There's a lot of human perception in all of this.
I think understanding the definition of critical play isn't pinnacle. It's knowing where and when it's needed the most, and I don't think it's needed the most to freely run out 8 balls in basically any order.
Your correlation between pool and basketball seems a bit mutated, but not mathematically, but in application. In pool if you have to run out 8 balls in this manner you always have the option to play safe and you know it, even when you don't play safe. But in the final 24 seconds of a basketball game, you know you don't have that option of playing safe, so it really is clutch in basketball. Options, it's always about options.
I think correlating sports to the game of pool is both a good and bad idea. The good is kind of obvious, but the bad comes from the mutation of human perception. For example, take Accu-Stats and playing safe. If you play safe it doesn't hurt you, EVER! But in baseball, if you play safe (bunt) and wind up with the same bases "on", it hurts your bating average because you made no advancement while gaining an "out". So if you played safe in pool, and the opponent "escapes" successfully, that should hurt your score as you obviously failed the intention. Ultimately someone's perception of playing "safe" in pool mutated the proper outcome as it should be the same as it is in baseball.
Anyways, I appreciate your approach and appreciate even more that you're not leaving anything to mystery. While I don't disagree that Fargo works, I kind of... well... maybe not so much appreciate that Fargo left it in a mysterious state. When the majority find a system to be mysterious, who is to blame for that? Also for Fargo to state there is no formulas being used just adds to the mystery because if no formulas are being used, where the hell does that integer come from... the mothership?