THE BOOK--Playing The Percentages In Baseball

Awesome stuff Tango - I can’t believe it is so close to the Markov approach ... I’ll probably give it a crack for 2005 data

Article has been updated.

Updated again…

I recommend reading this thread, as some people are trying to create the RE matrix based on this thread:

http://www.baseball-fever.com/showthread.php?t=41206&page=4

Tango,

This is excellent stuff.  When I learned that the RE charts in The Book were based on Markov chains, I wondered how you did that. This helps answer that question.  Thanks very much.

Are you familiar with the DLSI model?  It’s mentioned in the book “Curve Ball”.  With it you can take OBP, 1B%, 2B%, 3B%, HR%, BB% and produce a run distribution that is pretty close to observed events.  I’ve been tinkering with it to produce run distributions for all base/out states, which can be used to develop RE charts for parks, and, more interestingly, lineups.

Thanks again,

DM

DM, I read Curve Ball, but I don’t remember seeing that.  In any case, the authors are right, and if you follow my model to completion (repeating the steps for doubles and singles), you will get it.  I actually wrote a Javascript program that does it, so I should post it here soon, and everyone will also have access to the source code too.

You will have the problem that SB, CS, PK, BK will not be included.  As well, the program I wrote gives you the option to change the chances of moving the runner over an extra base on a single or double.

It’s pretty cool stuff, and I think once I release the source code, that others can pick up on it, and enhance it.

I also recommend reading what http://www.stat.harvard.edu/People/Faculty/Carl_N._Morris presented.  (I suggest you click the last link, and then right-click the 2nd link, save-target-as to your hard-drive, and then open it with your text editor, and make sure you put “wrap”.)

I read that a while ago, but I seem to remember that he forced in something like a single always advances a runner 1 base, and a double 2 bases.  Anyway, what he does is 95% of what I do.

Thanks, Tango.

The DLSI model assumes runners on 2B score on singles, but all else advance one base on a 1B and 2 bases on a 2B.

Dan Fox has written some articles for Hardball Times earlier this year (he’s now with BBPro) with averages for baserunner advance (e.g. 46% of the time a runner on first gets to third on singles to RF).  I wonder if we could work those averages into the model somehow.  I’ve been using rough figures like that to allocate RE value among batters and runners on base hits with runners on.

DM:

http://www.tangotiger.net/destmob.html

You would definitely use those numbers to figure out linear weights, and your Markov chain.

I expect to release my simple Markov program (including source code) for all to use and expand under some open source licence.  Hopefully, I can get to this within a few weeks.

I’m thinking I’ll include this licence:

http://creativecommons.org/licenses/by-nc-sa/2.5/

Tango,

Great post!  When I too purchased the book I was wondering how you did it with Markov chains.

I’m looking forward to the Markov program; it should be a useful tool!

When you mention Markov chains in the book, you say that they are particularly helpful beacuse you can change the input (in other words, you can put in Rivera, Papelbon or any other pitcher).  Other than finding out the “chance of scoring/winning” probabilities with these pitchers, what else can the markov chains tell you in terms of analysis/evaluation when changing the input to a major league pitcher?  I know DePodesta used markov chains to find values for the the 24-base out situations (which originates from a long time ago and is nothing new), but when you put Rivera in as your example, can the markov chains tell you anything else that a GM would want to know?

Not sure if you saw this post or not, tango.

The RE matrix is at the heart of everything baseball.  From the RE matrix, you can generate a win expectancy (WE) matrix.  The WE matrix is required to analyze in-game strategies like bunting and stealing.  Against certain pitchers or environments, the RE matrix will tell you how much each event is worth, to the point that player A might be a better option than player B in certain environments, and vice-versa in others.

Through the miracle of thread necromancy…

During the section on scoring from third with one out, you say:

1 - .553 = .467

Which is a typo; it should read .447.

Using (largely) this method (a few subtle tweaks here and there, like including WP/PB data) gave me this:

http://www.editgrid.com/user/cwyers/run_expectancy_all_years

I finally punted on working out a better estimate of scoring from third base on an out; the only method I came up with for it essentially coincides with the Retrosheet years entirely. Now I just need to work out what to DO with these.

Great Job!

Wasn’t SABR Matt looking for something like this a few years ago? What does necromancy mean? One of the songs on Rush’s 1975 album, Caress of Steel, is called “The Necromancer” It is one of my favorite Rush songs.

Look at the RE from the bases empty no out state from 1894: .851 runs. In 1930 NL, the REOI with a runner on 1st and 0 outs is 1.113 runs.

If you estimated a frequency table for each event in the 24 base-out states, you could calculate LW for every season dating back to 1871. Easier said than done, however.

Necromancy is, broadly speaking, magic having to do with life and death. More specifically, it’s the raising of the dead.

I can’t for the life of me figure out how to do this. Or I should correct myself and say I’ve figured out two ways to do this, and neither of them seems appropriate. The first is to just use a state-to-state transition matrix from the Retroera to determine the value of each event. I guess that would “work” if you were willing to accept that level of imprecision.

The other method involves estimating the frequency of each state from the available data - how ofen a PA happens in each state, essentially. The “problem” is that once I’ve estimated that I’m not sure I need the run expectancy matrixes I’ve calculated, because essentially by that point I’ll have a full Markov model!

(The problem is that you can’t sumarize the odds of the bases being loaded as:

Odds of runner on first * odds of runner on second * odds of runner on third

Which was what I was doing. This should have occured to me when I was figuring out these things in the first place. So essentially, in order to estimate all of these things properly I essentially have to build a Markov, I think. And once I’ve done that, I don’t need the RE tables from above, because I can build them from the state-to-state transition matrix. I could be wrong here.)

I’ve read a couple of books by Frederic H. Myers, including “Human Personality and It’s Survival of Bodily Death”, and I don’t recall coming across one reference to necromancy.

After thinking about your historical RE tables for a couple of days, the main problem I see with trying to derive LW from them is accounting for the advancement value of hits and batting outs. It’s not hard to figure out the “getting-on” value for each event. That component can be figured from the RE table. Do we have any idea how often a batter went from 1st to 3rd on a single during the 1880’s: 70%, 60%, 50%, 40%?

A lot of it can be assumed - some things, like going first to second on a batting out, seem very stable across the entire Retro era. Some seem a lot less stable, like scoring from second on a single - runners are less likely to take chances like that in high run-scoring environments.

Colin - Is it just that the runners are less likely to take chances or is there a different distribution of the type of singles (infield, ground ball through infield, fly ball or line drive) that may be affecting the rate of 2nd to home on a single?

It goes in the reverse direction for it to be that. If that was the case, you’d see MORE second to home on a single in the modern era, when in fact what you see is more runners holding up at third.

Colin - Are you guessing or do you have examples that you can show me from high run environments (around 2000) and low run environments (mid 60s)?

I ran the numbers year by year from the Retro database. I don’t have them available right now, but I’ll see what I can do tonight.

Here are numbers from a medium environment (4.3) and a high one (probably almost 5.0):
http://tangotiger.net/destmob1.html

Note that pre-1974 or so, you have to be careful with the PBP.  You won’t necessarily have it correct when it shows the guy went to 2B on a single.  Alot of times, Retrosheet doesn’t know.  So, they will PRESUME he ONLY went to 2B, even if he might have gone to 3B.  And so, a single with a guy on “2B” might be a single with a guy on 3B.

I been trying to follow this with 2007 data.  Here’s what I have so far

Innings 43425.2
Home Runs 4957
Runs Scored 23322

My first line is correct I think.  It reads:
.537 .288 .109

Now to get the next line I need to add .398 .276 and .134 to these numbers?  How do we know that 39.8% of runners score from 1st with no outs?  And when I do that it gives me the line:

.935 .564 .243 respectfully.  Is this correct?  It seems these numbers look a bit high?  Looking at the RE table on BP for 2007 I get

.926 .542 .235

Your figures are going to be a little high, because of some data you’re leaving out of the equation. Try this:

(IP*3) - (AB+SF+SH-H-ROE)

For 2007, that gives you:

(43425.6 * 3) - (167783 + 1540 + 1441 - 44977 - 1746) = 6235.8

That’s an approximation of how many outs on base there were. We have DP and CS data:

3985 + 1002 = 4987

That gives us:

6235.8 - 4987 = 1248.8

That’s (roughly) how many outs we’re undercounting in this analysis, as well as runners who aren’t scoring.

Ahhh thanks.

You can’t use the 39.8%.  The first thing you have to figure out is the chance of scoring from 3B, 2 outs:

In short, your chance of scoring from 3B = batting average + error average + “3 consecutive walks” average

The batting average is whatever it happens to be for the league (make sure to count SF as a regular out).  It was .267 in 1994.  The error average is typically around .015.  The do-over plays occur 10% of the time, which means 3 consecutive do-over plays is .001.  So, the chance of scoring from 3B with no one else on and two outs in 1994 is .283.

So, start from there…

Yeah.  After writing that I read down a bit futher and saw that. Thanks

Looking forward to seeing your RE chart…

Looks like Colin implemented the above in SQL:

http://basql.wikidot.com/run-expectancy-without-play-by-play

Great job!

I forgot Colin implemented this.

***

I noticed I made one mistake.  For chance of scoring from 3b and 2 outs, I said this:

Of the various base/out states, the easiest one to figure out the chance of scoring is the man on 3B, no one else on, and 2 outs.  What has to happen for this runner to score?  Well, the batter has to get a basehit, or reach base on error.  If he’s out, the inning is over.  If he walks or is hit by a pitch, it’s a “do-over”, unless you get three consecutive “do-over” plays.

In short, your chance of scoring from 3B = batting average + error average + “3 consecutive walks” average

The batting average is whatever it happens to be for the league (make sure to count SF as a regular out).  It was .267 in 1994.  The error average is typically around .015.  The do-over plays occur 10% of the time, which means 3 consecutive do-over plays is .001.  So, the chance of scoring from 3B with no one else on and two outs in 1994 is .283.

That’s incorrect.

It should be:
(hits + error) / (pa - walks - hitbatter) + .001

That’s because a do-over doesn’t count.  It’s like a 2-strike foul.

Bumping…

I’m trying to get to the probability of the runner on 1st (2nd and 3rd empty, no outs) scoring, the 39.4% here.

Is it enough to check if in those cases the total number of runs until the end of the inning is greater than 0 or not, at least if there are no baserunning, non-PA related outs in the remainder of the inning?

If that particular runner was out in a force out, and a run subsequently scored, isn’t that outside of the number that represents 0 outs, bases empty, the .555 here? Because in this case, it would be safe to trust the scoresheet information, namely that the forceout would have been a regular out without the particular runner on 1st.

In CWEVENT, Ted tracks the runner to the end of the inning.  There’s a field called something like RUN1_DEST_ID.  Something like that.

_DEST_ID fields track the runner for that event only. _FATE_ID fields track the runner to the end of the inning.

Also, Retrosheet uses a destination of 5 and 6 to account for unearned runs (IIRC, 5 is for unearned runs, 6 is for runs counted as unearned for the team but earned for the pitcher).

Colin, ah, thanks for the correction.  I should have known better than to say something without checking it first.

Thanks for the answers. I wish I was doing retrosheet It’s for my local amateur baseball league in Germany, and all I have is scoresheets from 15 games, involving just my own team, and team stats for my own and another team, accounting for 21 of 45 games in 2010.

My strictly empirical RE24 looks like this:
0 1 2
--- 1.62 0.85 0.22
X-- 2.50 1.52 0.33
-X- 2.11 1.44 0.45
--X 2.94 1.44 0.52
XX- 3.89 2.44 0.40
X-X 2.29 1.22 0.40
-XX 4.05 2.11 0.79
XXX 3.62 3.80 1.46

The secret ingredients tell me for the first line:
1.84 0.92 0.31
due to 0.02 HR/Inning.

Can you run it here and report back:

http://www.tangotiger.net/markov.html

I got this:

10.611 : Runs Scored per Game

Chances of Scoring
Event 0 outs 1 out 2 outs AVERAGE
1B/BB 0.612 0.416 0.191 0.406
Double 0.721 0.540 0.313 0.525
Triple 0.891 0.732 0.352 0.658

Run Expectancy
Bases 0 outs 1 out 2 outs
xxx 1.179 0.599 0.196
1xx 1.791 1.014 0.387
x2x 1.900 1.139 0.509
xx3 2.070 1.331 0.548
12x 2.580 1.622 0.733
1x3 2.696 1.768 0.761
x23 2.806 1.893 0.883
123 3.521 2.447 1.213

Obviously, because of catcher skill, the overall number runs is significantly lower (there are 16.54 runs per 9 innings). Average SB/CS is somewhere around 10/1, and there are a lot of PBs and WPs.

Your empirical of 1.62 runs per inning means 14.6 runs per 9IP.

If Markov is saying you should get only 10.6 runs per 9IP, then clearly alot of non-batter events are happening.  (Do you count reaching based on error as a single?  You should for Markov purposes.)

Because of that, you should modify the baserunner movement numbers alot higher to account for things like SB/CS being out of whack.  Instead of runners on 1B moving 30% to 3B, bump it up to 60% or 70% or something.

Play with those movement numbers until you get 14.6 runs per game.  Once you do that, then you’ve got a more realistic RE chart.  Try it and report back if you can.

The 1.62 runs per inning contains a lot of selection bias (my team’s good pitching and defense, and some scorers don’t properly note the sequence of non-batter events, and I can only safely reconstruct the low-scoring innings there). Using team stats I get 1.89 runs per inning.

With ROEs as singles (I could check for ROE doubles), and all extra base values except for ended innings at 1 I get this:

15.644 : Runs Scored per Game

Event 0 outs 1 out 2 outs AVERAGE
1B/BB 0.791 0.588 0.247 0.542
Double 0.887 0.634 0.385 0.635
Triple 0.978 0.884 0.385 0.749

Bases 0 outs 1 out 2 outs
xxx 1.738 0.903 0.281
1xx 2.529 1.491 0.528
x2x 2.625 1.536 0.666
xx3 2.716 1.786 0.666
12x 3.444 2.183 0.935
1x3 3.510 2.384 0.935
x23 3.606 2.430 1.072
123 4.432 3.108 1.444

Great stuff.  If you need an RE chart for that kind of run environment, that’s what you should use.

Since you said your team scores 1.89 runs per inning (though “empirically” you get 1.62).  I’m not sure what that means.  If you have your total runs and your total innings, then that’s what you should work toward.  You should exclude in your counts the bottom half of any last or extra innings.

Breakeven success rate on stolen bases is around 94%

Crazy

Going from 1st to 2nd or 2nd to 3rd gains only 0.1 runs with 0 outs.  If the player is caught stealing, the RE drops at least 1.6 runs.

Note that this basic Markov does not include DP.  So, that could be a big limitation possibly.

DPs on the ground are very rare, in fact I can’t remember one between 1st and 2nd. A good 1B has once thrown out a runner going from 2nd to 3rd after a GO last season.

My team had a SB-CS of 136-10.

Yeah, this explains (though it isn’t a good excuse for that) why I was fuming at my basecoach ordering a double steal and I was thrown out at 3rd, in a blowout win nonetheless.

The 1.62 figure is from scoresheet information of games involving my team only, excluding incomplete innings, and as written above, badly scored innings, the latter usually high scoring. I compared the runs to the end of the inning to the extremely small sampled RE.

Those are the only scoresheets I have right now.

In addition to that the offensive and defensive stats of another team (out of 6) are on the internet. Out of 45 total league games I have data for 27 games (15 games for each of the two excluding the 3 head-to-head meetings). That’s where the 1.89 is from (although incomplete innings are obviously not excluded here, I could do that for the games of my team only though).

xxx 1.738 0.903 0.281
1xx 2.529 1.491 0.528
x2x 2.625 1.536 0.666

Steal with 0 outs = +.104
CS with 0 outs = -1.626
breakeven = 1.626 / (1.626+.104) = 94%

Steal with 1 outs = +.045
CS with 1 outs = -1.210
breakeven = 96%

Steal with 2 outs = +.138
CS with 2 outs = -.528
breakeven = 79%

If your SB/CS numbers are 136-10, that’s 93%.  Your fast guys should be stealing ALL THE TIME with 2 outs. (*)

(*) Of course, we really should be using win expectancy not run expectancy.

Big thanks for the useful linear weights. And the big responsibility to explain to my teammates why wOBA is better than batting average. I may dive into the secret recipes again soon.

In your case, you’ll have a much different wOBA equation.  The HR weight and BB weight will both be closer to 1.