Hm, maybe it does and that's why it works out with BSU, which has a completed season where a stray .5 here and there wouldn't make a perceptible difference.

Anyway, that's the formula that WIS provided after round 3 of telling them I wasn't complaining about distribution and that I just wanted to know the Off% formula.

well that sucks ;)

I think I figured this out after going through OP's PbP and one from my own team's first game.

Formula appears to be: (FG Attempts + Possessions leading to FTs), as a % of total team's FG attempts and possessions leading to FTs.

The FGA+FTA/2 formula is not a bad approximation.  The differences between the two are:
- FTAs that occur after made baskets ("and 1" situation) should not count towards the distribution.  
- A non-shooting foul in the bonus leading to a one-and-one should count as one possession, regardless of whether the FT shooter got one FTA or two.
- Similarly, if a player get three FTAs due to being fouled on a missed 3PT FGA, that one possession counts the same as if he was fouled on a 2PT FGA.

In the OPs game, 
Browning has 9 FGAs, 2 possessions where non-shooting foul led to FTAs, 1 possession where fouled on missed FGA = 12
Axford had 9 FGAs, nothing else = 9
Williams had 6 FGAs, 3 possessions where non-shooting foul led to FTAs = 9

Whole team had 54 of these events, so Browning's share was 12/54 = 22.2% and Axford/Williams had 9/54 = 16.7%.

That sure seems like a way to get there for this example, but I doubt it would hold up over the entire season like FGA+FGA/2 does... not that anyone is going to spend the time to check.

It's also a direct contradiction to the explanation I was able to wring out of WIS through the ticket I opened.  Not saying that "WIS said it" means it's an unshakable truth, but it counts for something.