The NHL general managers are having their annual meetings this week and for the second year in a row they are discussing rule changes to decrease the number of games that are resolved by a shootout. The particular ideas they're tossing aroundâ€”centered around adopting a 3-on-3 overtimeâ€”stand a very good chance of working.

Since the 2005-2006 season when the NHL got rid of regular season ties by adding the shootout, roughly 2 out of every 5 overtime games ended with a sudden-death goal in overtime. The winners of the remaining 60 percent of games were decided by the shootout, which is a huge amount of games to end in such an unsatisfying fashion.

A couple seasons ago, the NHL decreased the value of shootout wins by decreasing their impact as a tiebreaker in the standings. Prior to this season, the league changed the overtime rules so that teams would switch sides between the third period and overtime. The idea was that playing defense in the zone that is further away from your team's bench (as teams do in the second period) will drive up overtime scoring rates and diminish the number of shootouts. Unfortunately neither of these changes to the rules had the desired effect, so the GMs need more ideas about how to get shootouts down to the desired 40 percent.

There are two proposals on the table to accomplish this. The first proposal is to play 4-on-4 for the first three minutes of overtime and then switch to 3-on-3 for another four minutes. This is the hybrid overtime model currently used in the minor league AHL, where shootout rates are much lower than the NHL. The second proposal is eliminate 4-on-4 entirely and play 3-on-3 for five minutes. Presumably teams on a powerplay during a 3-on-3 will be allowed an extra skater and can play 4-on-3. The question then is how the two of these proposals may change the percentage of overtime games which go to a shootout.

To answer this question I used ten seasons' of play-by-play data to estimate the goal-scoring rates when teams played at 4-on-4 and 3-on-3. When the score is close and teams are playing at 4-on-4 there are approximately 0.091 goals per minute. The extra space on the ice when they are playing 3-on-3 results in a substantially higher scoring rate, 0.168 goals per minute. I used this information to simulate 10,000 NHL seasons under each of the two proposals, as well as a couple other alternatives.

The left half of figure below shows the percentage of NHL overtime games which were resolved in a shootout. Each of the last eight seasons has had about 55 to 60 percent of its overtime games go to a shootout. Despite the rule changes this year, there is not a big difference in the shootout rate compared to previous seasons.

On the right side of the figure you can see the shootout rates under some alternative overtime rules scenarios. These rates were estimated by simulating 10,000 seasons in which approximately 23 percent of games go into overtime, which is the overtime rate over the last ten years. The results also account for the variance in the estimate of the goal scoring rates.

The first scenario, 5 minutes of 4-on-4, represents the current rule structure. It is immediately obvious that the estimated shootout rate, 63.3 percent, is higher than rate in the empirical data. The reason for this is that my simulations do not account for powerplays, which will tend to drive down the number of games that go to a shootout. Because of this, the estimated shootout rates on the right side of the graph are ceiling estimates and the real-world rates would almost certainly be lower.

Both proposals being considered by the GMs are likely increase the number of games that end in overtime and thereby decrease the number that go to a shootout. Playing five minutes of 3-on-3 results in a shootout rate of about 43.1 percent, while the hybrid 4-on-4/3-on-3 scenario has a shootout rate of 38.8 percent.

Because the hybrid rules would increase the number of minutes of overtime from five to seven, I also estimated the shootout rate in two other seven-minute-overtime scenarios. If the only rule change implemented was extending overtime by two additional minutes, 52.8 percent of overtimes would have zero goals. It is interesting to note that this scenario still results in more shootouts than the 5 minutes of 3-on-3 scenario. Similarly, adding two minutes to the overtime period and playing at 3-on-3 would have the most dramatic impact, decreasing the number of shootouts to 30.8 percent.

It is unclear which of these rules changes, if any, the NHL will pursue. Given that the topic is being discussed yet again this year, it seems likely that they will make another change in the near future. And because more radical proposals, like giving teams better incentives to win the game in regulation by changing how the standings are calculated, do not seem to be on the table, hockey fans should expect to see a shake up in overtime rules again next season.