THE BOOK--Playing The Percentages In Baseball

Tango—what’s the source for this? Is it actual retrosheet pbp data or is it Markov generated?

I think this was from actual 1999-2002.  And now that I think about it, it’s only innings 1 through 8, excluding partial innings.  I think.

Out of interest here are my numbers for the 2006 season, which are generated from a Markov

       0 out    1 out    2 out Total  
xxx    24.1%    17.0%  13.3%   54.4%
1xx    6.2%    7.3%    7.5%    21.0%
x2x    1.5%    2.7%    3.5%    7.6%
xx3    0.2%    0.8%    1.4%    2.4%
12x    1.6%    2.5%    3.2%    7.3%
1x3    0.5%    1.1%    1.6%    3.2%
x23    0.3%    0.7%    0.8%    1.8%
123    0.4%    0.9%    1.0%    2.3%

Fairly close, except for the 1xx line.  Does your Markov process include GIDP, SB?

Tom, I can very easily update that to reflect 2000-2006 using Retrosheet logs.  Interested?

Sure feel free to post it here, or on a Google Docs.

Yes, it includes both (although SBs are reasonably situational and I don’t adjust for that). I have been wondering about the discrepancy and I think it may be to do with how I treat errors. If there is an error on the fielding play my Markov logs that as a batting play from xxx to 1xx and then a “non-batting” error advancing from 1xx to x2x. I think that accounts for the difference.

For instance assume that that 24% of PA are xxx_0 and single + walk (ignore HBP) are .25 and the out rate is .66—these are 2006 data, pretty much.

Then you get

xxx_0 = 24%
1xx_0 = 6%
xxx_1 = 16%
1xx_1 = 6%*.66 + 16%*.25= 7.9%
1xx_2 = 8.5% (by the same process)

1xx_Y = 22% ish, which is more in line with my Markov than the actual. Of course there are other situations to get in the 1xx state as well that will add and through SB/ force outs/ errors other ways to get out of the 1xx state. This is dynamic rather than the static picture I present above.

Given the difference is between the 1xx and x2x in my model, and given how I account for errors I think that is the issue.

Thoughts?

On second thoughts my error explanation probably isn’t correct. After all the majority of errors on first are those which turn an out into 1xx (from xxx). Errors that allow players to get x2x from xxx after a single will be much more rare.

Hmm. I’m a bit stumped.

Taking out SB/CS changes the % of 1xx by about .3% (up). Taking out GIDP change 1xx % by another .8% (up).

As I said, thoughts appreciated.

Tango—if you are interested I am happy to share my markov with you. The complete version is large but I can send you a cut down version which will allow you to see the logic at least.

Here is 00-05 Retrosheet data

       0 out   1 out   2 out   Total
xxx    23.4%   16.7%   13.3%   53.4%
1xx    5.9%    6.8%    6.8%    19.6%
x2x    1.8%    3.1%    3.9%    8.9%
xx3    0.3%    1.0%    1.6%    2.9%
12x    1.4%    2.6%    3.3%    7.3%
1x3    0.5%    1.2%    1.6%    3.3%
x23    0.3%    0.9%    1.0%    2.2%
123    0.4%    1.0%    1.2%    2.5%

I seem to be having a one man conversation here. No matter it is fun.

I think I can account for the discrepancy between Markov and actual. It is situational hitting. Here is the probability of getting either a single or walk by base state:

xxx    0.234
1xx    0.248
x2x    0.292
xx3    0.308
12x    0.236
1x3    0.278
x23    0.361
123    0.251

xxx    0.093
1xx    0.094
x2x    0.089
xx3    0.087
12x    0.087
1x3    0.097
x23    0.092
123    0.102

The biggest difference is definitely in walks.  The next big one, far behind is HR.  The others (singles, doubles, triples, hit batters) are fairly random, from what I remember.

Yup, you’re right. Walks are a bigger factor than 1B, but 1B aren’t altogether unimportant

       1B/AB    BB/PA
xxx    17%    7%
1xx    19%    7%
x2x    17%    14%
xx3    18%    14%
12x    17%    8%
1x3    20%    8%
x23    18%    20%
123    19%    6%

I’m ok with it, as long as “AB” really means “AB+SF”.

No it didn’t. But below it does

      1B/AB
xxx    17.1%
1xx    19.0%
x2x    17.2%
xx3    17.0%
12x    17.0%
1x3    18.7%
x23    17.0%
123    17.9%
Average = 17.5% ... effect of 1B there but pretty small, as you said it is mostly walks

					
				

The 1xx for the singles doesn’t surprise me.  It’s one of the findings in The Book, especially for LHH. (Not really a big finding, since it’s conventional wisdom.)

Tom—a quick question. In your data how do you account for SB? If a batter goes from 1xx to x2x on a SB even though this is still the same PA I assume you add 1 to the 1xx bucket and 1 to x2x bucket?

I track two items, “n” and “PA”.  So, for a SB, I add 1 to each n-bucket.  But, the PA-bucket is only added once (the end of the PA). 

Saves me the trouble of trying to justify anything by doing everything.