Getting Percentages in Pivot Table Values

I've got a spreadsheet cooking where I am tracking "events" taken by players in a board game. Each event has a few different categories of data associated with it, and ultimately each event ends in a binary outcome: either a success, or a failure. If this seems a bit abstract, think of it in terms of baseball: each batter will either get on base (success), or not (fail), and you can breakdown each attempt in terms of the handedness of the batter, the handedness of the pitcher, which teams the various players are on, etc.

Ultimately, I would like to track the success rate for these events, and analyze that rate in the context of the different categories involved: "for [a certain combination of categories], there were four attempts and two successes, for a success rate of 50%." That sort of thing. As such, I have built out a pivot table, where for each combination of groupings, I can see the number of attempts vs. the number of successes. I have dropped these two bits of data into the "value" section of the pivot table, while my various categories are strewn about the rows and columns. It's all quite grand. And, as long as the numbers are small, I can always eyeball the data and get the rates I'm looking for: 1 success in 3 attempts =33%, that sort of thing. But I'm hoping that I'll eventually be plugging in enough data that I would want to get the table to calculate this rate for me, and that's where I'm having trouble. I can tell the table to show my success values in various percentage formats, but none of them seems to fit. Does anyone have suggestions I can try? Thanks in advance!