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Strange argument. How does modern soccer (quite attacking these days) compare to the number of goals per game in ice hockey, touchdowns per game in the NFL, or

by gd1 12y ago

Strange argument. How does modern soccer (quite attacking these days) compare to the number of goals per game in ice hockey, touchdowns per game in the NFL, or home runs in a baseball game?

mturmon 12y ago
This is addressed in the article, but I think it's worth expanding on, because the article is (I admit) unclear and imprecise. NFL gameplay has a state variable (field position) that strongly affects score probability. This state variable accumulates over long periods of time in the game, and is thus influenced by skill. On the other hand (the claim goes), scoring potential in soccer is mostly affected by possession of the ball, which changes frequently, and there isn't a persistent state. The effect is that, with each possession, there is a small chance of Team A scoring. The ball passes to Team B, and then back to Team A. Team A then has another shot at scoring, which (due to lack of persistent state) is largely independent of its earlier chance. To be more definite, the final score of Team A is: S = C1 + C2 + ... + CN where the Ci's are almost statistically independent, 0/1 random variables, with P(Ci = 1) rather low. Each Ci indicates a score on a given ball possession. This is a situation where the Poisson limit (http://en.wikipedia.org/wiki/Poisson_limit_theorem http://en.wikipedia.org/wiki/Poisson_limit_theorem) is applicable. The NFL situation does not decouple this way, because the Ci's are not independent, due to the field position issue. The corresponding state variables with baseball are balls-strikes and players-on-base. If you believe in the Poisson model, then Poisson model + low counts is an unfavorable regime to determine if Team A's score-probability is less than Team B's. On the other hand, if it's high counts (i.e., S is large) then it's easy to tell. This validates a commenter nearby who says he thinks season-wide scores provide more insight than tournaments. As you mentioned, hockey would seem to be another good parallel to soccer (I think). It was smart to notice that. Incidentally, I don't care one way the other about any of these sports, but I think the probabilistic analysis is interesting.
- gd1 12y ago
  Can't say I agree with that. Soccer has a state too, just because they don't pause the game after every completed pass for a few adverts, a timeout, and 12 replays, doesn't mean it doesn't have state.
  - mturmon 12y ago
    OK, if we define one interval as a ball possession (one of the Ci's above), then what factors from C(i) influence C(i+1), and how strong is that influence? The question is not "does it have state", it's "how much does it have relative to other sports mentioned". Incidentally, I notice you're digging at NFL ("a few adverts, ..."). This is off the mark for two reasons. First, this is not about whether NFL or soccer is better. But also, pauses in the game don't affect the argument. It's typically very hard to move the ball way downfield in NFL, but (seems) pretty easy in soccer. This gives rise to a state variable that persists across drives in NFL gameplay. Basically, every NFL yard is a pseudo-point, and they add up in a fine-grained way.
    - secstate 12y ago
      Yes, but a team with tons of yardage has no promise of putting it in the endzone, or even field goals. It's the same issue as with possession. The Netherlands just dominated Chile in their last pool match today, but they had 34% possession. As long as I'm commenting I might as well also complain about how silly and reductionist the whole OP is. I was a nerd long before I followed sports, so my allegiance is in data organization and mathematics. But anyone who has set foot on a field in an athletic endeavour where they, as part of a team, had something to win, don't really give a shit for your mathematical odds. Sometimes I fear for nerds who don't appreciate the spirit and gift of being human. And especially for the magic in fleeting moments of exhilaration that probably don't matter at all in the life cycle of your friendly neighbourhood quasar.
- kybernetikos 12y ago
  The discussion of the 'state variable' was interesting. However, it seems as if your model would give a wrong result for a game where one side had near 100% possession (and so relatively few possession changes). In particular, being stronger at maintaining possession often leads to multiple attempts on the goal because of the rules about corners). Perhaps that model would be more applicable for basketball? The other strange thing about this whole discussion is that it seems to suggest that you could field a team of random people and have a nonzero (within normal human experience) chance of besting the top team in the world. This is so false it's laughable. Even in top tier play, where the teams are all closer together, there are predictable differences in skill and teamwork that ensure some teams would almost never win against particular other teams. If the Poisson noise theory is correct, I would hope it could lead to specific predictions at odds with the way current professional bookmakers evaluate teams chances, and could therefore lead to a quick and easy way for this author to put his money where his mouth is.
  - mturmon 12y ago
    The notion of "possession" plays a very strong role. As noted by other people on this thread, there is strategy in sitting on the ball once you pull ahead. In the light of the simple model above, this can be seen as controlling "N", the number of possessions, rather than any single Ci (goal). The model above does not allow for such an "N" (i.e., where "N" is a function of the partial sum C1 + ... + CM). It basically assumes possession trades back and forth a significant number of times, independently of other stuff. "team of random people...so false it's laughable..." -- Absolutely true. This fallacy is implicit in some of the language in the OP, which, incidentally, seems chosen to goad fans. But I don't think it's a problem for the model. Basically, there are two per-possession goal probabilities when team A plays team B (call them G_AB and G_BA; they are between 0 and 1). These numbers are a function of both A and B, because if Team A is really bad, and B is good, then G_AB ("chance A scores on B") will be really low. But if C is just as bad as A, than G_AC will be moderate. The expected points scored by A is N * G_AB, and by B, N * G_BA. The model allows G_AB << G_BA, and indeed G_BA ~= 1, so then it predicts B will almost always win the game. Note that the Poisson limit will not apply if G is not pretty low (say, less than 0.1), and you need N moderately high (say, bigger than 10) so that N * G will itself be moderate. * The issue (not well articulated in TFA) is that when both Poisson variables are expected to have low counts, it's difficult to distinguish slightly-different per-possession probabilities.

by gd1 12y ago

Strange argument. How does modern soccer (quite attacking these days) compare to the number of goals per game in ice hockey, touchdowns per game in the NFL, or home runs in a baseball game?

mturmon 12y ago

This is addressed in the article, but I think it's worth expanding on, because the article is (I admit) unclear and imprecise. NFL gameplay has a state variable (field position) that strongly affects score probability. This state variable accumulates over long periods of time in the game, and is thus influenced by skill. On the other hand (the claim goes), scoring potential in soccer is mostly affected by possession of the ball, which changes frequently, and there isn't a persistent state. The effect is that, with each possession, there is a small chance of Team A scoring. The ball passes to Team B, and then back to Team A. Team A then has another shot at scoring, which (due to lack of persistent state) is largely independent of its earlier chance. To be more definite, the final score of Team A is: S = C1 + C2 + ... + CN where the Ci's are almost statistically independent, 0/1 random variables, with P(Ci = 1) rather low. Each Ci indicates a score on a given ball possession. This is a situation where the Poisson limit (http://en.wikipedia.org/wiki/Poisson_limit_theorem http://en.wikipedia.org/wiki/Poisson_limit_theorem) is applicable. The NFL situation does not decouple this way, because the Ci's are not independent, due to the field position issue. The corresponding state variables with baseball are balls-strikes and players-on-base. If you believe in the Poisson model, then Poisson model + low counts is an unfavorable regime to determine if Team A's score-probability is less than Team B's. On the other hand, if it's high counts (i.e., S is large) then it's easy to tell. This validates a commenter nearby who says he thinks season-wide scores provide more insight than tournaments. As you mentioned, hockey would seem to be another good parallel to soccer (I think). It was smart to notice that. Incidentally, I don't care one way the other about any of these sports, but I think the probabilistic analysis is interesting.

gd1 12y ago
Can't say I agree with that. Soccer has a state too, just because they don't pause the game after every completed pass for a few adverts, a timeout, and 12 replays, doesn't mean it doesn't have state.
- mturmon 12y ago
  OK, if we define one interval as a ball possession (one of the Ci's above), then what factors from C(i) influence C(i+1), and how strong is that influence? The question is not "does it have state", it's "how much does it have relative to other sports mentioned". Incidentally, I notice you're digging at NFL ("a few adverts, ..."). This is off the mark for two reasons. First, this is not about whether NFL or soccer is better. But also, pauses in the game don't affect the argument. It's typically very hard to move the ball way downfield in NFL, but (seems) pretty easy in soccer. This gives rise to a state variable that persists across drives in NFL gameplay. Basically, every NFL yard is a pseudo-point, and they add up in a fine-grained way.
  - secstate 12y ago
    Yes, but a team with tons of yardage has no promise of putting it in the endzone, or even field goals. It's the same issue as with possession. The Netherlands just dominated Chile in their last pool match today, but they had 34% possession. As long as I'm commenting I might as well also complain about how silly and reductionist the whole OP is. I was a nerd long before I followed sports, so my allegiance is in data organization and mathematics. But anyone who has set foot on a field in an athletic endeavour where they, as part of a team, had something to win, don't really give a shit for your mathematical odds. Sometimes I fear for nerds who don't appreciate the spirit and gift of being human. And especially for the magic in fleeting moments of exhilaration that probably don't matter at all in the life cycle of your friendly neighbourhood quasar.
kybernetikos 12y ago
The discussion of the 'state variable' was interesting. However, it seems as if your model would give a wrong result for a game where one side had near 100% possession (and so relatively few possession changes). In particular, being stronger at maintaining possession often leads to multiple attempts on the goal because of the rules about corners). Perhaps that model would be more applicable for basketball? The other strange thing about this whole discussion is that it seems to suggest that you could field a team of random people and have a nonzero (within normal human experience) chance of besting the top team in the world. This is so false it's laughable. Even in top tier play, where the teams are all closer together, there are predictable differences in skill and teamwork that ensure some teams would almost never win against particular other teams. If the Poisson noise theory is correct, I would hope it could lead to specific predictions at odds with the way current professional bookmakers evaluate teams chances, and could therefore lead to a quick and easy way for this author to put his money where his mouth is.
- mturmon 12y ago
  The notion of "possession" plays a very strong role. As noted by other people on this thread, there is strategy in sitting on the ball once you pull ahead. In the light of the simple model above, this can be seen as controlling "N", the number of possessions, rather than any single Ci (goal). The model above does not allow for such an "N" (i.e., where "N" is a function of the partial sum C1 + ... + CM). It basically assumes possession trades back and forth a significant number of times, independently of other stuff. "team of random people...so false it's laughable..." -- Absolutely true. This fallacy is implicit in some of the language in the OP, which, incidentally, seems chosen to goad fans. But I don't think it's a problem for the model. Basically, there are two per-possession goal probabilities when team A plays team B (call them G_AB and G_BA; they are between 0 and 1). These numbers are a function of both A and B, because if Team A is really bad, and B is good, then G_AB ("chance A scores on B") will be really low. But if C is just as bad as A, than G_AC will be moderate. The expected points scored by A is N * G_AB, and by B, N * G_BA. The model allows G_AB << G_BA, and indeed G_BA ~= 1, so then it predicts B will almost always win the game. Note that the Poisson limit will not apply if G is not pretty low (say, less than 0.1), and you need N moderately high (say, bigger than 10) so that N * G will itself be moderate. * The issue (not well articulated in TFA) is that when both Poisson variables are expected to have low counts, it's difficult to distinguish slightly-different per-possession probabilities.