This could be a very short discussion. Just use Pete Palmer's linear weights values of .22 runs for a stolen base (SB) and -.35 runs for a caught stealing (CS) and you're done (Palmer is editor of the latest baseball encyclopedia). Jim Furtado had .18 for SB and -.32 for a CS in the 1999 Big Bad Baseabll Annual. That was based on linear regression analysis where a team's runs was the dependent variabele and all the various offensive stats were the independent variables.
But there is the issue of whether or not the runner on first bothers or distracts the pitcher. If they do, this can improve the performance or stats of the hitter. A couple of good studies on this are
"The Theory of Theft: An Inspection Game Model of the Stolen Base Play in Baseball" by Ted Turocy at
Do Base Stealers Help the Next Batters? by Mark Pankin at
I did something different and simpler than what they did (which was to see how specific runners affected the hitters). I looked at how whole teams did with a runner on first versus no runners on base (the normal pattern is an improvement). Then I looked to see if there was a correlation between the team's improvement in their hitting stats when going from none on situations (NONE) to the runner on 1B only situations (R1B). I found the data for this by subtracting data on runners in scoring position situations from data on runners on base.
I looked at all teams from 1989-2002 (I took out the 1994 and 1995 teams because they did not play full seasons). Then I found out how much their batting average (AVG), slugging percentage (SLG), on-base percentage (OBP) and OPS (OBP + SLG) changed between the NONE and R1B situations. Again, these stats generally go up. Here is the average increase for each of these stats for all teams
For OBP, only walks, hits and atbats were used.
Here are the corrleations between these stats and stolen base stats. First, SBs
Now SB attempts
Now SB runs. I used Palmer's values mentioned above, with .22 for a SB and -.35 for a CS. The idea here was to measure a team's quality of stealing. A team could have alot of SBs or attempts, but with alot of CSs, they might not be that good. Here are those correlations.
Notice in no case is there much correlation. It does not appear that the more a team steals or the better they get at stealing, the better they hit with a runner on first base only as opposed to with no runners on base. That is, the value of stealing could be completely explained by the kind of formula used by Palmer or Furtado.