3 ms·

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% po

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.
- kybernetikos 12y ago
  When one team is dominating another, they get multiple attempts to score for a single possession event (powerful shots on target are commonly redirected by the keeper which allows the attacking team another chance from a corner or rebound), and their probability of scoring from any shot increases because their control of play allows them to take more certain shots. And of course, brief possession in a teams own half does not really translate into any kind of scoring chance for them. Of course I'm not sure that those factors are enough to completely sink the model, but there certainly are such factors in play. > 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. I take this to mean that in a match up between broadly comparable teams, the outcome will be indistinguishable from chance, which most fans would accept as completely fine (and possibly even preferable). I still find it hard to reconcile this with the dominance of a few teams over quite long periods of time in international soccer, even in the presence of relatively low scores although I suppose I would have to do some actual number crunching to tell whether this was relevant or not.

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.

kybernetikos 12y ago
When one team is dominating another, they get multiple attempts to score for a single possession event (powerful shots on target are commonly redirected by the keeper which allows the attacking team another chance from a corner or rebound), and their probability of scoring from any shot increases because their control of play allows them to take more certain shots. And of course, brief possession in a teams own half does not really translate into any kind of scoring chance for them. Of course I'm not sure that those factors are enough to completely sink the model, but there certainly are such factors in play. > 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. I take this to mean that in a match up between broadly comparable teams, the outcome will be indistinguishable from chance, which most fans would accept as completely fine (and possibly even preferable). I still find it hard to reconcile this with the dominance of a few teams over quite long periods of time in international soccer, even in the presence of relatively low scores although I suppose I would have to do some actual number crunching to tell whether this was relevant or not.