I actually work and travel frequently with a Math PhD and have a fairly strong math background as well and we have tried and failed to experimentally determine the tie breaker. This much we have more or less proven:

1) Status first
2) Fare class second
3) Distance of travel prior to flight third (small sample size but seems to work)
4) ???

As we were both Elite last year and E75K this year and usually travel on flight passes (M-class), we should normally clear the first 3) tied. However, it appears that neither time of check in nor time of upgrade are reliably 4) and I have never seen confirmation on this board (long time lurker) of how to break the tie at step 4).

To answer another question on this and another thread, I have been upgraded after boarding on a few occasions although not consistently. It is definitely more likely if the flight is full and arguably more likely if you've had a conversation with the gate agent. It is definitely controlled at the gate. Several FA's have confirmed that they are not permitted to upgrade Pax on board (though I am sure there have been exceptions, as there seem to be to most of the "rules").