# Is there a mathematical rationale for this tie-breaking formula?

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.

Just curious.

D18

This formula is definitely not an improvement over GF/GA. In fact (GF+GA)/GA = GF/GA + GA/GA = GF/GA + 1. Seems kinda like a dumbass extra step.

Actually, D18, your hypothetical would never happen. Since it’s a round robin, if there was a 6-0 shut out, that one team would be the undefeated champions. There would be no need of any tie breakers.

That would be the case if there weren’t ties - two teams could win all their games against everyone else, and then have a 0-0 tie against each other! But admittedly, that’s a long shot.

That’s been my suspicion from the start, but I just wanted to see if there was something I had missed.