# NHL Overtime Math

For a long time now the NHL has settled ties, after a suitable overtime period, with a shootout. The reason they went to this format is the typical American fan hates a tie result and they hate seeing games go on for hours with no result. At least they think the fans hate ties. For some reason soccer fans seem to be OK with ties, but then again soccer fans are not really sports fans. There’s also the television factor. The TV people want the games to last a predictable length of time in order to sell ads

Regardless, the motivation for adding the shootout was not due to some practical issue of accounting. The NHL managed just fine for decades without the shootout. It was an attempt to address what they thought was a concern of casual fans and it was a way to add some excitement. Shootouts are fun, even if you think they are stupid. It’s not hockey, but it is a competition, one with something at stake. That’s the appeal of sports, seeing men match wits, skill and strength with one winning and one losing.

The thinking way back when was that teams would seek to avoid the shootout and take risks in regulation and overtime in order to avoid the luck of the shootout. Hockey people think of the shootout as random chance. Elite scorers will beat elite goalies more often than not. It is really not a test of the goalie’s skill. It is more random chance. Even if that is not true and skill plays some role, the players and fans think it is chance. Therefore, the players should be desperate to avoid it. That’s was the thinking.

The trouble is it did not work out that way. At first it seemed to, but it has settled into the same old routine with the road team playing for a tie late in regulation and overtime, figuring the odds favor them. They get the point for the tie and a 50/50 chance of getting the shootout point. It is quite rational if you do the math. Playing for the tie means a 90% chance of getting one point. It also means a 50% of getting the additional point. A little math means that approach is worth 1.4 points.

Throwing caution to the wind and going for the win means the game ends in a loss 50% of the time (let’s assume). That’s one point – 50% of 2 points for a win. For the “go for the win” strategy to make sense, you would need a win chance of greater than 70%, which is unlikely, even for the top teams. Obviously, if you had such an advantage, you would not be headed into overtime often enough to care. You would win 70% of your games and the risk of losing in overtime would not matter very much.

Turns out hockey teams are not that dumb after all.

Now the NHL is thinking about changing the rules to get rid of the shootout. The main motivation is that it is stupid to decide games this way. After that, they are finding that NHL teams are doing the simple math I described above and responding to risk in a rational way. Modifying overtime by taking a skater off the ice will change the math. The teams with better skaters will have some new advantages. It’s an effort to add more risk to over time in order to encourage risk take by certain teams in regulation.

The other thing they could do is change the points. A win should be three points and the ties one point. Let’s do the math again. Playing for the win, assuming the same 50/50 probability, results in 1.5 points while the tie is just a point. Add back in the advantages and disadvantages of 4-on-4 hockey and you get a lot more teams either winning in OT or desperate to avoid OT, thus playing to win in regulation.  The result could lead to more exciting finishes and far fewer ties. The teams will figure it out and act accordingly.