THE BOOK--Playing The Percentages In Baseball

MVN is no more, of course, but the Internet Wayback Machine has a copy of Pizza’s article from StatSpeak here:
http://web.archive.org/web/20080507153539/http://mvn.com/mlb-stats/2008/04/03/how-to-make-your-team-better-by-firing-your-third-base-coach/

At some point I need to republish my own StatSpeak articles.  I have the text ready to go, but I have to dig up the images from archives, and that’s a little bit of work.

I posted this at BPro too, but I’d like your take…

Doesn’t that 85.4% number assume an even distribution of chances?  Shouldn’t we expect that more plays are 100% chances than all others given the geography of the ball field?  And wouldn’t that cause the maximized average (84.5-91.5)to be shifted upwards?

Sure absolutely.  This was purely an illustration.

I’ve seen/heard people make this mistake a lot.  If someone is above the break even point for stolen bases, they say they should steal more and more until they get to it.  Obviously this doesn’t make any sense, because if you’re at the break even point, then you are adding the exact same value that you would by standing pat: none.

The key is, as you illustrated, that it’s a good idea to go if you have a better than 75% (or whatever the break even point is in that particular situation) chance of making it.  This is why it’s hard to critique baserunners and third base coaches based on overall rates.  Obviously, if they are very far from the break even point, as is the case with third base coaches, then it’s pretty clear that they are being too conservative.

I think you need to analyze each attempt, which can be done fairly well with play by play data.

For stolen bases, look at the runner, the pitcher and the catcher to determine an expected succes rate. Then look at the inning, base/out situation and score to get the WPA for success and the WPA for failure, then use the expected success rate to get the expected WPA if an attempt is made in that situation.

Then see, at each expected WPA, the rates at which each manager/baserunner attempts the steal.

Please read this, as it answers the question:

http://www.insidethebook.com/ee/index.php/site/article/chase_utley_sb_wizard/

Yeah, I goofed on the break-even rate.  The split is still way too big.  I buy the idea that there are a lot of gimmes on sac flies.  If that’s screwing with the distribution, that’s fine.  In that case, if there are a bunch of gimmes, then some of the send rates look even that much more silly.

73.2% was the break-even rate using the run expectancy matrix assuming you started the PA with a runner on third and no outs.  The StatSpeak article goes into more detail about my contention that just about all situations call for the sending of the runner.

"Here’s an interesting one: What would happen if third-base coaches just sent everyone, playground-style, on these potential sac flies, regardless of whether it was a good idea? It turns out that teams probably would score more runs than they do now.”

That is a fantastic assertion, if true, and I would not be surprised if it were.

So, Tango, we should be seeing Toronto and Seattle sending runners left and right?

Speaking of faux pas from article:

“If offered the chance to lay $1 on a heads-tails coin flip with the chance to win $10, would you take the wager?...Because if you play the game long enough, you have a chance to come out slightly ahead.”

Slightly ahead?  Long enough?  You would be A LOT ahead very quickly of course, getting 10-1 on an even money proposition!

I think he meant to write “laying $9 to win $10” or something like that.

Anyway, good article for he mainstream…

"Indeed, it was rare that it was a bad idea to send the runner, even after controlling for the distance of the fly ball and the speed of the runner. It was almost always the case that the chances of the runner succeeding were above the break-even point.”

We don’t know what “rare” means, but surely there are plenty of short fly balls and slow runners where the success rate would be far less than 70% or so…

Great statspeak article.

I think Wally’s point is spot on though.  This regression is going to overestimate the chances of the runner making it at different OF distances since it’s only looking at situations when the runner was sent.

I can understand why (and believe you, of course) distance is by far the most important variable but I do find it hard to believe that 3 other variables aren’t important in on closer plays:

1. OF arm
2. Runner speed
3. OFer direction (is he coming in on the ball, moving laterally or going back on the back when he catches it).

Distance from home would, of course, be correlated with OFer direction.

I’d definitely like to see a follow up with all of your research; I think this is really interesting stuff.

I can’t read the ESPN article because I am not a subscriber, but the StatSpeak article was terrible.  All of the points brought up by Wally and BW in the comments to that article were correct, but they were basically ignored by Pizza.  The bad methodology led to an erroneous conclusion which was made worse by the hyperbole of the title.  With articles like these it’s no wonder that real baseball people think we are stupid.

The only truth in the original article was that attempting extra base advancement is almost totally dictated by the situation, with the distance the ball was hit being the most important factor.  But as J. Cross mentioned above, whether the outfielder had time to set up under the ball and be moving forward as he caught and threw the ball, instead of running laterally and have to stop, set himself and throw flat footed, is another important factor.  So is the score.  There is not much value to be gained by running when you are 4 or more runs ahead or behind, particularly if you factor in the risk of injury on a play that almost requires either a slide or collision at the plate.

Using Gameday hit ball locations when the ball caught over 275 feet from HP with one out the runner attempts to score from 3d 98.9% of he time and is successful 98.9% of the time.  He only remained on 3d 37 times in 5 years. Here is the full 1 out table:

DISTANCE----SCORED----ON_3d----OUT----TOTAL
OVER_275-----3202------37------31-----3270
250to275------1005-----175------75-----1255
225to250-------320-----451------62------833
UNDER225-------70-----345------13------428

Well given that for the third base coach the payoff for successfully sending the guy (either on a potential sac fly or when taking extra bases on a 1B or 2B) is next to zero and the penalty if the guy is out is usually quite harsh he would have to be a fool to NOT be conservative.

If you want your third base coach to make the right decision you better make his payoff matrix closer to the teams payoff matrix. Give him cash bonuses for each runner scoring from first on a double, each runner scoring on a sac fly etc and I am sure you’ll see more aggressive behaviour.
(Obviously you need to perhaps make it more sofisticated than that, but you get the general idea.)

Looking at Peter’s table

           ATT  SAFE


OVER_275  .979  .990


250to275  .801  .931


225to250  .384  .838 


UNDER225  .164  .843

Being safe 84% of the time when attempting to score on a fly ball of less than 225 feet does not mean that there is an 84% of scoring on all flies of that distance. The runners only attempted 16% of the time when the coach thought the chance of success was above the break even point. The remainder of the time the chance was too poor so they did not attempt.

As in my post above, they used the situation of each play (runner’s speed, the outfielder’s arm, the score, etc) to judge the benefit of scoring vs the cost of being caught. When the coach decided the chance was worth it there was an 84% success rate.

Tango’s method looks fine as a shortcut, but it only looks at the ‘true’ success rate of the runner derived over a large sample size. If we are to model reality, those real decisions are made by judging the cost/benefit of each opportunity. You look at the score, at the arm of the defender, etc in addition to the speed of the runner.

I noticed a similar thing in the baumer jqas baserunning paper.

He has mlb data on the proportion of attempts and success for the following

going from 1 to home on a double 93% success
2 to home on a single 95%
3 to home on a fly ball 96%

All of these rates are very high for what is the same decision. (stay on 3rd or try and score but risk an out.) with a breakeven point around 73%

What we need is the range of probabilites of success for different classes of oppertunities to determine if you were more agressive and ran in less likely situations when does the cost-benefit ratio turn negative e.g chance of success for a class of oppertunities drops below 73% (or whatever figure you calculate depending on run environment and number of outs).

So I agree that there are gains to be made if people were more agressive when base-running

More interesting is his data on staying on 2nd or going to 3rd

2 to 3 on a fly ball 87%
1 to 3 on a single 96%
stealing 3rd 69%

This is much more surprising as while base stealing is probably at the break even point overall and you can use game theory to explain why it is not higher than the break even point. why is the success rate so high on fly balls and singles?

Although there is no game theory aspect to these decisions to encourage lower probabilitiey attempts I still think it could be down to 3rd base coaches being too conservative.

James

James: there are no gimmes in basestealing.  Everyone is starting from the same spot.

There are plenty of gimmes in advancing an extra base.  When a runner is rounding a base, the ball could be anywhere from hitting the wall to already in a fielder’s glove.

This is good data:
225to250 .384 .838

And it follows to what I was saying in my illustration.  Imagine that at this distance, there are no gimmes, and so, you have one-third at 85%, one-third at 73.2% and one-third at 50%.

So, you send the runners 100% of the time at 85% and you send the runners 15% of the time at 73.2% and runners 0% of the time at 0%.

The overall average?  83.5%

I swear I got lucky here with my initial illustration.

And, sending a runner 0% or 15% or 100% of the time at 70-76% is the same call.

I think you can illustrate like I do that the coaches are sending the runners the right way.

Tango - Yes, as I put the table together I noticed how well it fit your illustration.  I think you diagnosed this one perfectly.  I also think the 3d base coaches are doing a pretty good job.  I am sure that more err on the conservative side, but not often enough to cost a team more than a couple of runs a year at most.

Brian - I made an error with 70 that scored from less than 225 feet.  27 of those were times that Gameday had not recorded distances on the hit balls and so they were showing up on my query because I forgot to check for 0s.  And another one that has the center fielder catching a fly ball on the infield grass near third base appears to be a transcription error.  So that leaves 42 in 5 years.  5 of the 42 are catches by shortstops or second baseman instead of outfielders.  I bet that if you looked at video on the remaining 37 that almost all of them would be diving catches or collisions where the outfielder held the ball but could not get up immediately and make a throw.

It seems that someone writes this article about once a year.  It gets thoroughly knocked down.  And then a year later someone writes it again.  Very odd.....

It’s especially odd that many saberists assume 3rd base coaches are too conservative, while it has also become nearly conventional wisdom that baserunners on first are too aggressive in attempting steals of 2B.  Why would “the book” be too conservative in one case but too aggressive in the other? 

In fact, I’m quite sure both assertions are either wrong or true only at a trivial level. Runners are sent at such a high frequency that there simply can’t be much to gain here, as Peter suggests.  And once you account for extra bases gained and DPs avoided when the ball is put in play on SBAs, the extent of “over stealing” by teams is greatly diminished.  But the urge to find fault with baseball decision-makers can’t be restrained.

To really answer whether 3rd base coaches are too conservative, I think you’d have to compare the success rates of very conservative and very aggressive coaches (while trying to control for speed of runners).  See how many extra runners the most aggressive coaches send, and then infer the success rate of those marginal attempts by comparing the overall success rates.  My guess is you’d find that the marginal attempts are roughly a break-even proposition, which if true would mean that sending all runners would in fact cost you runs.

Guy, one thing I noticed in The Book was that for basestealing of 2B, the ACTUAL (overall) breakeven point was 69% even though the RE chart says 72%.  That’s because the game state is important, and you can lower the breakeven point by selecting situations where the cost of getting caught isn’t so high.

So, yeah, you really need to break this down, similarly as Peter did.  And, it would certainly help if the stringers would tell us when the ball is actually in the throwing hand of the outfielder.

Similar to hang time for a flyball, I need to know when the ball is actually in the throwing hand.  We don’t have this problem with catchers, because a pitch is going to be around 85-90mph, and the distance between catcher and pitcher is static and between catcher and 2B is static.  So, we don’t need to really know all that (though it would still be good to have).

For OF though, so much can happen, slides, long runs, going back, etc.  What we need to know is when is the OF actually in a position to throw the ball.

Such small things like this, hang time, number of bounces to the SS, ball in fielder’s hand.  That’s what I want.  And, for all of FIELDf/x, this is pretty much what we’re going to try to distill all our information into.  That is, when we create an event record for the one thousand things that are happening, this is what we’ll be recording as the summary.

Third-base coaches have to make gut decisions.  The real-life takeaway is that teams should advise their coaches to resolve borderline cases in favor of sending the runner, especially when the decision involves sending home a runner on 3rd base.

If you want a real-life example to persuade “old-school” baseball people, look at the Angels under Mike Sciosia.  He’s been preaching aggressive baserunning long before anyone proved statistically that it was sound strategy.  And there’s always the “putting pressure on the defense” canard that’s probably false, but impossible to refute.

This seems like an area where old-school and new-school analysis should agree.  Old-schoolers ought to grasp that fear of embarrassment causes base coaches to hold runners when the “right” move is to send the runner and challenge the outfielder to make a strong, accurate throw.