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On The NHL Scoring System (Part I)

More Hockey Stats

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Original post.

 

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...

 



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Although this topic is covered in other threads already, there is one fundamental problem with a 3-2-1-0 points system which is not solvable:

 

If you install a 3-2-1-0 points system, then you admit that some victories are worth more than others and also that some losses are worse than others.

 

To draw an analogy (and to shine a light on how big this flaw is), if the same system were applied to baseball it would mean that winning a game in the first 9 innings is worth 3 wins in the standings, a win in extra innings is only worth 2 wins, and if the game goes to a home run derby after 15 innings, the winner gets 1 win in the standings.

 

 

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12 minutes ago, WordsOfWisdom said:

Although this topic is covered in other threads already, there is one fundamental problem with a 3-2-1-0 points system which is not solvable:

 

If you install a 3-2-1-0 points system, then you admit that some victories are worth more than others and also that some losses are worse than others.

 

To draw an analogy (and to shine a light on how big this flaw is), if the same system were applied to baseball it would mean that winning a game in the first 9 innings is worth 3 wins in the standings, a win in extra innings is only worth 2 wins, and if the game goes to a home run derby after 15 innings, the winner gets 1 win in the standings.

This "problem" is a matter of definition, actually.

 

The 3-2-1-0 point system states that any game is worth 3 points. After a tied regulation it is ruled that 2 out of the 3 are split, and the OT/SO is just a lesser hockey-like competition for a lesser prize of the remaining 3rd point.

 

If baseball's extra innings would be reduced to: one inning for each side without the outfielders, and then a "shootout" between the pitcher and the batter (one pitch, ball/hit/miss), then, yes, the analogy would be in place, however the baseball's current extra innings resemble playoff OT and not the regular season OT.

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2 hours ago, More Hockey Stats said:

This "problem" is a matter of definition, actually.

 

The 3-2-1-0 point system states that any game is worth 3 points. After a tied regulation it is ruled that 2 out of the 3 are split, and the OT/SO is just a lesser hockey-like competition for a lesser prize of the remaining 3rd point.

 

If baseball's extra innings would be reduced to: one inning for each side without the outfielders, and then a "shootout" between the pitcher and the batter (one pitch, ball/hit/miss), then, yes, the analogy would be in place, however the baseball's current extra innings resemble playoff OT and not the regular season OT.

 

In leagues that have used a 3-1-0 point system (such as European soccer), a victory was worth 3 points, a tie was worth 1 point, and a loss was worth 0 points. Under such a system, wins and losses had a consistent value under all scenarios (regulation, OT, or whatever). This is a very different concept from what a 3-2-1-0 system offers. 

 

Although there may be 3 points available in each game, such a system creates an environment of "spoiled victories" and "good losses". You essentially create shades of grey. Some wins are good wins, others are bad wins, etc. Some losses are good losses to have, others become bad losses.

 

We've already seen a bit of what this looks like with the NHL's current loser point system, and most fans dislike it. It's also fundamentally flawed in a purely mathematically way: 0-0-82 = 82 points > 40-42-0 = 80 points. A team with 0 wins (and 82 losses in overtime) can be positioned ahead of a team with 40 wins. It's the most outrageous math fail in NHL history that the league adopted such a system. 

 

A 3-2-1-0 system carries the same idea forward and applies it to both wins and losses, further magnifying the problem. At first glance it may seem like the answer, but I liken it to the scene in Indiana Jones where the Nazis open the ark. 

 

Good discussion though. :)

 

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Just now, WordsOfWisdom said:

 

In leagues that have used a 3-1-0 point system (such as European soccer), a victory was worth 3 points, a tie was worth 1 point, and a loss was worth 0 points. Under such a system, wins and losses had a consistent value under all scenarios (regulation, OT, or whatever). This is a very different concept from what a 3-2-1-0 system offers. 

 

Although there may be 3 points available in each game, such a system creates an environment of "spoiled victories" and "good losses". You essentially create shades of grey. Some wins are good wins, others are bad wins, etc. Some losses are good losses to have, others become bad losses.

 

We've already seen a bit of what this looks like with the NHL's current loser point system, and most fans dislike it. It's also fundamentally flawed in a purely mathematically way: 0-0-82 = 82 points > 40-42-0 = 80 points. A team with 0 wins (and 82 losses in overtime) can be positioned ahead of a team with 40 wins. It's the most outrageous math fail in NHL history that the league adopted such a system. 

 

A 3-2-1-0 system carries the same idea forward and applies it to both wins and losses, further magnifying the problem. At first glance it may seem like the answer, but I liken it to the scene in Indiana Jones where the Nazis open the ark. 

 

Good discussion though. :)

 

My biggest objection to the 2-2-1-0 system is not that it creates the 0-0-82 paradox, but because it simply creates a mutual incentive to steer the game into the OT. A wrong incentive (Goodhart).

 

In a 3-2-1-0 system OTW is not the same as W (unlike 2-2-1-0), as soon as you let the linguistic similarity go, it's easier to treat these outcomes differently. Call them "Win, Overtime Advantage, Overtime Disadvantage, Loss".

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30 minutes ago, More Hockey Stats said:

My biggest objection to the 2-2-1-0 system is not that it creates the 0-0-82 paradox, but because it simply creates a mutual incentive to steer the game into the OT. A wrong incentive (Goodhart).

 

In a 3-2-1-0 system OTW is not the same as W (unlike 2-2-1-0), as soon as you let the linguistic similarity go, it's easier to treat these outcomes differently. Call them "Win, Overtime Advantage, Overtime Disadvantage, Loss".

 

I agree. The existing system encourages teams to get into OT.

 

However, that can be easily solved in a few different ways:

 

  1. Back to 2-1-0 (wins, losses, and ties). No points just for reaching OT.
  2. My modern 2-1-0 + shootout idea (where the only way you can tie is after 3 shooters in a shootout)***.
  3. Introduce a 3-1-0 system and bring back ties. (Could remove the shootout for example.)
  4. Wins and losses only. (Teams play until someone wins. No more points system.)

 

***My 2-1-0 + shootout system was actually discussed over the radio one time (because I submitted it to the host as an idea). I can truly call it "my" idea without sounding arrogant (I hope) :) because I'm the only person on earth that has ever suggested it. It is truly unique. The notion that you could have a shootout and still have the game end in a tie is something that most people can't wrap their head around. It's a concept that blows people's minds. You could end the shootout after 3 shooters and call it a tie game. At that point, the fans would have seen 60 minutes + 5 minutes of OT + a shootout. They're not being shortchanged. If a team still can't win the game after all of those opportunities, they don't deserve 2 points in my book. And so it would be: the teams would split the 2 points, leaving with 1 each. Ties would be a rare occurrence, but they would happen from time to time. The NHL could stop with the gimmicks in overtime (4 on 4, 3 on 3, etc.) and just play a normal overtime session. Shootouts would be exciting because the stakes are raised. You could win (getting 2 points), tie (1 point), or lose (0 points). Ditto for overtime. There wouldn't be a safety net like there is now. It's what the NHL has been missing.

 

The NHL had a problem of too many games ending in a tie back in 1997, 1998, whenever it was. I'm the only person that has ever created a points system that would have solved that problem 20 years ago without damaging the current points structure, without changing the value of wins and losses, without introducing loser points, and while allowing the NHL to either have or not have the shootout. (Okay I promise not to toot my own horn any more tonight.) :cool[1]:

 

 

 

Edited by WordsOfWisdom
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All these systems have merits, except that 3-1-0 has been argued against in the way I mentioned in my article, and it indeed can create a deep standings disparity over a 82-game season, whereas European soccer leagues last up to 38 rounds only.

 

The other solutions with non-playoff OT scenario leave a perception problem that the win is achieved not in the game of pure hockey, but in some variant. Imagine a chess game (I always drift to examples from chess because I have a rich background there) that is played with 2hrs for each player, ends in a draw, and then the decider for a full point is played in a blitz game (5 min/player) that has completely different texture, and many top players are known to be much worse or better in blitz games than in full time ones. The difference from basketball and baseball is that the OT there is still the same full game, unlike hockey. I know that ties at the end of basketball regulation are very rare compared to hockey, and I don't know how baseball compares.

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18 hours ago, WordsOfWisdom said:

Although this topic is covered in other threads already

 

 

For Reference:

 

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