Stealing a base is a bet: succeed and the runner advances, fail and the team loses both the runner and an out. This calculator finds the success rate at which that bet pays off, using run expectancy, the average runs scored from each base-out state.
How it works
Every steal attempt moves the team between run-expectancy states. Define the gain on success and the loss if caught, then solve for the success probability where the expected change is zero:
gain = RE(success) - RE(now)
loss = RE(now) - RE(caught)
break-even = loss / (gain + loss)
Because being caught removes the runner and adds an out, the loss is large relative to the gain, which pushes the break-even rate well above half.
Example and notes
With a typical MLB table, a runner on first with no outs has a run expectancy near 0.83. Stealing second cleanly raises it to about 1.07, a gain of roughly 0.24 runs. Getting caught drops it to about 0.24, a loss of roughly 0.59 runs. The break-even is 0.59 / (0.24 + 0.59), about 71 percent. So a runner who succeeds 75 percent of the time adds expected runs, while one at 65 percent is hurting the team. This model uses average run expectancy, not win probability, so in late, close games adjust for score and inning.