THE BOOK--Playing The Percentages In Baseball

I believe that the WE was 0.4% entering the inning and 0.9% after the Olivo single.

It actually shows a 0.4% chance of winning.  Whoever wrote that must have grabbed the value after Olivo’s single by accident.

I have the historical data here for +/- 5 runs:

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

Here’s what I’m showing for -5 to 0 runs:
-5 0.0081
-4 0.0132
-3 0.0338
-2 0.0790
-1 0.1852
0 0.6540

The sum of that is .9733, which means still 0.0267
chance of winning if down by 6+ runs.

Could we have figured any of those numbers?  For the score tied, that’s easy.  That’s because we should know that 70% of innings are scoreless.  (You don’t know that you say?  Well, now you do.  Remember that number.)

So, 30% of the time, you score, you win the game.  70% of the time you don’t score, it goes to extra innings and you win half those games.  So, 30% + 35% = 65%.  And that goes very well with the .6540 from the historical.

We can also go here:
http://www.tangotiger.net/retrosheet/reports/re.htm

Look at the first line, and that tells you how often you score 0,1,2,3,4,5,6,7,8,9,10+ runs.

The historical is actually .727 chance of scoring 0 runs (the more recent era is closer to .700).  Anyway, 1-.727 plus .727/2 = .6365

How about if you are down 1?  Well, you lose when you score 0 runs (.727), you win half the time if you score 1 (.148 / 2), and you win otherwise (1-.727-.148).  That’s .199 win% expected, compared to the .1852 historical.

Cool?  Ok, so with 6 runs downs, you win half the time if you score exactly 6 (.002 / 2), and win if you score at least 7 (1 minus .997), or .004 in all.

And, that matches what David is reporting from my Markov.

You can ALSO go here:
http://www.tangotiger.net/markov_wes.html

Wes expanded my Markov program to give you the run distribution, and you see there that scoring exactly 6 is .003, and scoring 7+ is 1 minus .996, so you get .0055.  But with all the rounding to three decimal places, I wouldn’t be so fixated on that.

Anyway, as you can see, everything revolves around the run expectancy matrix, and it all makes perfect sense.

How much does playing in Coors field increase the chances of winning this one?  I guess we could look at all innings in Coors to see what % have a team score 6 or more runs.

Don’t forget run environment here. Location, location, location.

Well, the tool is right there for you to use:
http://www.tangotiger.net/markov_wes.html

How to interpret the numbers was explained in post 3.  So, just run it, and tell us the answer!

Home team down by 6, bottom of the ninth. I used the actual NL totals divided by games started, park adjusted, and extrapolated advancement on hits from the league totals. Basically, you hit less, you advance more. I get 5.211 runs/game using this. There’s an 0.4% chance to score six runs, 0.2% to score seven, 0.1% eight—halving the 0.4%, we get 0.3% in all.

How about the real Rox numbers? Using just their home numbers, I get 6.516 runs/game. I get 0.6% of six runs, 0.3% of seven, 0.1% each of eight and nine—0.8%. So we’re more or less in the same ballpark, so to speak.

You know, I’d love for BB-Ref.com to get more detailed baserunning stats, and to be able to dump outs on base and steals into this tool.

Oops. League totals should have been 0.5%. My bad.

It happened again!  This is killing me.

Well, at least the Cards chose the old-fashioned, highly probable way of losing today!  Thank goodness!