In the ORG thread concerning the changing landscape of baseball based on speed, it seemed to be generally accepted that it would be much better to have Billy hamilton steal in front of "singles hitters like Cozart & Hanigan" rather than in front of Votto & Bruce.
I decided to to some very amateur statistical analysis to test this, and decided to expand the test to the starting fielders, and then use that to decide when it what sort of success percentage Billy hamilton would have to have to justify stealing in front of a given batter with only one out left in the inning (actual inning and game score were not considered). I focused just on whether or not Billy would ultimately score, not the total runs scored. I used the last three years for every player wxcept Fraxier (2 years) and Cozart (1 year) for obvious reasons... I also just did one year for Ludwick since I think being in Cincy has changed what to expect from him as a player. I also rounded numbers and kind of swagged the three year OBPs for the players since I did not want to take the time to figure that out.
So the situation is that Billy is on first with 2 outs. I am presuming that Billy will score from first with any extra base hit, and from second for any base hit.
For Joey Votto, there is a 43% chance he will get on base, but only a 26% chance that this will be by an extra base hit that will score Billy. (26% of the time Votto reaches first base is by extra base hit). Therefore, if Billy remains on first, there is only an 11% chance that Votto will drive him in. There is a 32% chance Joey will walk or get a single. If he does, there is a 25% chance the next batter will drive Billy in (using the Reds team batting average) plus a 2 percent chance (using Reds OBP) that the batter will walk and the batter after him drive in Billy by walk or hit for a total of 27%. That means there is an addittional 9% chance that Billy will score after Joey walks or gets a single. Add that to the 11% chance for an extra base hit and you have a 20% chance of scoring if Billy does NOT steal first.
If Billy steals second, there is a 27% chance that Joey will knock him in with a hit. Plus an extra 4.5 percent odds of scoring from Joey getting a walk and the follow on batter (or batters) getting the necessary hit/walk to drive in Billy. Thus if Billy successfully steals with Votto up, there is a 31.5% chance he will eventually score versus the 20% if he does not successfuly steal. A 57 percent increase the possibility of scoring.
The whole list:
Votto: 20 to 31.5 - 57% increase
Bruce: 16.5 to 26.5 - 60%
Cozart: 14 to 25 - 79%
Hanigan: 14 to 28 - 100%
BP: 15 to 28.5 - 90%
Ludwick: 18 to 28 - 55%
Frazier: 16.5 to 26.5 - 60%
Choo: 16.5 to 29 - 76%
So on the one hand the thread was right... stealing in front of the thumpers (Votto, Bruce, Ludwick & Frazier) is less advantageous than stealing in front of the others (Hannigan, Cozart, Choo and surprisingly Phillips). However, if Hamilton can maintain a 75% success rate (he was over 76 last year), even for Ludwick, the worst increase, he will score 21 times out of 100 versus 18 times out of 100 if he does not attempt the steal. At the other extreme, when Hannigan is batting, he will score 21 times out of 100 if he attempts the steal versus only 14 times if he sits at first.
I realize there are more factors, such as the effect on the pitcher and fielders when a basestealer is on base or the fact that getting CS for the last out also means that you prevent the batter from scoring, but I cannot measure the former, so I am just going to say it at least balances out the latter.
One final lesson i got from this... If we call up Hamilton and lose Choo... I am convinced more than ever to bat BP second.