A Question to the Readers / A Cry for Help

A long, long time ago, I can still remember...

OK, wrong opener.

A long, long time ago, I wrote an article about a system I created called EWP. EWP stood for "Earned Win Percentage," and what I did is assign a percentage to every type of pitcher's start, saying what percentage of a pitcher's starts would he win if he pitched a certain way.

For instance, 6 innings, 3 runs was worth 52.25%. 9 innings, 0 runs was worth 100%.

My methodology for deriving this stat, however, was crude and primitive. I failed to account for thirds of innings, just dropping them for the sake of simplicity.

A year later, I had a brainstorm with it: derive them by using probabilities!

I started with a list of the percentages of games that finished a certain way...

0 runs - 5.329%
1 run - 9.424%
2 runs - 12.428%
3 runs - 13.745%
4 runs - 12.346%
5 runs - 12.099%
6 runs - 9.156%
7 runs - 7.202%
8 runs - 5.576%
9 runs - 4.177%
10 runs - 3.066%
11 runs - 1.749%
12 runs - 1.193%
13 runs - 1.173%
14 runs - 0.473%
15 runs - 0.370%
16 runs - 0.247%
17+ runs - 0.247%

My goal with this was to figure out the probability of scoring a certain number of runs per each out. The vast majority of outs are achieved without any runs scoring.

I started my list with this:

0 runs / third inning = .05329^(1/27)

This worked, in my mind, because the only way to achieve a shutout (which happens slightly more than 5% of the time) was to get 27 straight outs without giving up a run. Hence the 1/27 exponent.

From there, you can get the 1 run / third inning value by noting that for 26 of the outs, no runs will score, and the only other time will get the proper probability.

This methodology produces negative probabilities at 4 and higher, so it essentially breaks down.

I don't know if this is the way to do it, but I do want to reexamine this. So my question / request is: can anyone derive the probabilities of scoring a certain number of runs in 1/3rd of an inning? There's a LOT that can be done with that data, starting with bullpen stats.

Thanks for your time.