First of all, here's the two charts:
1941 total players (all pitchers from 2003-2005)
Within X%: 5%, 10%, 15%, 20%
Old Formula: 673, 1140, 1411, 1624
New Formula: 684, 1144, 1424, 1614
479 pitchers with 90 or more IP from 2003-2005
Within X%: 2%, 5%, 10%
Old Formula: 479, 90, 195, 327
New Formula: 479, 94, 214, 332
What we see here is that the two formula return very similar results but the new one seems to be a tiny bit better. More importantly though we've switched to using the league average .300 BABIP without causing any degradation to the quality of the formula. I'd say that while further research (especially by real statisticians) is in order I highly prefer the new formula. I didn't like making that adjustment from using .300 BABIP as a general rule of thumb to using .286...it definitely didn't feel right.
So the general format for the new formula would be as follows...
Projected Hits in Play:
pHIP = (BABIP / (1 - BABIP)) * (2.82 * IP - K)
pWhip = (pHIP + BB + HR) / IP
And the general formula for PHIP would be as follows:
pHIP = (3 / 7) * (2.82 * IP - K) or if you want the straight decimal values pHIP = 1.20857 * IP - 0.42857 * K
From a technical aspect the new formula gives a bit more weight to strikeouts or to but it more accurately it gives the correct weight to strikeouts. We were using too low of a BABIP number to compensate for using too high of a number for the IP. While this worked for the most part it would have skewed our results as we shifted the BABIP since IP were 3 times as important as a strikeout in the original formula when the correct weight is a 2.82-1 ratio.