taking the bat out of Pujols’s hands twice in the pivotal game 5. Spinning narratives is so much fun!

I haven’t run the numbers - in fact, I’ve got so little time this is my first post/read on a sabr blog in over a week - but don’t dismiss my point just yet!

Isn’t the old phrase, “A bird in the hand is worth two in the bush,” apt here? The Cardinals are down by two runs, with a runner on first and zero outs (I believe). The run expectancy is 0.953. (using RE because I don’t have WE handy).

At that point there are a two options, as you mention.

Craig runs.
Craig stays put.

Getting Craig to second without sacrificing an out is 1.189. A modest gain.
Having him thrown out puts the RE at .297. A pretty huge loss given that the team needs two runs.

So, we’ve got three outcomes (assume here Pujols doesn’t get out)

1. Craig runs and is safe. Result: +.236
2. Getting Craig thrown out. Result: -.656
3. Craig stays put. Result: Result: No change RE = .953.

Now, if LaRussa is going to send Craig he has to take into account the probability of success and discount the +.236 RE gain by the chance that Craig fails.

What’s that chance? Well, as mentioned above, it’s hard to tell because of all the variables. What is Craig’s typical success rate? Is Craig more likely to be safe on a hit and run? More likely to be safe with Napoli and Feliz as the battery.

Lets say, hypothetically of course, that we knew Craig had an 80% chance of success going into the attempt. We need to discount the RE gain by the 20% of failure.

If you do the RE becomes .951! Less than what it would be if he just had stayed put! La Russa should have never sent him. And again, the RE gain is nominal down by two runs and the best player in the world was at the plate.(And 80% is probably generous).

Thoughts?

Forget RE when it comes to the ninth inning.  Please!

As for not having WE handy, you have two online choices:
1. Go to Amazon’s Look Inside (free!), and do a search for all of this

inning: 9

Select the Page 43 entry. 

2. Go here:
http://tangotiger.net/wins.html

That’s empirical, but because each combination is not directly comparable to the other combinations (i.e., comes from different pools of games), you will get little “hiccups”. 

But you can use the two, and come up with what you need.

Please, no talk of RE in the 9th inning.

Well, I figured it was better than not commenting at all! Anyway, thanks for the links. I a) don’t have my copy on the book on me and b) lent it to a friend anyway. These will be helpful…

Tom, As per my discount methodology/rationale… Thoughts?

Down by two runs, it is next to irrelevant whether Craig moves up a base or not.  Also, with a 3-2 count, the 3 options listed aren’t possibilities.

Pujols will either reach base, make an out, or hit a foul ball.  There is no chance of Craig being safe or out at 2B with Pujols still at the plate.

Foul or walk: irrelevant whether he runs or not.
Safe hit or error: Craig might advance an extra base than he otherwise would have, but Pujols is the runner the Rangers actually care about.

Out - Here’s where we need to run the numbers.

On a strikeout Craig is dead meat considering he’s not a fast runner, and is trying to run on the God-King, Napoli.  If Pujols swings and misses, it is very bad to have sent the runner.  Although this is what happened, Pujols has a very low strikeout rate.

On a flyball out, it is irrelevant.  Craig should have time to get back to first.

On a linedrive out (to infield), he’s going to get doubled off.  But line drive outs are a fairly rare occurrence.

On a groundball out, Craig running likely puts him on 2B and saves the Cardinals an out by avoiding the DP.  Pujols hit into 29 DP this year, most in the league, and has always had high GIDP totals.

The next step would be to estimate the chance of each type of out for Pujols vs Feliz, since if the pitch does not result in an out, it is largely irrelevant whether he runs or not.

My observation is that much of the blame should go to Pujols, he swung at a few pitches out of the strike zone when he had a 3 ball count.  You don’t need to protect the runner in that situation, obviously.  I can understand some hitters getting their reactions confused, but Pujols is as smart a hitter as they come and should know better.

Rally, I totally didn’t realize it was a 3-2 count. Thanks for the heads up.

To further simplify, I think it comes down to how to minimize the chance of a DP.  While Pujols strikes out less than the average batter and hits into more GIDP, he still had twice as many K (58) as DP (29).

But then, you can only GIDP if there is a runner on first and less than 2 out.  You can strike out anytime.

For his career, Pujols has batted 1722 times with runner on first, less than 2 outs.  In those, he has 162 strikeouts and 232 GIDP.  Even without considering the infinitismal chance of stealing a base on the Napoli, I say send the runner.

Though, the reason why Pujols has hit into so many double plays MAY BE because the runner is never sent.

Rally/7, but in many (most?) of those PA with a runner on first, he didn’t have 2 strikes.  Obviously the chance of a strikeout goes up when he has two strikes, as he did here.  (I.e., he can’t really strike out any time.)

Good point.  I should have considered that.

On a full count, Pujols will strike out 50% more than he otherwise would.

Of course, he’ll also walk alot more, thereby reducing his opportunities for GIDP.  The opps for GIDP goes down about 20% on a full-count.

So, taking Rally’s numbers of 162 K and 232 GIDP with runner on 1B and less than 2 outs, and then “full-count-isize” it, it’ll be around 240K and 190 DP.

Therefore, it looks like you are accepting the 240 strike-em-out-throw-em-out rather than the 190-batted-ball-double-plays.

Obviously, you’d have more considerations (GB tendency of pitcher, where are the fielders playing, etc).

He’s also practically guaranteed the extra base on a single and double, which is not something we should forget about.

Great back and forth; thanks.

I think the discussion of whether Craig should have been sent on the 3-2 pitch could go either way. There are reasons to back either choice. (I would have sent him.) What I can’t understand is Pujols’s swinging at Ball 4 the way he did. McCarver said sending the runner makes hitters more likely to swing. He’s the retired player, but I never heard anyone else make that comment, and it seems counter-intuitive, as nothing protects the runner any better than a walk. Maybe that’s true for a hitter who takes too many close pitches with two strikes, but not Albert Pujols.

Dana - While driving yesterday I heard a radio talking head (Mike Francessa, maybe) saying that he wouldn’t send the runner because he didn’t want anything to distract from Pujols’s at bat.

I’ve never played at a high level, and I have no idea how to quantify such an effect if it might exist, but I also can’t rule out that such an effect might exist. Perhaps simply knowing the runner is going might subtly change the batter’s approach.

As for McCarver’s comment, that’s something I’ve often heard in hit-and-run situations, that the batter tries to swing to “protect” the runner: if it’s a rather slow runner, you really want to make contact to avoid the runner being easily thrown out. And even if you swing and miss, that may affect the catcher’s ability to make as efficient a throw.

"Therefore, it looks like you are accepting the 240 strike-em-out-throw-em-out rather than the 190-batted-ball-double-plays.”

So if Craig is expected to steal the base about 20% of the time (50/240), that would about even things up.

Even a runner with a 50/50 SB success rate should probably be running here.  Though running against Napoli the God-King, you’re probably better off sticking on first.

"saying that he wouldn’t send the runner because he didn’t want anything to distract from Pujols’s at bat.”

I think that’s worth considering, but I think Pujols is great enough that he can tune out any distraction, and he seems OK with runners going since it was reported that he called the earlier hit and run himself.

Even less than 10% actually, since if he’s successful, he’ll have gained a base. 

(And of course, since he’s in motion, he’ll have gained a partial base on singles and doubles… partial because there’s a decent chance he would have gotten the extra base anyway.)

It doesn’t seem like something to argue about, though learning about this is fun.

The real issue is Pujols swinging at such a pitch.  It doesn’t seem a smart hitter like him would have swung at a pitch like that in other conditions.

What if say Larussa said: “you call for the hit and run, and you swing even at pitches outside the zone”, to explain the first muff.

And then Pujols, not thinking about the 3-2 count specifically, remembers Larussa’s explanation of how to approach H&R?

Seems to hard to believe that a guy that experienced would look to “protect” the runner on a 3-2 outside swing, when the walk removes the issue altogether.

Pujols is human.

Geoff/14
I’ll accept that, though on a hit-and-run you HAVE to swing. I’d like to think a hitter as great and experienced as Pujols would be able to push the potential distraction aside.

What’s jarring about this discussion is the player under discussion. A certain Hall of Famer who put on the show of a lifetime a few nights ago. I’m a Pujols fan and hate to say this, but except for Game 3, he has stunk out the joint in the series.

All of this is ignoring the potentially increased ground ball BABIP on the hit and run.  At least, commentators always talk about “opening up the hole” on the right side.  That would increase the benefit of the H&R.  Pujols has hit the ball to the 2B for an out 388 times in his career (5.2% of PAs, 7.5% of BIP). Putting that in context of Rally’s numbers, that’s as many as 43 extra hits.  That’s obviously a high estimate, since it includes pop-outs in addition to ground outs.  But it adds to the case in favor of the H&R there.

I was of the opinion the the H&R was bad because the extra base seemed worthless, but it seems the play is really about lowering the downside.

1) We’ll never know why Pujols swung at that pitch or whether he would not have swung had Craig not been going.

2) I’m sure that isn’t the only time that Pujols has swung at a bad pitch on a 3-2 or other count.  Hitters, including great ones, do that all the time.

3) Dana and others, when the runner is going, the batter MUST swing at more borderline pitches (than if the runner was not going).  That is the CORRECT thing to do.

4) Rally, on 3-2 counts and the runner going, the ML average success rate is 53% (that was from someone else - I did not confirm that).  I suspect that in that situation, it is something like 25% for Craig.  Almost any decent runner has around 20% based on a bad throw.

5) You have to adjust Pujols K and walk rate for that of Feliz, as well as his GB rate on a BIP for that of Feliz.

I like to put lower and upper limits on everything that we can only estimate and then see whether at those limits, the answer is “run” or “don’t run.”

Or alternatively, you can say, for example, “If Craig is going to be thrown out X percentage of the time, the answer is this, and if he is going to be thrown out Y percentage of the time, the answer is that.” That way, you can appease or at least have an answer for those people who say, “You can’t computer the answer on paper because you don’t exactly know (fill in the blank).” My response to that is also, “Well if I can’t know the answer because I don’t know the exact values of all the variables, well, one, I an at least estimate them, and come up with a possible answer, and two, if I can’t come up with an exact answer using the correct model (because I don’t know the exact values of all the variables), you sure as hell have no idea of the exact answer, since not only do you admittedly not have those values either, but you also have no idea of the model to use!”

Larry, right, with the runner going (can we stop calling it a “hit and run”?), presumably there will be more ground ball (and even bloop pop ups) hits, although the ground ball hits to the 2B will be at least somewhat offset by more ground outs on balls hit up the middle.  I think the few extra base hits are really because of the infielder moving…

Let’s call it a run-and-swing.

Its not called anything other than “going on a 3-2 count”. A hit and run is a completely different animal. 

I’m shocked at how many people, including Posnanski, are automatically assuming it was a terrible play.

I think part of the issue may be that some folks are confusing the ninth inning 3-2 pitch with the 7th inning hit&run allegedly called by Pujols.

Whether was the right call or the wrong call, Pujols has to swing at the pitch over his head in the 7th inning, and should have taken the 3-2 in the 9th, though the former is the greater error. Swinging at bad pitches happens to even the greats once in a while. It’s just ironic in this case for the two to come in consecutive at bats, and he was wrong both times.

MGL, I think the view of that play is also influenced by some of the other moves during the game, namely Craig running on the pitch earlier. The reality of the situation is that the 3-2 running on the pitch is likely not as risky or dumb as we make it out to be.

I freely admit that I think it’s a completely unnecessary risk because I have a strong, very strong, preference to let my best hitters hit without being cute about it. If I lose with them at the plate, I can deal with that, even though I hate losing.

If I thought the quantifiable positive gain from Craig running was anywhere close to the negative of him being thrown out (i.e. ~50/50), then I might understand taking the chance (even then the risk is likely too high for me, given who is at the plate and who is coming up next).

But, based on my reading and experience, I feel that the positive/negative ratio is more along the lines of 15-25%, which for is a big “no way” in Game 5 of the WS, especially given what has already happened with Craig earlier.

IIRC, Pujols fouled off more than one pitchch with 2 strikes. Doesn’t fouling off multiple 2 strike pitches increase the likelihood of the batter chasing out of the zone on an upcoming pitcch?

I don’t recall where I heard or read this. I also don’t know where I could check the data to see if it’s true but the idea is that the batter gets locked into a “protect the zone” mode and expands the zone for himself.

It could be another aspect to consider (or not).

Would we also need to consider career 3-2 count results for Pujols and Fekiz or would that just be SSS?

Oh apologies. Had this window open while I worked on that matrix and there’s a few more comments now. I think some of these probabilities can fit right into the matrix.

Where did my other comment go? Anyway, here’s the matrix that Jack Moore and I came up with… does it describe all the probabilities of the situation? would they all add up to one?

Wow. Full comment fail.

Here’s the matrix

http://yfrog.com/od7fydj

"Would we also need to consider career 3-2 count results for Pujols and Fekiz or would that just be SSS?”

I’d probably use their overall numbers adjusted for league-wide 3-2 numbers.

What I was interested in things like this:

Feliz 3-2 count: ~100 PA, 25% BB, 25% K, 50% BIP
Pujols 3-2 count: ~900 PA, 26% BB, 15% K, 59% BIP

I don’t know how much to regress to league average, or how to combine the two along with league average data to figure what % of the time Pujols should K in that situation ... and then combine it with the leverages of the possible results to “% positive” for having Craig run versus “% negative”.

Just guesstimating, but maybe around 75-80% of the time Pujols walks or puts the BIP, meaning that Craig is able to coast to second, remain on base due to a hit, or retreat on a fly ball ... and then ~20% of the time he K’s or lines out, etc where Craig is at high risk for making the second out?

-------------------------

Really what I was initially interesting in was how/if being in a 3-2 count change Pujols’s “swing %” (zone/outofzone, contact/miss, etc).

@Circle Change : I believe our probability matrix answers your question (although I admit it’s not ‘solved’.

The ten variables are Pujols’ swing percentage, probability of a BIP that is a single, probability of a double, triple, HR, probability of contact, Craig’s SB success rate, probability of a good ball in play, probability of a ball, and probability of a bad ball in play air. (Bad ball in play ground is 1 minus that last one.) It does ignore Feliz’ probabilities.

Those eight base state probabilities (the left side of the equations) should add up to one, allowing you to solve for “B,” or Craig’s stolen base percentage. If all the variables are correct. And the likelihood we made an error in there is high, admittedly.

One thing that I found interesting in diagnosing the break-even point on the first steal is that I don’t think I’ve seen much research on ‘true talent’ stolen base percentages. So if you have a break-even point, even if you use a career stolen base rate for your player, it’s unclear how much you regress that to the league average.