My son’s hockey league is embroiled in the playoffs. If there is a tie in wins/losses/ties at the end of the round-robin, the tie-breaking formula is:
(goals for + goals against)/ goals against
None of we parents can ever recall seeing a formula like this before - you usually get goal differential or goals for divided by goals against (or vice versa).
My question is, as far as the mathematics go, is there something about this formula that makes it an improvement over the others? I can think of at least one hypothetical flaw, which is if you have 6 shut outs, you wouldn’t be able to calculate the formula - but that’s highly unlikely to happen.
Yes, we’ve enquired to the league why they chose this and the answer was along the lines of it seemed like a good idea at the time! Which is the way minor sports seem to be traditionally run.