What is the best accuracy of predicting ice-hockey game winner ever achieved? I have found many sites where some mathematical models can predict winner of NHL game with accuracy from 55% to 60%. Is this the best accuracy we can get?

When can we say a model has a good accuracy? These models with 60% accuracy are really complicated and take to account so many stats and still I think that if I randomly choose a winner with a little knowledge about past games, I will have a better accuracy than 60%.

  • 3
    "I think that if I randomly choose a winner with a little knowledge about past games, I will have a better accuracy than 60%." If you can actually do this, you should be able to make a lot of money on the sports betting markets. Come back in a year and tell us your profit.
    – Philip Kendall
    Sep 9 '21 at 10:00
  • Actually I made a few hundreds from a few tens o bets with 1 euro bet :D And when you take to account that absolutely random tip has a chance of 50% being correct.
    – Rikib1999
    Sep 9 '21 at 10:03
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    Survivor bias is a fallacy. One person making money over a series of random bets does not outweigh the many hundreds who lost, bringing the real expected value down to basically the theoretical, around 90% depending on the vig. If all bets are even money, EV is still 0. Especially with the number of games in a season, it is exceptional luck to get much past the low 50s, much less above 60%.
    – Nij
    Sep 10 '21 at 22:24
  • Of course, but I wasn't asking because of betting initially. I am just curious how well can be an ice-hockey game predicted, only the winner. We have so much data from the matches and still it is totally unpredictable. 50% accuracy is just no accuracy at all, and these few percent up to 60 is really not amazing, in practical world.
    – Rikib1999
    Sep 11 '21 at 15:10
  • You seem to have a very different idea of what it means to be practical, and what counts as amazing in that respect.
    – Nij
    Sep 11 '21 at 23:28

The better team doesn't always win

The best teams in hockey in the 2020-1 season were the Colorado Avalanche and the Vegas Golden Knights, with 82 points. They won 69.6% and 71.4% of their games respectively. So even if you knew a priori that they were the best teams and picked them to win, you would only get about 70%.

The worst team was the Buffalo Sabres, with 37 points. They lost 73.2% of their games.

Not every team wins or loses 70% of its games

Those examples are the most extreme. But many games do not include any of the Avalanche, Knights, or Sabres. What happens when the New York Rangers face the Montreal Canadiens? Who's the better team? In games like that, your chances of being wrong are much higher.

Not every opponent is average

The Avalanche and the Golden Knights are in the same division. Some of the time, they play each other. Again, your chances of being wrong are much higher.

Look at the playoffs for more examples. In eight first round matches, five undercards won, including two of the number one seeds losing to the number four seeds, despite home rink advantage. In the four second round matches, the lower seed won every one. Including the Montreal Canadiens, who had a losing record in the regular season but went to the finals. Overall, the better seed only won five of fifteen matches. Of course, the year before, the better seed won a majority of the matches.

Most decisive

It's as useful to us for a team to be at the bottom of the rankings as at the top. Either way, it tells us how that team is likely to do in games. So rather than think of the Sabres as winning only 26.8% of their games, think of it as their opponent wins 73.2%. If we think of every team like that, the Sabres were the most decisive team. If we guessed that they'd lose, we'd be right 73.2% of the time. The worst team would be a team that won and lost equal numbers of games. Such a team would only be 50% decisive.

Give every team a decision score. They will all be between 50% and 73.2% (in the 2020-1 season). If you average those numbers together, you get that the average team is around 60% or so decisive. Hey, that's about the same as the predictions!

So what is this telling you? The fundamental problem with consistently guessing the winner with more than 60% accuracy is that games are only 60% accurate at determining who is the better team. If we had a perfect system that could tell who was the better team, it would still only be 60% accurate at predicting games. Because on average the games themselves are only 60% accurate. This should not be terribly surprising. It is after all, the reason why playoff matches are seven games and not just single games.

More rigor

It would be better for this analysis to look at head-to-head matchups rather than overall records. But I could easily find the overall records (thanks Wikipedia) and could not as easily find the head-to-head results. Also, I doubt that there would be enough data for a truly rigorous examination. Note that 31 teams played 56 games each. That's less than 2 games per matchup. Even in a full 82 game season, that's less than 3 games per matchup average with 2 (other conference) to 4 (same division, maybe) being the actual numbers.

Neither 2 nor 4 is a large enough sample. Really, 82 is rather on the small side. Statistics usually work with hundreds if not thousands. But that to helps explain the problem. There isn't enough data to make really accurate predictions.

Survivorship bias

One of the problems with your initial analysis is that I strongly suspect that you are looking mostly at the easy matchups. The Avalanche or the Golden Knights will usually beat the Sabres (at least as the teams were in 2020-1). But other teams are going to be far more evenly matched. For example, in the playoffs, they were 4-2 (so the better team only won 67% of the time--assuming the Golden Knights were the better team; perhaps the better team only won 33% of the time).

If you get to pick which matchups, you can do better than 60%. But if you have to pick every game, then you have to pick a lot of games where either team could win. And naturally the matchups that you measure are those where you came to a decision. If you couldn't choose between two evenly matched teams, you don't score yourself with a miss. You just figure that you didn't have time. But those hard matchups should pull down your percentage.

This is why the comments keep telling you to try it. Because if you actually tried to pick all the games this season, it is very unlikely that you would do much better than 60% overall. You might well do better than that for some teams though.

Practical use

It's not clear to me that even a perfect predictor would have a practical use. What does it change for managers and coaches? Anything short of perfect, they still have to play the games. Perhaps it might help them plan a bit as to when to rest players (if you're going to lose, might as well lose with your second team on the ice). But even then, what if that would have been the game where you would have beat the odds?

For bettors, to have a bet, you need two sides. So the weighted win percentage in betting is always 50%. It may feel like you're betting against the bookie, but that usually isn't true. Bookies don't normally pick a side. Instead, they lay off their bets with other bookies such that, they come out a little ahead regardless of what happens. If there was a service that provided perfect predictions, then everyone would use it and you could never place a bet. There would be no one to bet the other side.

With our current imperfect system, what happens is that they use odds and/or the spread to balance things. But the average return is such that if you bet both sides, you will lose money. Because the winnings are less than the cost of placing the bet both ways so that the bookie has a profit margin.

That's not to say that you can't win individual bets. Or even beat the odds on average. But everyone can't do that all of the time. Someone has to take the losing side. People who tend to beat the odds are the ones who pick games where bettors are likely to be irrational. For example, where people are betting on their home team, even when it's not that good. That can skew the odds.

  • Thanks for your answer! So the problem is that NHL teams are really balanced in strength. Maybe current models used for predictions should instead of analysing each team and player individually (in context of other teams and players) try to analyse and train on types of teams and players, that would mean a lot of more data could be used for predicting a single match. So two similarly playing players would be processed as one.
    – Rikib1999
    Sep 15 '21 at 20:28
  • "So the problem is that NHL teams are really balanced in strength" - citation needed
    – CGCampbell
    Sep 17 '21 at 17:18

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