Saturday, June 17, 2006

Optimum Scoring Frequency in Sports

All the hubbub surrounding the World Cup has finally motivated me to post my treatise on optimum scoring frequency in sports. So, here it is.

I believe that, in sports based on a points system, both participant and spectator, the frequency of scoring should be neither very high nor very low.

When the scoring frequency is too low, the score doesn't always identify the superior individual or team. Consider (non-American) football, otherwise known as soccer. I've seen games where one team is clearly better than the other: Team A controls the ball for most of the time, and most of the game is played on Team B's half of the field, but the game ends in a (usually scoreless) tie, so the score does not reflect team A's superiority. Worse, in low-scoring sports, an inferior team can get lucky and win by a single score.

At the other end of the spectrum are sports where the scoring rate suffices to ensure the superior team wins but is so high that it makes each individual scoring incident unexciting. Consider basketball. Scores of 100 or so provide plenty of resolution but the entire arena doesn't erupt in a chorus of "Gooooaaaallll!" each time a basket is sunk.

In my opinion, American football has a scoring rate close to the "Goldilocks" value: not so low that there is insufficient resolution or too many lucky breaks, but not so high that scoring is uneventful.

This is all my opinion; your mileage may vary.


  1. Anonymous3:02 PM

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  2. I would say that properly-refereed hockey (this year's NHL or Olympic hockey, for example) is just a shade under the optimal point. The game as played scores about three goals per side per game, so the shot noise is about 1.73 goals. I'd think if you increased scoring to more like four goals per side per game, that would bring the relative shot noise to 50%, which is more like what it is in football, without making goals basketball-common. Maybe a bigger net?

    Soccer-football is hopeless; the game is nothing but an exercise in noise statistics.

  3. Nick,

    Good point about the shot noise. I think your bigger-net suggestion should be applied to soccer, too. Just make the net twice as wide and then see what happens.

  4. I'm sorry, but bookmakers disagree with you about soccer as an exercise in noise statistics.

    Nonetheless, one must accept that whoever set the dimensions of the field, number of players, weight of the ball, etc. did not have over a hundred years of data on how fast players can run, how hard they can shoot, etc.

    However, the rectangular penalty zone should have made no sense since its introduction: it should have been oval.

    Games should be about magnifying the greatness of their players. In a high scoring game like basketball, great baskets are always confined to the last 3 minutes of a game 7. In soccer or hockey, you can have a great goal any minute.

    I just watched the game 7 of the Stanley Cup: 3-1 (last goal an empty netter). That is not that much different than the World Cup matches I've seen. Besides, most hockey goals (especially goals scored by Edmonton Oilers) are plain ugly by soccer standards: interference with the goalie, wraparound, etc. You had to watch Alexander Ovechkin to see any beautiful goals last season.

    Nonetheless, I follow all three sports, and it's more than just the points.

  5. Standing in front of the goalie in soccer constitutes interference and is a penalty, while the same activity in hockey is called a screen and is considered an essential part of offensive strategy. This fact serves as a lovely illustration of why I like hockey and dislike soccer. And a good wraparound is a thing of beauty, in my mind.

    NHL hockey averages about 6 goals per game, and a brief perusal of the internet suggests that World Cup soccer averages about 2.3 goals per match. That is a very significant difference in goal scoring, not one that can be written off by pointing out that both soccer and hockey are capable of generating a 3-1 game.

    Mabye I was a bit too flip in my dismissal of soccer earlier. I should say that while there likely are large differences in the talent levels of soccer teams, the method of analysis used to evaluate this talent level (the standard 90-minute international-style soccer game) is of very low quality due to its high inherent noise statistics. I would think that one aim of an athletic tournament would be to reward the team that best played the game. A single elimination soccer tournament is just not going to do this particularly well, as the difference in play quality between top teams will be completely swamped by the randomness of the scoring.

  6. Nick,

    I freely admit to knowing little to nothing about hockey. How does the reffing in this year's NHL and 'Lympic hockey differ from that of pervious year's NHL? Does it lead to higher-scoring games?

  7. The refs in the NHL this year finally started enforcing the rules against hitting and grabbing players who don't have the puck; this brings more in line with Olympic-style hockey standards. The result is about a one goal per game increase in total scoring over the 2003-04 NHL season and a more open game.