# On The NHL Scoring System (Part I)

There was nothing wrong with ties. The 2-1-0 point system works fine in various sports around the world. It's just ... not fitting into the mind of a North American sports fan. "Who won?" - "It was a tie." - "Who won on a tiebreak?" Basketball and baseball do not have ties, and American Football has them at a rate of 1-2 times per whole season. So more than ten years ago NHL went with the flow and abolished ties, introducing the shootout, and with a twist, where the team making it past the regulation would still get the point, and a 2-2-1-0 point system came to life.

Since then the argument rages, whether the ties should come back, or whether the consolation point should be taken away, or whether the much more energetic 3-2-1-0 point system, adopted across the ocean and by the IIHF should make its way into the NHL as well. The feeling that there is something unhealthy when a team loses and still gets something, while the winner is not penalized is nagging.

The argument from the NHL leadership claims the system creates denser standings and thus more interest and drama throughout the season is a valid one. However, this system, as we show below, creates a wrong incentive.

The standings in the NHL are defined by a points total, and the seeding in the playoffs are first and foremost the divisional standings. The relative standings across conferences have a rather minor effect of the potential home advantage in the Stanley Cup Finals, the same standings within the same conference but across divisions have an impact on the seedings in the whole playoffs, but also to a limited effect. Therefore, at least with the exception of intradivisional games, but possibly including these games too (especially against the competition that has fallen out of the playoff picture), the only thing that matters are the points accrued by the team itself, and not the points the opposition gathers. Let's wield the statistic that says that 25% of the games go to the overtime and the

So what are the point expectations in a 2-2-1-0 system? Let's compare a few situations when teams A and B play.

- Team A has 75% chance of winning the game (that's a huge, possibly maximum imaginable favorite odds)
- Team A has 67% chance of winning.
- Team A has 60% chance of winning.
- Team A has 50% chance of winning.

Let's wield the statistic that says that 25% of all games go to the overtime and the shootout occurs in 40% of these games. Let's also assume that the 3-vs-3 overtime is more random and reduces by half the advantage of the better team (i.e. 75-25 becomes 62.5-37.5), and that the shootout is completely random, so the chances of winning it are 50/50. Then, the probabilities of the outcome become:

Chance PwReg PwOT PwSO xPoints

Team A 75% 0.5625 0.09375 0.05 1.51875

Team B 25% 0.1875 0.05625 0.05 0.73125

Team A 67% 0.5025 0.08775 0.05 1.39275

Team B 33% 0.2475 0.06225 0.05 0.85725

Team A 60% 0.45 0.0825 0.05 1.2825

Team B 40% 0.3 0.0675 0.05 0.9675

Team A 50% 0.375 0.075 0.05 1.125

Team B 50% 0.375 0.075 0.05 1.125

Now let's consider than the stronger team A plays intentionally for overtime and manages to force it in 75% of the cases.

Chance PwReg PwOT PwSO xPoints

Team A 75% 0.1875 0.28125 0.15 1.55625

Team B 25% 0.0625 0.16875 0.15 1.19375

Team A 67% 0.1675 0.26325 0.15 1.49825

Team B 33% 0.0825 0.18675 0.15 1.25175

Team A 60% 0.15 0.2475 0.15 1.4475

Team B 40% 0.1 0.2025 0.15 1.3025

Team A 50% 0.125 0.225 0.15 1.375

Team B 50% 0.125 0.225 0.15 1.375

In ALL cases it's worth for both teams to steer the game into OT. For the even odds case, the expectation gain is a whopping 0.25 points! Even in the case of super, uber favorite, it's still worth for that team to head to overtime, as it projects a gain of 0.04 points. And the gains for the underdogs are so big that there is no reason for the underdog to disturb the force of the overtime, so they will happily comply! Meaning: we'll see more fun overtime, we'll see more dumb shootouts, but more importantly the 60 minutes of hockey will lose a lot of their significance. The only quantitative incentive to finish the game in regulation becomes denying extra points for your opponents - hardly a significant matter in what, fifty out of the eighty-two season games!

Now, let's repeat these calculations with 3-2-1-0 point system and combine them into another table:

2-2-1-0 3-2-1-0

Chance Exp25%OT Exp75%OT Δexp Exp25%OT Exp75%OT Δexp

Team A 75% 1.51875 1.55625 +0.0375 2.08125 1.74375 -0.3375

Team B 25% 0.73125 1.19375 +0.4625 0.91875 1.25625 +0.3375

Team A 67% 1.39275 1.49825 +0.1055 1.89525 1.66575 -0.2295

Team B 33% 0.85725 1.25175 +0.3945 1.10475 1.33425 +0.2295

Team A 60% 1.2825 1.4475 +0.165 1.7325 1.5975 -0.135

Team B 40% 0.9675 1.3025 +0.335 1.2675 1.4025 +0.135

Team A 50% 1.125 1.375 +0.25 1.5 1.5 0

Team B 50% 1.125 1.375 +0.25 1.5 1.5 0

Now there is no incentive for the stronger team to push for overtime, and even the gain for the weaker team decreased. 3-2-1-0 definitely encourages a regulation decision!

Reasons where brought up against the 3-2-1-0 system. One states that the spread over the standings will be too thin, and more teams will be eliminated from the playoff race early. This argument has had no statistical support, and the element of drama when a team pulls a goalie in a tied score trying to force a 3-0 point win may actually more than make up for it. Another argument refers to soccer studies that claim the 3-1-0 point system there encourages teams to sit on their early leads trying to stifle the game, which decreases the attractiveness of the game. This argument is more valid, although it's notably harder to preserve a lead in hockey than in soccer. But beyond that this argument prompts for another, a truly revolutionary suggestion...

## 7 Comments

## Recommended Comments