THE BOOK--Playing The Percentages In Baseball

Here’s another way to look at it.  Extra Inning games guarantees that the home team bats in the bottom of the inning.  But it still won’t guarantee that it will use up those 3 outs.

This is what happens when I run this report on baseball-reference.com:
From 1995 To 2006,
Home Games,
Exactly a 1 Run Margin of Victory,
and Extra Innings

Home team scores 7942 runs and allows 7428 runs, for a difference of 514 runs.  And, of course, the home team won exactly 514 more games than they lost (remember, I forced a 1-run margin of victory).

When the margin of victory was exactly 2 runs, the home team won only 21.5% of the time!  Why?  Because if you are in extra innings, and you are down by say 2, 3, or 4 runs, the way to win the game is to score 3, 4, or 5 runs.  But, you are likely to score 0 or 1 run, and thereby, not getting a win.

This becomes more clear in this situation:
From 1995 To 2006,
Home Games,
Greater Than or Equal to a 5 Run Margin of Victory,
and Extra Innings

What is the chance of the home team having won the game?  ZERO!  Any extra inning game that ends with a 5-run margin or more immediately implies that the home team did not win.  A home team can only win by up to 4 runs, in extra innings. 

Is there any wonder that the aggregate is very skewed in the direction that the authors are showing?

If we look at all extra inning games, regardless of margin of victory:
From 1995 To 2006,
Home Games,
and Extra Innings

The home team scored 0.28 runs LESS than the visiting team, but won 52.4% of the time.

Winning 52.4% of the time is EXACTLY what probability theory expected, if the HFA was such that the home team scored 0.4 runs more than the road team:
http://www.tangotiger.net/innwin3.html

(See top 9, score tied entry)

That should be “0.4 more runs per 9 full innings”.

Tango, do extra-inning games occur often enough that they provide a full explanation of why HFA disappears in 3+ run games?

Here is the wonderful link:
http://www.baseball-reference.com/games/situational.shtml

For 1995-2006, the win% for 3+ margins of victory is .508 for the home team.  Take out the extra inning games (only 2%), and it balloons to .515.

A much better study would have stopped the game after 8 innings.  You would have seen far different numbers.  And numbers that actually make sense.

The issue discovered is a baseball-related issue: starting from the bottom of the 9th, the home team doesn’t have to keep playing.

Let’s take Phil’s wonderful data:

http://www.philbirnbaum.com/probs2.txt

If we focus on the start of ninth inning (visitor at bat, no outs, no one on base… includes leadoff HR to start inning, but let’s go with it anyway), and score differential of at least 3 runs:
the home team is ahead 9925 times, and behind 7910 times (17,835 games).

That is, if we played only 8 full innings, the home team wins .556 times when the margin of score is at least 3 runs.

(By the way, Phil’s text shows 1979-1990, but when I compare to Forman’s data, it’s likely 1974-1990.  That’s my assumption going forward.)

If we use Sean’s tool, for complete games that ended with at least a 3-run margin of victory, in 17,340 games that ended like that, the home team won 8919 and lost 8421 (.514).

It’s pretty clear that we’ve got a bottom of 9th issue going on here.

>It’s pretty clear that we’ve got a bottom of 9th issue going on here.

Yup, that’s what I said.  But you have real numbers and I used the back of an envelope ...  sure is nice to have non-lazy people around!

And thanks too for the correction, the data probably *was* 1974-90 ... that’s what Retrosheet had at the time.  It was 1979-90 for a long time before that, and I probably just put that out of habit.

You can tell it’s 74-90, cause when you compare your “visitor, 1st inning, bases empty, tie game”, the number of occurences comes pretty close to the number of games in that time period.