What Are the Odds?

Now that we know how many bases a double is worth for each arrangement, let's figure out the average value of a double. In math terms, the equation looks like this, where B is the average number of bases hypothetical teammates advance on a double:

B = 0* (% nobody on) + 2.5*(% 1st) + 2*(% 2nd) + 1*(% 3rd) + 4.5*(% 1st and 2nd) + 3.5*(% 1st and 3rd) + 3*(% 2nd and 3rd) + 5.5*(% loaded)

The coefficients are just the number of bases teammates advance from each arrangement on a double.

We just need to find a way to figure out what those percentages are. Fortunately, ESPN has some ridiculous stat-keepers who record how many plate appearances a hitter gets with each baserunning arrangement. Unfortunately, they only do it on a player-by-player basis, nothing league-wide. (And league-wide is what I'm looking for.)

So...I just have to take a good cross-section of hitters across different leagues, at different spots in their batting order, and on both good and crappy-hitting teams. I chose to honor the following 6 hitters:

Freddy Sanchez (top/NL/crappy)
Luke Scott (middle/AL/decent)
Ryan Howard (middle/NL/good)
Orlando Cabrera (top/AL/decent)
Mark Ellis (bottom/AL/crappy)
Jason Kendall (bottom/NL/good)

Using their summed 2008 stats, I got the following percentages for coming to bat with the following arrangements:

Nobody on: 56.6%
1st: 17.5%
2nd: 9.7%
3rd: 2.9%
1st and 2nd: 6.4%
1st and 3rd: 2.3%
2nd and 3rd: 2.0%
Loaded: 2.6%

Now we can calculate that sum from above. The total number of bases that the average double is worth is... 3.25 bases. This is actually a little higher than what OPS tells us it's worth, which is about 3 bases (1 for OBP, 2 for SLG).

So that's how I calculated the number of Bases Advanced a double is worth. Later I'll post how many Bases each of the other plate outcomes is worth and show you all my formula for Bases Advanced.

Feedback is welcome! So if there's something you think I fucked up or overlooked, lemme know.