Tuesday, July 27, 2010
SABR 101 - Bases
Triples and homeruns will advance all runners on base the maximum number of bases possible. Runners on first base will advance three bases, runners on second base will advance two bases, and runners on third base will advance one base.
On average, there are 0.3 runners on 1B, 0.2 runners on 2B and 0.1 runners on 3B. Therefore, the total number of bases advanced by the triples and homeruns is 0.3 times 3, plus 0.2 times 2, plus 0.1 times 1, or a total of 1.4 bases. This is the base-advancement value of a triple and home run.
Doubles have the same base impact for runners on 3B and 2B. For runners on 1B, 40% of the time, they will advance the runner three bases, and 60% of the time, it will be two bases, for an average of 2.4 bases. Following the same calculation above, we have 0.3 times 2.4, plus 0.2 times 2, plus 0.1 times 1, or a total of 1.22 bases as the base-advancement value of a double.
For singles, they’ll advance the runner on 2B two bases 60% of the time and one base 40% of the time (average of 1.6 bases), and the runner on 1B will advance two bases 30% of the time and one base 70% of the time (average of 1.3 bases). The calculation follows: 0.3 times 1.3, plus 0.2 times 1.6, plus 0.1 times 1. That’s a base-advancement value of .81 bases for the single.
Walks advance all runners from first base one base. The runner on 2B will advance only when there is also a runner on 1B (so the overall frequency is about .10). And the runner on 3B will advance only when the bases are loaded (about 2% of the time). So, we have: .3 x 1, plus .1 times 1, plus .02 times 1, equals .42 bases for the walk.
All these numbers are nicely rounded for ease of illustration.
Here’s the summary:
1.40 HR
1.40 3B
1.22 2B
0.81 1B
0.42 BB
This was based on having 0.60 runners on base per plate appearance. If you have more runners, say 0.90, then all those numbers go up 50%. If you have fewer runners, say 0.30, then all those numbers need to be cut down in 2.
Added to that is the number of bases the batter himself gets (4 for HR, 3 for 3B, 2 for 2B, 1 for 1B, BB). Those numbers are independent to the run environment. So, a HR gets 4 bases for the batter and 1.40 for the runners, or a total of 5.40 bases. Here’s the summary of that:
5.40 HR
4.40 3B
3.22 2B
1.81 1B
1.42 BB
In this SABR 101 article (required reading) from Patriot, he shows some data I provided using actual data:
5.41 Home Run
4.46 Triple
3.23 Double
1.83 Single
1.39 Walk
You can see here how the theoretical pretty much matches the empirical. This is how run scoring works in baseball.
Given that there are 4 bases required to score a run, you can take the number of bases and divide by 4. Taking the theoretical numbers, we have:
1.35 HR
1.10 3B
0.81 2B
0.45 1B
0.36 BB
That’s more or less the number of runs each event is worth. All this is pretty standard for the regulars around here. Hopefully, this brings all the new readers up to speed.
minor typo:
“On average, there are 0.3 runners on 1B, 0.2 runners on 2B and 0.1 runners on 1B. “
I assume should be:
“....and 0.1 runners on 3B.”