## Expected Value, Expected Gain and Hockey

Hockey has a strange system to determine who makes the playoffs. Each team receives two points for every match they win, zero points for every match they lose in regulation and one point for each game that they lose in overtime. This point total, not overall record, determines which teams make the playoffs.

For simplicity, let’s assume in any given match that each team has an equal chance of winning. The expected value for any regulation match is one point (the average of the winner’s two points and the loser’s zero) and the expected value for any overtime match is one and a half points (the winner gets two, the loser gets one).

In-conference matches involve one team trying to gain ground on the other. The expected value is not important. In this situation, teams only care about the expected gain (or loss) in points relative to their opponent. An overtime win results in a net gain of one point while a regulation win awards a net gain of two.

Teams from different conferences don’t compete with each other for playoff spots. So while teams playing within their conference care about expected gain, teams playing outside their conference care about expected value. If teams try to maximize these values, they will prefer for conference games to end in regulation and non-conference games to go into overtime. This affects third period strategies in close games. More importantly, it provides plenty of incentive for unspoken collusion between teams in different conferences.