The following table shows scoring probabilities for various onbase situations. Each inning was evaluated by counting the number of instances of runners on first with no outs, one out, and two outs, runner on second with no outs, one out, etc. If the runner scored in that situation it got counted as a score and divided by total instances of that occurrance. The result is a percentage that could be used as probabilities for betting purposes or other mathematics.
This table shows that a runner on first with no outs has a 33.4% chance of scoring. A runner on second with 1 out has a 38.5% chance of scoring. Thus, a manager who bunts a batter on first to second increases probability of scoring by 5% but it costs an out. A batter who steals from first to second increases scoring probability from 33.4% to 57.3%, a significant increase and doesn’t cost an out.
The data used to derive this table was taken from the 2013 set of events. It is quite possible there may be a bug in my script used to do this counting. To make this table more accurate I should pull data from one or more decades of events.
The baseline of scoring with no one on base and no outs is 28%.