Converting Projected Runs to Percentages

[curinator]

I had a quick question regarding projected runs in baseball and converting these to percentages with a method that provides the smallest margin of error. I tried using the pythagorean theorem with 1.8 as the exponent, but this didn't do too well for the time I tracked it (using Pinny's lines mid-day). It didn't do well in terms of units nor beating the closing line.

I then collected 100 games (all differing lines using matchbook closers) comparing the run line to the moneyline to determine the value of 1 run (I realize this is very crude in analyzing specific games and I only used this to compare road dog to home fav) and this worked fairly well. This did well in terms of units and beating the closing line at Pinny when the hypothetical wager was placed mid-day. I don't feel as this is the best way to convert projected runs to winning percentages though. I wanted to get input from others on better ways you may have to convert projected runs to winning percentages with the smallest margin of error. Thanks.

[curinator]

Let me give a recent example to help illustrate what I mean in case there was confusion:

On August 5th, BOS@TB had a line of TB -120 that moved to TB -143 by gametime (lines from Pinny). In terms of projected runs I had BOS at 4.2 and TB at 4.5 . Now if you plug this into the pythag. theorem using 1.82 as the exponent you get:

4.2^1.82 = 13.6242846
4.5^1.82 = 15.4470935
15.4470935 + 13.6242846 = 29.0713781
15.4470935 / 29.0713781 = 0.531350576

So with this we have a winning percentage of 53.14% for TB. Now if the spread and moneyline were compared to come up with the value for 1 run this game, we have a moneyline of approx. -139 to a spread of -1.5 ( +152).

Converting these to percentages, I get approx. 58.2 - 39.7 = 18.5
Comparing home favs to road dogs, the value of 1 run comes up right around this number generally (maybe slightly lower for an average), obviously differing somewhat with different teams (hence why I don't think this is the best way of converting runs to a percentage).
Now assuming my projection is accurate, I get a difference of .3 runs so....

18.5 x .3 = 5.55

This would give TB a 55.55% win rate, different from the pythag. theorem. With a -120 line, we would need TB to win more than 54.54% of time. Tampa Bay did win this game: 6 to 4. The line movement also suggested a play on TB was the right based on the opening line. Using the second method of calculating a winning percentage, there is a play on TB, not so with the pythag. theorem. Now this is just 1 example, but I found this happens a lot with the projections I have. The pythag. theorem seems to undervalue favorites and overvalue dogs.

As I have said, the second method seems very crude even though it is somewhat effective. Once again, Is there any better way I can convert projected runs to winning percentages? Any input is welcome. Thanks.