THE BOOK--Playing The Percentages In Baseball

MGL, Brantley sounds like he’s from the church of walk = plate discipline. I’ve maintained for a while now that it’s just as disciplined to take a fastball down the middle of the plate and put it in the bleachers.  He’s also commiting a minor version of a gambler’s fallacy in his comment.  A batter should make a mental calculation of how likely he believes that the next pitch will be a ball, and base his decision on that probability.  That calculation would be based on previous performance (historical) and what he’s been doing lately (so looking at the last few pitches is fine), but expecting a “run” to continue in a nice linear fashion is a losing game.  When does a “run” start?  4 balls?  Suppose a coin comes up four heads in a row?  Would you keep calling heads indiscriminately?

The other thing to consider is what usually happens to the ball when the hitter at the plate puts it into play.  Do I want my .067 hitting pitcher taking 3-0?  Of course.  Pujols?
Pujols when he knows a fastball is coming to the middle of the plate?

The one difference between a the gambler’s fallacy and this situation is that this situation is not a random process.  Throwing a strike is a difficult thing, and if a pitcher is struggling badly with his control (which was the case in this situation), then it might, in fact, be more likely that the next pitch will be a ball.  The context of the situation does matter.  It is not the same thing as a coin flip, which is always random.

If a pitcher is struggling with control, my take advice is to look for one specific pitch in one specific location, but otherwise lay off it. 

But hey, what do I know.
-j

Your’re right on with the fact that a coin flip is random while pitch result isn’t.  I was more referring to the small sample size there.  Your strategy seems about right though.

Mgl - There is an important reason to take a strike that you didn’t list.  If the pitcher has thrown a pitch that you aren’t prepared to hit for a base hit.  There are some pitches that are in locations or pitch types that a batter knows that he can’t hit with authority.  Unless he already has two strikes he is better off taking a strike than putting a weak ball in play.

what’s harder to get on 3-0? A walk or a hit? Perhaps those numbers should be looked at first. Because there’s 2 possibilities that I think are most common with 3-0 counts.

1)Pitcher is having control issues - most likely can’t find the plate. Take.

2)Pitcher is just trying to nibble and has missed. Since he knows you’re probably taking on 3-0, he’s going to throw a meatball up there at 80% just to get the free strike - he’d be nuts not to.

So if the pitcher doesn’t look to be having issues, I think it’s nuts for even a decent MLB hitter to be blindly taking on 3-0. If that pitch is anywhere near your happy zone, SWING DAMMIT. Drives me crazy to watch 3-0 counts and the hitter is backing out of the box as a weak fastball floats across the middle of the plate.

The luxury of 3-0 is that you can decide to swing at “your pitch” - a luxury you don’t have with 2 strikes, since you have to protect the plate.

As I said initially, I think that in most cases, after a long string of balls, the probability of throwing a strike is quite high, since the pitcher is often going to throw a fastball in the middle of the plate.  That is true even if the pitcher is indeed “having” trouble with his control and that is likely to continue (which I am not sure it is).

There is some game theory involved.  If I am a pitcher and I just threw 8 balls in a row, I KNOW that the next batter is NOT going to swing at the first pitch, so I am literally going to throw a batting practice fastball right down the middle. If batters start to swing in that situation (which they surely should), then I cannot throw that pitch. Luckily for the pitcher, the batters are generally using such a suboptimal strategy, that I don’t have to worry about game theory.

There are so many ways a sabermetric approach can help a team.  One of these days, I am going to try and quantify how much it would be worth to a team to play perfect “basic strategy” versus the average player/manager/coach, or even the best one.

Let’s not forget that one of the main reasons why batters do not swing at pitches after a run of balls is that, as Brantley actually said during that game, if they were to pop out or weekly ground out, or G-d forbid, hit into a DP, they would be crucified by their manager and teammates.  Much of bad decision-making in baseball and in life is about risk avoidance or simply “looking bad” in the eyes of others.  Sometimes risk-aversion is a good thing and sometimes it is only in our heads that it makes a difference.  For example, if a batter were to swing at a pitch after a run of balls, perhaps he loses his starting job or gets a reputation for being a “maverick.” Who could blame him for not using an “optimal strategy.” IOW, one man’s optimal strategy is another man’s suboptimal one.  Depends on your perspective.  My perspective in analyzing baseball is usually from the standpoint of maximizing a team’s chances of winning the WS, getting into the playoffs, and winning the game, in that order.  That does not always equate to someone else’s perspective, such as the manager’s, owner’s, player’s, fans’, etc.

I looked at the sequence of pitches for all pitchers in 2006. I did not count any bunts or bunt attempts or any intentional balls.

Overall, .371 pitches are balls and of the .629 that are strikes, .274 are called.  IOW, 46% of the pitches are swung at.  Of course, many of the pitches that are swung at are actually balls, so that .371 does not represent how many pitches overall would be balls if none were swung at.  It is probably closer to .45 pitches overall are out of the strike zone (20% of all swinging strikes are at balls?).

Anyway, after 4 balls in a row (and sequence of 4 balls), the next pitch is ball 41% of the time.  However batters are swinging at 29% of the pitches, so again, some of those are balls, maybe another 3% (10% of the pitches swing at are balls?), so that makes 44% balls after 4 balls in a row, around the same as overall.

After 7 balls in a row, batters are still swinging at 14% of the next pitch.  Pitchers are throwing only 36% balls, so if batters are again swinging at 10% balls, that means that pitchers are throwing only 37.4% balls after 7 balls in a row, which is better (more strikes) than overall and better than after 4 balls in a row.

Here is an estimate of the strike % after X balls in a row.  I have to estimate what percentage of swinging strikes are balls.  I am assuming that it is somewhere between 5 and 10%, and the less often they swing, the less often they swing at balls.

# balls in a row est. % balls in zone by pitcher

overall 58%
1 62%
2 65%
3 65%
4 57%
5 64%
6 63%
7 63% *
8 68% *
9 63% *
10 or more 56% *

* Small sample sizes

I don’t know why there is that “blip” after 4 balls in a row, other than it tends to be on the first pitch after a 4 pitch walk.

In any case, it certainly appears that after any ball, the pitcher is much more likely to throw a pitch in the strike zone.  It also appears that the number of balls thrown in a row is not a predictor of the chance that the next ball is a strike or ball.  It may be that several balls in a row suggests that a pitcher is going to be wild on the next pitch (or that he is simply a wild pitcher) but that his desire to throw a strike on the next pitch cancels that out.

It also appears that batters do in fact swing at quite a few pitches even after a bunch of balls in a row.  Here are the numbers:

Balls in a row % Swinging at the next pitch

overall 45.7
1 51.6
2 51.1
3 31.2
4 28.8
5 34.7
6 29.9
7 14.7
8 31.3
9 18.2
10 33.3

I think we see a little bit of an odd/even pattern because odd sequences tend to be on 3-0 counts.

cephyn, while I agree with you, whether to swing at 3-0 depends on the game situation, especially the runners on base and outs, the pitch recognition ability (how often will he swing at a bad pitch) of the batter, and the batter’s power (for example, if a guy, like Pierre, only hits singles, no reason to swing at 3-0, since a walk is just about as good as a hit, unless there is a runner on second or third).

Certainly, when a power hitter is taking all the way, which you often see, with runners on base, that is usually the wrong thing to do, unless his team is down by a lot of runs late in the game.  Same thing in a tied or one run game with no runners on base, especially with 1 or 2 outs.  The extra base hit, especially the home run is worth a lot of WE, as compared to the walk.

The primary factor in determining the red or green light with 3-0 is the swing in RE between the walk and the ball in play, by that batter.  Obviously the value of the ball in play is determined by the pitch recognition (will he swing at some bad pitches) and power (when he puts the ball in play, what is the average run value) of the batter.

Hmm this also seems like another fairly simliar situation.

The pitchers throws say 4 or 5 balls out of the strike zone.  The pitching coach visits the mound to talk to the pitcher.  I dont have any data to back this up but im willing to bet that the pitch right after the pitching coach comes out to talk will be a strike the majority of the time so the batter should definitely look for that.

I don’t have The Book handy, but this chart will do:
http://www.tangotiger.net/RE9902event.html

Go to the last line, “bases loaded, 2 outs”.  The Leverage Index (LI) for this situation is around 2.7.  So, divide all the numbers you see by 2.7 to get a sense of how it compares to a neutral situation.  HR is 1.22 runs, double is 0.81 runs, single is 0.57 runs, and a walk is 0.39 runs.  In terms of the “hit being worth much more than the walk”, I wouldn’t agree with MGL necessarily here. 

An average hitter should change his approach to relax on HR, and increase on 1B and BB. 

But, more importantly, since the leverage is so high, you want a really good hitter here, which overrides anything else.

Yes, it looks like this is a fairly neutral situation in terms of the value of the walk as compared to the hit.  Of course, it would depend on the score and inning.

Absolutely, the score/inning plays a (huge) role, which is why we want LWTS by game state (or equivalently, a separate wOBA equation for each game state).

To be fair, Aquino (the Brewer pitcher) had completely lost it after he gave up the lead on an RBI single by Philips:

http://scores.espn.go.com/mlb/playbyplay?gameId=270417117&full=1

Here was the pitch sequence in the next AB to Hatteberg:

strike
ball
wild pitch
intentional ball
intentional ball

That loaded the bases for Gonzalez:

ball
ball
ball
ball (went soaring to the backstop)

8 balls in a row (although 2 were intentional), including 2 that the catcher never had a chance of stopping.  It was at this point that Valentin’s AB occurred.

It would be interesting to rerun those “probability of a ball” numbers but only including strings that included at least one wild pitch.  I think you might get very different results.

How about taking a pitch for the purpose of seeing more pitches and tiring the pitcher.  Has anybody studied the effectiveness of pitchers as a function of number of pitches thrown?

That would be particularly interesting if we looked at it in terms of effectiveness after throwing a large number of pitches to a single batter.  You often hear announcers go on about how a terrific at-bat (defined by seeing a large number of pitches) tires out a pitcher either mentally or physically (or both), allowing subsequent batters to get him.

The problem is controlling for other factors...like the probable case that pitchers who can’t get a batter out and thus throw a large number of pitches aren’t likely to be on top of their game.  I’m not sure how to approach it. -j

"The Book” found that starting pitchers actually do a little better than expected the 4th time though the order (when the are likely over 100 pitches), so I don’t know if there is any obvious benefit to taking a pitch to just to take it.  The cost to the batter is probably just too great.