I guess before you try and figure out the how, we should figure out the why. Why not let probability play out naturally? Why play god? I think it has to do with fluctuation. In order to let probability play out naturally, you have to have enough trials to reach normal distribution, or that smooth bell curve. When you have less trials, you have greater fluctuation within that bell curve. When you have greater fluctuation, you have people complaining about unexpected results. This is a limitation of frequentist probability.

The only way to increase trials as it relates to WIS is to either run each game's simulation thousands of times and take an average, or greatly increase the number of possessions as previously mentioned. One takes a lot of server power, the other breaks the immersion of a basketball game. The important thing here is that simply tweaking the weight of the coin before running the trials doesn't fix fluctuation. You just change the shape of the curve. This is where the modifier comes in. How it works? I'm not sure. It would have to be a formula based on statistical inference.

Bump due to the discussion on the HD Discord - Phelan Channel - I think this is a great thread. for historical reference adding in the dev chat (someone can state changes since then as it was in 2010) - https://www.whatifsports.com/devchat/devchat.asp?chatid=86 - tinfoil hat here, are there possible nerfs or buff roles for players or teams each half?