THE BOOK--Playing The Percentages In Baseball

Here’s the number of runs scored, from each base/out state to the end of the inning (i.e., Run Expectancy, or RE).  It’s the classic chart in The Hidden Game, but updated for the Retrosheet years:

0 1 2 1B 2B 3B
0.492 0.262 0.099 — — --
0.870 0.519 0.223 1B — --
1.112 0.684 0.330 — 2B --
1.336 0.940 0.377 — — 3B
1.496 0.922 0.443 1B 2B --
1.750 1.165 0.500 1B — 3B
1.975 1.379 0.597 — 2B 3B
2.348 1.565 0.770 1B 2B 3B

I’ve removed all tie games (though I could have kept those), partial innings, and home half of 9th and later innings.

If you go here:
http://www.tangotiger.net/markov.html
and change the AB figure to “38.7”, click CALCULATE, you can see the resulting RE chart and compare to the above.  They are fairly close, except for the 1B (and that’s because of the assumptions noted on that page).

If I’ve read the charts correctly using Away,0 outs, 0,0,0, the home team has won 64.4% of the time with a 1 run lead after 1 inning, 65.4% with a 1 run lead after 2 innings, 65.4% with a 1 run lead after 3 innings and 67.6% with a 1 run lead after 4 innings. 

Are those figures right?  If so, it does seem that the first inning has more importance than I thought, and that the break-even point for 1 run strategies in the first inning anyways is different than my understanding. 

The figures might also suggest that the strength of the top of the order is very important in the game result, and that this shows up primarily in the first inning score.

The “importance” of any game state is exactly Leverage Index:
http://www.insidethebook.com/li.shtml

I wouldn’t try to look at the gap of win% between scores.  That’s what BP’s LEV does, and it’s the wrong way to look at things.

Same exclusions as the previous post.  The event is typically the same as the Retro event types, with these changes:
- I created an “FC no out” event type, basically splitting code 19 into 19 (min 1 out) and 80 (no outs)
- all events are grouped by the bunt_flag, and if there was a sac situation (man on base, less than 2 outs), which lead to event “bunt” and “sac bunt”

All remaining events match the Retro.  The pickoff isn’t as low as the CS, because some pickoffs(around a quarter) lead to the runner being safe.

The LWTS values were determined based on the Run Expectancy (RE) chart I posted a few days ago.  It was simply a matter of determining the starting state prior to the event, the ending state (plus runs) after the event, and taking the difference.

If ever you wanted a “standard” set of LWTS values, these would probably be it.

LWTS EVENT N
1.402 Home run 161,542
1.033 Triple 40,790
0.760 Double 284,146
0.677 FC no out 5,640
0.479 Error 78,805
0.461 Single 1,113,505
0.371 Interference 842
0.333 Hit by pitch 44,712
0.308 Walk 545,972
0.273 Wild pitch 51,404
0.269 Passed ball 14,016
0.264 Balk 9,069
0.194 Stolen base 106,176
0.174 Intentional walk 52,409
0.129 Defensive indifference 1,379
0.066 Bunt 27,780
0.000 Foul error 2,967
-0.085 Sac Bunt 95,498
-0.236 Pickoff 22,648
-0.270 Out 3535825
-0.274 Strikeout 1,040,637
-0.435 Caught stealing 45,777
-0.436 Other advance 2,260

Tango,

Are those run weights for 1969-92 or for the entire Retrosheet pbp era, 1957-2006?

Thanks.

Everything in this thread and in the main blog entry is the same years (1957-2006, except 1999).

Tango, I’d like to play around with the RC type weights, but I don’t know what the total runs should be.  Do you happen to have the total runs scored or # of innings you considered handy?

809,358 runs

You can somewhat infer the innings, by the “.492” in post 1.  That’d be .164 runs per out.  I’ll report back the exact figure a little late.

4,934,790 outs