Originally Posted by AtomicDumpling
Correction: Your numbers for the 0 out scenario are correct, but the other two scenarios are off.
runner at 1st: .941
runner at 1st and 2nd: 1.556
runner at 1st: .562
runner at 1st and 2nd: .963
runner at 1st: .245
runner at 1st and 2nd: .471
Thanks for catching that.. Obviously, that mistake was not intentional.
Hamilton singles and steals scenario:
0 outs and Hamilton at the plate -- 0.544 expected runs (starting point at beginning of inning)
Hamilton singles, runner on 1st with no outs -- 0.941 expected runs (Hamilton added 0.397 expected runs by hitting a single 0.941 -0.544 = 0.397)
Hamilton steals second, runner on 2nd with no outs -- 1.170 expected runs (Hamilton added another 0.229 expected runs by stealing 2nd)
I guess my point is that the runner at 1st no outs 0.941 expected runs also benefits from all stolen bases.
That makes this analysis a little bit flawed. (Using run expectancy)
I'm making up numbers here.. but let's say you have a sample of 100 guys at 1st base, no outs in your data where you
calculate run expectancy. If all 100 of them stole second successfully, wouldn't the run exepectancy for this sample
be higher than .941? Because the guy started out at 1b.. the run gets counted when computing run expectancy.
If you had a second sample of 100 guys at 1st base.. All of them get caught stealing.. When you calculate run expectancy
of this sample for runner at 1b, no outs, wouldn't it be zero runs expected?
I guess that's my point. The stolen bases are already factored in, thus you can't use Run Expectancy to calculate the benefit of the steal.
If I am wrong on this, please explain, but I think since actual game data is used to calculate run expectancy, the SB (and the caught stealings) are already factored in.
That's why I think one needs to have a run expectancy calculation with only station-to-station samples vs a calcuation of the various stolen bases/caught stealing scenerios. Maybe there's not enough data to accurately calculate this though.