How about introducing a new term "BPA Probability"?

With top cubers these days, I've been seeing a lot about their BPAs on 4th solves. The problem I had was a lot of the time the BPA is extremely unlikely, and that is sometimes ignored in say youtube videos.

So I wanted to introduce a term that gives an approximation of how likely the BPA was too. The value would range between 0 to 1 as probabilities do, and

I have a couple ideas but I'm sure people more versed in statistics could find a more ironed out formula.

My idea is to base it off of the difference between the fastest vs second(and maybe 3rd) fastest solve. So if we call the 3 fastest solves t¹,t²,t³ respectively and BPA average ε

A) ε = [t¹/t²]⁸

B) ε = [2t¹/(t²+t³)]⁸

Raised to the power 8 because getting faster times clearly becomes exponentially harder, and I played around with some example values.

 

I feel like both are quite inaccurate in their scaling but either way I think this could be a useful figure to talk about.

I think theres something interesting here