Pythagorean Theorem and Soccer

[rfr3sh]

Has anyone used the Pythagorean Theorem for soccer season total points?
If so is it as useful as for football baseball and basketball?
I dont think it would work because of the chance of a draw but am I wrong?

[Optional]

I hope this doesn't sound dumb, but how do the dimensions of triangles help us with sports betting?

[Justin7]

I hope this doesn't sound dumb, but how do the dimensions of triangles help us with sports betting?

http://forum.sbrforum.com/nfl-handicapping/567833-betting-nfl-2010-season-wins-video.html?slf=2

[rfr3sh]

Justin do you have any experience with this, if it wasnt for ties I think it would be straight forward you get the season wins * 3 for points but its hard to account for ties since each team will have different amounts of ties maybe depending on goal difference a team is more likely to get more ties if there goal diff is closer to 0 but I feel like it is much more complex than this

[That Foreign Guy]

I had a quick look at the premier league for last year (was doing a Fantasy football team anyway)

http://www.premierleague.com/page/Statistics

There seems to be little relationship between draws and goal difference - three of the five most drawing teams - Hull city 12 draws -41 gd, man city 13 draws +28 gd, stoke 14 draws -14 gd,

[rfr3sh]

ya I noticed this too so back to me having no idea how to account for them

[Dark Horse]

I'm somewhat skeptical where it comes to the Pythagorean Theorem and predicting season wins. Why? One reason would be that 'they' found that a different number should be used for different leagues, like NHL and NFL. So my question is: how did they find that out? And the obvious answer seems that they fitted the number to fit the theory. Does anybody have data going forward on how accurate this magical formula really is?

I may be wrong in my skepticism, and have not delved deeply into this topic, but I do like the question: how the f*ck does a triangle offer the key to season wins? I'm always interested in working theories, and not interested in fitting results to a theory.

I'd love to fit sports into the Golden Mean or the Fibonacci sequence too.

[That Foreign Guy]

For the world cup I had a little success by using the fair odds for each group match to calculate a probability for each team and each points total. It's a much shorter timeframe though so more accurate and easier to calculate.

I'd probably approach it by starting at how many points the team got last season, then adjusting based on their position in a goal difference / shots on target ranking for last season basically I want to use a measure of quality to control somewhat for luck, then adjusting based on the team getting stronger or weaker over the summer.

I don't think I know enough to do this accurately though and already have corner and yellow card models to work on. Would be happy to discuss further though.

[PRC]

I haven't had much success with it, still working though.

[Justin7]

I'm somewhat skeptical where it comes to the Pythagorean Theorem and predicting season wins. Why? One reason would be that 'they' found that a different number should be used for different leagues, like NHL and NFL. So my question is: how did they find that out? And the obvious answer seems that they fitted the number to fit the theory. Does anybody have data going forward on how accurate this magical formula really is?

There have been studies on what exponents to use for various sports. 2 is obviously not the best, but it works reasonably well in NFL.

[Dark Horse]

There have been studies on what exponents to use for various sports. 2 is obviously not the best, but it works reasonably well in NFL.

Yes, but aren't the studies based on the past?

If you or someone else can explain the theory to me, i.e. the philosophy behind it as to why this is such a good approach, I could easily 'flip' from skeptical to enthusiastic. That would have to include an explanation for each number used per league... And the explanation would have to be better than 'because it produces the best results'.

[hutennis]

I may be wrong in my skepticism, and have not delved deeply into this topic, but I do like the question: how the f*ck does a triangle offer the key to season wins? I'm always interested in working theories, and not interested in fitting results to a theory.

I'd love to fit sports into the Golden Mean or the Fibonacci sequence too.

I also have heard somewhere that there is a very powerful force which is capable of creating a connection between an individual and bodies in space, of influencing a person's life, and which is dependent upon the exact moment of his or her birth. They say it can also influence the movement of stocks.

Would be nice if it can work for MLB handicapping.

[buby74]

In MLB a teams pythag record is a better predictor of the following seasons WL record than the actual WL record as it reflects how runs lead to wins and reduces the luck element of wins

[Dark Horse]

I also have heard somewhere that there is a very powerful force which is capable of creating a connection between an individual and bodies in space, of influencing a person's life, and which is dependent upon the exact moment of his or her birth. They say it can also influence the movement of stocks.

Would be nice if it can work for MLB handicapping.

Many things are possible, but the person(s) who came up with the original formula(s) did so only because of an underlying insight. To use a tool or formula without such understanding makes no sense. The person who does understand the underlying theory will use it correctly and apply it in the appropriate fields. All others are merely guestimating (and that would include the vast majority of astrologers). Is it possible to hammer a screw into the wall? Yes. Just don't tell the guy who invented the screwdriver.

[hutennis]

In MLB a teams pythag record is a better predictor of the following seasons WL record than the actual WL record as it reflects how runs lead to wins and reduces the luck element of wins

Is actual WL record supposed to be a good predictor of future WL record or it is sh!tty in a first place and can be outperformed by a smart invertebrate?

[Wrecktangle]

Many things are possible, but the person(s) who came up with the original formula(s) did so only because of an underlying insight. To use a tool or formula without such understanding makes no sense. The person who does understand the underlying theory will use it correctly and apply it in the appropriate fields. All others are merely guestimating (and that would include the vast majority of astrologers). Is it possible to hammer a screw into the wall? Yes. Just don't tell the guy who invented the screwdriver.

Bill James first came up with the concept in his Baseball Abstracts published in the 80s (I have all of them, BTW), and it is simply fitted (regressed) data. It works in baseball, NFL, and surely a few other sports with differing exponents found from a fitting equation.

I'll let you in on a little secret. Most of all those formulas you see in the Physics books are the result of guys sitting around in labs and taking measurements, and then fitting lines / curves to the results. Just because the result is from fitted data, does not mean an underlying relationship is bogus. Rather, when the "statistician" drops/adds data to prove some favored theory is when you must worry. BTW, THIS is the current state of medical research, advertising, and politics in the US.

[hutennis]

I'll let you in on a little secret. Most of all those formulas you see in the Physics books are the result of guys sitting around in labs and taking measurements, and then fitting lines / curves to the results. Just because the result is from fitted data, does not mean an underlying relationship is bogus.

I would have to respectfully disagree.
There is a huge difference between approaches and methodologies of true scientists and those of sport results “predictors”.
In fact, “predictors” move in the exact opposite direction of how science operates.

Scientific theories are designed to incorporate more and more data, absolutely.
But scientists prefer fewer theories which describe more phenomena rather than many theories which each describe very little.

One of the greatest achievements of a human civilization is a simple and very short mathematical formula (E=MC²) which describes a mind boggling range of physical phenomena.
Compare it to mind boggling number of theories all going (still unsuccessfully, I might add) after the same thing – trying to predict an outcome of a simple ball game

[Pokerjoe]

For soccer, use the poisson distribution. Hockey, too, although pythagenpuck is fine.

[Pokerjoe]

http://www.hockeyanalytics.com/Research_files/Win_Probabilities.pdf

This is specifically for hockey, but it does mention soccer distributions and has a very good summation of pythagorean formula development.

[Pokerjoe]

Download >> poisson-distribution-to-predict-the-probability-of-sports-matches

This is a spreadsheet, if the link works, that will allow you to plug in score estimates to get home/draw/away estimates.

[Dark Horse]

I'll let you in on a little secret. Most of all those formulas you see in the Physics books are the result of guys sitting around in labs and taking measurements, and then fitting lines / curves to the results. Just because the result is from fitted data, does not mean an underlying relationship is bogus. Rather, when the "statistician" drops/adds data to prove some favored theory is when you must worry. BTW, THIS is the current state of medical research, advertising, and politics in the US.

I'm not sure about the accuracy of that depiction. It think it starts with an idea, and then the idea can be tested and finetuned with the help of measurements.

This is rather different from taking a triangle (!) as basic idea, and backfitting different sports into it in order to 'predict' those sports. Show me the underlying theory. Without it, science is but one step away from superstition.

I think I see what you're saying though. Throw a lot of data into a machine, and patterns will begin to emerge. Those patterns have predictive value, and it isn't necessary to understand their origin. I'm just not comfortable with it. There's something almost cynical about it. To me. lol

[Wrecktangle]

I would have to respectfully disagree.
There is a huge difference between approaches and methodologies of true scientists and those of sport results “predictors”.
In fact, “predictors” move in the exact opposite direction of how science operates.

Scientific theories are designed to incorporate more and more data, absolutely.
But scientists prefer fewer theories which describe more phenomena rather than many theories which each describe very little.

One of the greatest achievements of a human civilization is a simple and very short mathematical formula (E=MC²) which describes a mind boggling range of physical phenomena.
Compare it to mind boggling number of theories all going (still unsuccessfully, I might add) after the same thing – trying to predict an outcome of a simple ball game

Hutennis: I am a scientist. Please don't presume to tell us what we do. BTW, Einstein's work was a direct result of the empirical measurement of the speed of light in the late 1800s with attendant statistical data sets.

[hutennis]

Hutennis: I am a scientist. Please don't presume to tell us what we do.

Does it mean that you, as a scientist, find this statement

scientists prefer fewer theories which describe more phenomena rather than many theories which each describe very little.

inaccurate?

BTW, Einstein's work was a direct result of the empirical measurement of the speed of light in the late 1800s with attendant statistical data sets.

Should we now try to find some NBA game parameters to substitute energy, mass and celeritas with them and see if it leads us to correctly predict totals?
I'm sure if we can shuffle enough data around, we can make it work for a couple of past seasons.

[brettd]

I think people in this thread would benefit reading a guy called Nicholas Nassim Taleb and his two books:

"Fooled by Randomness" and "The Black Swan"

Probably the most enlightening books on probability i've come across.

[bztips]

If you don't know what you're doing, blindly applying the pythagorean approach to sports prediction is likely to give you completely bogus predictions, but there IS a sound theoretical basis for it -- statistically it's equivalent to using a logit model to estimate win share. There's no way I can even begin to describe the theory behind it in a short post, but those interested can google on it.

In applied economics, this approach has been used primarily in the context of "choice" models where consumers choose among a discrete set of alternatives that are available; for example, in a travel mode study consumers choose among a pre-defined set of modes (car, train, air), etc. In a sports context, the "choices" would be the two (or more) competitors in a contest, and the basic idea would be to identify attributes of those choices thought to affect the outcome and use data to estimate the coefficients that best tie the attributes to the outcome. The Bill James-type pythagorean approach simplifies everything by choosing just a single attribute (runs scored in the case of baseball), but there's no reason you couldn't simultaneously include others attributes as well (which may give you a better model).

As mentioned by others, you would definitely expect the coefficients to be different in different sports settings, so you would not want to use the coefficients that might apply when predicting baseball outcomes to soccer.

[Pokerjoe]

[quote=bztips;5689643]If you don't know what you're doing, blindly applying the pythagorean approach to sports prediction is likely to give you completely bogus predictions, but there IS a sound theoretical basis for it -- statistically it's equivalent to using a logit model to estimate win share. There's no way I can even begin to describe the theory behind it in a short post, but those interested can google on it.

In applied economics, this approach has been used primarily in the context of "choice" models where consumers choose among a discrete set of alternatives that are available; for example, in a travel mode study consumers choose among a pre-defined set of modes (car, train, air), etc. In a sports context, the "choices" would be the two (or more) competitors in a contest, and the basic idea would be to identify attributes of those choices thought to affect the outcome and use data to estimate the coefficients that best tie the attributes to the outcome. The Bill James-type pythagorean approach simplifies everything by choosing just a single attribute (runs scored in the case of baseball), but there's no reason you couldn't simultaneously include others attributes as well (which may give you a better model).

As mentioned by others, you would definitely expect the coefficients to be different in different sports settings, so you would not want to use the coefficients that might apply when predicting baseball outcomes to soccer.[/quote]

Did I somehow not make it clear that poisson is the way to go for soccer, not pythagorean?

And as far P-theorems, or poisson go, for that matter, for predictive value, they are only as good as the data input. Meaning, it's coming up with that, which will make or break you. In the spreadsheet I posted, for example, its author's idea of using average scores from each team's last 6 games is ridiculous.

But once you have good estimates of a team's abilities, expressed as GF and GA (or PF and PA, or RF and RA, whatever), then, yes, either the pythagorean or the poisson or the other ways mentioned in the paper I linked to will get you where you want to be.

But this thread illustrates why this forum can't work: even when you tell guys the answer, if it isn't the answer they wanted or expected or are comfortable with, they just ignore it, LOL.

[wrongturn]

I'm not sure about the accuracy of that depiction. It think it starts with an idea, and then the idea can be tested and finetuned with the help of measurements.

This is rather different from taking a triangle (!) as basic idea, and backfitting different sports into it in order to 'predict' those sports. Show me the underlying theory. Without it, science is but one step away from superstition.

I think I see what you're saying though. Throw a lot of data into a machine, and patterns will begin to emerge. Those patterns have predictive value, and it isn't necessary to understand their origin. I'm just not comfortable with it. There's something almost cynical about it. To me. lol

I don't think they started with triangle as basic idea. It is pretty much a given that a team scoring more than being scored against is more likely to have higher winning percentage in a season. And the more PF-PA, the higher the percentage. If I am new to this, I will try to backfit (PF)/(PF+PA) to see how accurate it is. I then try PF^2/(PF^2+PA^2) and find it much better, and so on. Some people tried other exponent, others have more complex formula. It is not as simple as they throw a random bunch of math formula to the wall to see what sticks kind of approach. Although you may say there will never be a perfect formula because there are many random factors. I agree with that. But the purpose is to have a simple enough formula that produces good prediction. Whether they are good enough for gambling is another issue.

[bztips]

poker, no need for a hissy fit. Believe it or not, your approach -- whether it be pythagorean or Poisson or something else -- is NOT the only valid "way to go" for soccer (or any other sport). While in your universe "runs scored" or "goals scored" are the only relevant variables, that could be a very restrictive approach, and as I already stated you could develop other reasonable models that utilize other variables that help to predict game outcomes. If you insist on sticking with goals scored as the only possible relevant explanatory variable, then the Poisson approach may be great, but that's not the only way to do it.

[BadaBingSports]

I hope this doesn't sound dumb, but how do the dimensions of triangles help us with sports betting?

+1

Good Stuff.

[BadaBingSports]

I think people in this thread would benefit reading a guy called Nicholas Nassim Taleb and his two books:

"Fooled by Randomness" and "The Black Swan"

Probably the most enlightening books on probability i've come across.

Yes. Great book by a very smart man. I question his trading ability at times, but nonetheless a very interesting man to listen to.

It is remarkable how often "fat tails" occur both in the markets and here in sports (like why chase systems blow up...as teams continue their streaks for much longer than one might think).

[Dark Horse]

How reliable are the coefficients used for each sport in this model, statistically, where it comes to forecasting season wins? Based on results going forward only.

[Pokerjoe]

poker, no need for a hissy fit. Believe it or not, your approach -- whether it be pythagorean or Poisson or something else -- is NOT the only valid "way to go" for soccer (or any other sport). While in your universe "runs scored" or "goals scored" are the only relevant variables, that could be a very restrictive approach, and as I already stated you could develop other reasonable models that utilize other variables that help to predict game outcomes. If you insist on sticking with goals scored as the only possible relevant explanatory variable, then the Poisson approach may be great, but that's not the only way to do it.

Dude, I never said they were the only way to go.

The question was asked about using pythag for soccer, and I helped the OP by pointing out that the poisson distribution is a better fit.

And you helped how, exactly? Oh, yes, by continuing to talk about pythag when the sport in question was soccer.

In my "universe" runs scored aren't the only variables. In fact, they aren't even included in my baseball model. That's right, in my MLB program, which produces a run estimate, to which I then apply something of a pythag formula to get an odds estimate, I don't even include runs scored or allowed.

In my runs scored estimates, I don't use runs scored. Unbelievable, huh?

I'll go further: if you ARE using runs scored in making your runs scored estimate, you have no shot in baseball. Or soccer, either. Goals in soccer have very little value in make soccer score estimates.

And--here's the kicker--if you knew anything about modeling, you would know that all these "other variables" you talk about can and should be included in the score estimate the model produces in the first place. That's the whole point of a model: to incorporate "other variables" into a score estimation.

And then once your model produces a score estimate, you have to convert it properly into an odds estimate so that you can find value.

And to do THAT, you need math.

Even if all you do is make an educated, gut-based guess that Chelsea, say, will win by about 2-1 over ManU, if you're faced with a DNB line of 1.6 on Chelsea, do you have a bet? Even if you don't use math to make your estimate, you need to use it to translate your gut-based instinct into something you can use to find value.

And in soccer--the original question in this thread--poisson is the formula you use.

[Pokerjoe]

+1

Good Stuff.

No, not good stuff. The dimensions of triangles "help us" because they were our original understanding of ratios. Scoring's impact on win chances isn't linear.

A team that will average two goals advantage over an opponent isn't twice as likely to win as a team that will average one goal advantage.

[bztips]

Poker, I'll take you at your word about your self-proclaimed modeling skills, but you're obviously not getting my point. Put simply, your blind insistence that "poisson is the formula you use for soccer" is on its a face a ridiculous claim.

IF what you're interested in is producing a SCORE estimate, then yes, a poisson formula may work well, better than pythagorean, etc., I get that.

But if your real ultimate objective is to produce a "probability of winning the game" (odds) estimate, then there are other statistical approaches to consider that will allow you to do that directly -- rather than your two-step approach which is to estimate a score model via Poisson, and then convert it to odds. That's all I'm trying to get across; everyone can benefit by thinking a little bit outside their own box of knowledge.

[Optional]

http://forum.sbrforum.com/nfl-handic...deo.html?slf=2

Thanks Justin