Agreed - I don't think it maximizes the win probability per se. I just think it's better than the current system.
Point taken about the "exploding near zero". I could do something like Population / (.2 + 5^(x/3-1) ), where x is average spread, ... but that just gets ugly. I wanted to communicate a general concept, not propose a specific formula.
The problem is your function doesn't really maximize the win probability either. I am not an expert here, but there may be a way to more accurately characterize the probability. Also, your function blows up when "average spread" tends to 0. An appropriate sigmoid transform should fix that.