Home field advantage

[reno cool]

I see this doesn't work. Hold on I'll make up a better theory.

[reno cool]

OK, I'm with you so far ... but I'm afraid I just don't see your mathematical rationale for multiplying A's expected neutral field probability by the fair home field odds ratio in an attempt to determine A's expected home field probability.

Look at it this way ... if instead of a 61% home win probability we had a 90%, then the quotient would be 9/7 ≈ 1.285714 > 1, which isn't a valid probability.

yes, I just realized this.

[Ganchrow]

Hold on I'll make up a better theory.

If you're looking to make up a better data-blind theory, then I'd suggest that such would be a waste of time. What I've presented is really the core theory derived solely from first principles.

As I've previously mentioned, the real problem however is the degree to which home field advantage (technically, we're talking about advantage expressed in terms of the log of the fair odds ratio) is evenly spread across all ranges of relative home/away team quality.

This problem at its core is really a data issue and is not something which can be derived from first principles alone ... it's going to differ from sport to sport, league to league, time frame to time frame and home field/court to home field/court (among countless other factors).

So I'd recommend that for those interested one's next step here would probably be to apply this to an actual data partition and examine its performance, carefully focusing on any factors that tend to systematically bias the results, and then determine how best to adjust for these factors.

But if the input data is accurate and the log of fair home field advantage fair odds is spread evenly across all tranches, you're not going to do any better than the above model from a pure mathematical.

So in other words, the theory is 100% right given the underlying assumptions ... one just needs to determine under what circumstances and to what degree these underlying assumptions fail to hold.

[Wheell]

OK, time for some clarity. There has been some confusion as to the effects of home field. Let give a simple example.

Duke -45 Grambling
Duke pk'em UNC

Let's set those as the neutral court values for these matchups. Let's now set lines for the home and away game between Duke and UNC

UNC +4 @ Duke
Duke +4 @ UNC

Let's say that the moneylines are set at +150 for the road teams in the matchup. We can expect that over a large series of games the home teams would win around 60% of the time.

Now, I don't particularly care would spreads you set for games between Duke and Grambling but I will say Gramblin isn't winning 10% of their home games against Duke, so even if Duke NEVER loses at home against Grambling the home team will win less than 60% of the time. In fact the home team might win exactly 50% of the time since Duke might never lose to Grambling, period.

This is not to say that HFA's affect on the spread diminishes as your get further from zero.

[Wheell]

The 90% hfa example actually opens up a fairly beautiful can of worms under the logic that Ganchrow is using we'd get lines these three lines:

Team A -150 Team B at team A
Team A +600 Team B neutral court
Team A +5400 Team B at team B.

Very amusing.

[Ganchrow]

The 90% hfa example actually opens up a fairly beautiful can of worms under the logic that Ganchrow is using we'd get lines these three lines:

Team A -150 Team B at team A
Team A +600 Team B neutral court
Team A +5400 Team B at team B.

There's no can of worms to be had.

90% HFA is just ridiculously high in all but the most extreme and pathological of cases.

[Ganchrow]

OK, time for some clarity. There has been some confusion as to the effects of home field. Let give a simple example.

Duke -45 Grambling
Duke pk'em UNC

Let's set those as the neutral court values for these matchups. Let's now set lines for the home and away game between Duke and UNC

UNC +4 @ Duke
Duke +4 @ UNC

Let's say that the moneylines are set at +150 for the road teams in the matchup. We can expect that over a large series of games the home teams would win around 60% of the time.

Now, I don't particularly care would spreads you set for games between Duke and Grambling but I will say Gramblin isn't winning 10% of their home games against Duke, so even if Duke NEVER loses at home against Grambling the home team will win less than 60% of the time. In fact the home team might win exactly 50% of the time since Duke might never lose to Grambling, period.

This is not to say that HFA's affect on the spread diminishes as your get further from zero.

Wait ... so now you're arguing parameter selection? Come on. I'd have expected better from you.

It's up to the practitioner to appropriately select his predictive model parameters.

The issue here is that the 60% parameter you've selected is simply not indicative of league-wide HFA but rather of some subset thereof.

To go a step further, in a sport with as much discrepancy between team quality as college BBall, the HFA figure may well be vastly different across very widely disparate classes of teams (say majors, mid-majors, etc.) -- especially when those classes don't tend to frequently play one another or when there exists bias in assigning home court. This would clearly render a league wide-HFA wholly inappropriate.

But yet again ... this is completely beside the point of this exercise.

If you have a problem with the underlying math or if you want to propose sound quantitative methodologies for improving upon the model based on what we know from the historical record for a given sport then by all means please do share it.

As I keep repeating ... this is a simple Bayesian model that will be just as accurate as its inputs are predictive and underlying assumption are correct.

[acw]

What causes home team advantage?

[reno cool]

the best theory I've heard is biased refs

[Wheell]

Much of it comes down to the refs being influenced by the crowd. There are also issues with familiarity with the field, playing at a time your body is accustomed to, and testosterone issues. There is also the issue of the players at home providing a greater level of effort. Mostly though, refs.

[Wheell]

Wait ... so now you're arguing parameter selection? Come on. I'd have expected better from you.

It's up to the practitioner to appropriately select his predictive model parameters.

The issue here is that the 60% parameter you've selected is simply not indicative of league-wide HFA but rather of some subset thereof.

To go a step further, in a sport with as much discrepancy between team quality as college BBall, the HFA figure may well be vastly different across very widely disparate classes of teams (say majors, mid-majors, etc.) -- especially when those classes don't tend to frequently play one another or when there exists bias in assigning home court. This would clearly render a league wide-HFA wholly inappropriate.

But yet again ... this is completely beside the point of this exercise.

If you have a problem with the underlying math or if you want to propose sound quantitative methodologies for improving upon the model based on what we know from the historical record for a given sport then by all means please do share it.

As I keep repeating ... this is a simple Bayesian model that will be just as accurate as its inputs are predictive and underlying assumption are correct.

OK Ganchrow, let me make my point as explicit as I comfortable doing so here:

The Bayesian model is nothing more than a mathematical tool, and anyone who trusts it to produce accurate handicapping lines will find their bankroll dwindle with unfortunate regularity.

It is a useful tool but saying it produces correct answers overstates its accuracy.

Again, it is a tool, and only a tool. It cannot be the only tool in your handicapping toolbox. To prove the point, think of this:

Bulls -10.5 Knicks in London. The money line is approximately +600.

What are the lines in NY and Chicago? What are the moneylines? And finally, what is the aggregate home court advantage in terms of home win rate in the NBA.

[Ganchrow]

OK Ganchrow, let me make my point as explicit as I comfortable doing so here:

The Bayesian model is nothing more than a mathematical tool, and anyone who trusts it to produce accurate handicapping lines will find their bankroll dwindle with unfortunate regularity.

It is a useful tool but saying it produces correct answers overstates its accuracy.

Again, it is a tool, and only a tool. It cannot be the only tool in your handicapping toolbox.

You're building yourself as nice strawman argument here.

I'm not arguing that it should the only tool in one's arsenal, merely that it should be explained and understood. This is in just the same manner as one should be able to understand the calculation of supposed fair value given a money line market, despite the fact that most such markets are skewed and hence the results often highly biased.

You presented two other pairs of answers (both obviously and crudely based on what is indeed the mathematically correct answer), which you've deemed "better" but offer no explanation whatsoever as to why you believe them so. I'd still love to hear your rationale. What's more you've not even attempted to offer any mathematical reasoning or any historical evidence in opposition to the underlying theory -- now that would actually be helpful.

[Wheell]

You're building yourself as nice strawman argument here.

I'm not arguing that it should the only tool in one's arsenal, merely that it should be explained and understood. This is in just the same manner as one should be able to understand the calculation of supposed fair value given a money line market, despite the fact that most such markets are skewed and hence the results often highly biased.

You presented two other pairs of answers (both obviously and crudely based on what is indeed the mathematically correct answer), which you've deemed "better" but offer no explanation whatsoever as to why you believe them so. I'd still love to hear your rationale. What's more you've not even attempted to offer any mathematical reasoning or any historical evidence in opposition to the underlying theory -- now that would actually be helpful.

The two other answers are "Albuquerque" or Bugs Bunny lines. Let's look at the case of two average teams facing each other such that the home team wins 61% of the time. using the method I outlined above we get the road team as approx .4444 and the home team approx .5556. Applying the 1/7 team as facing these teams at home or away gives +480 and +750 lines respectively.

Have you guessed yet why these are Bugs Bunny lines?

I have alluded to other tools in the toolbox. At this point one would take a left turn in Albuquerque and end up at the correct destination as opposed to one of the many random places Bugs Bunny would find himself. how you do this is up to you but let me suggest that if you are still in the 300's or 400's when at home and in the triple digits when on the road, well, you haven't reached the correct destination yet. Actually, RJT wasn't answering the question you meant to ask, but provided a decent enough answer.

For the record the reason I gave full credit to the +453 and +795 answer is because the methodology that provides that answer generally presumes you understand the flaws in the system and has a second step built in. That system knows it can only get the correct answer at 1 point (which can be chosen arbitrarily, although 0 seems the natural choice), and then build in a second step.

The reason that I prefer this methodology is that it allows me to have a control team and a variable team. In the game listed above we can know the strength of Team B relative to Team A on a neutral court, maintain team A's strength at both home and away as their neutral court strength for part one of the methodology while using Team B's true home and away levels (given that they are defined as a .500 team), and then take the left turn at Albuquerque in part two.

There are other people who prefer a one step methodology. What they do is create and maintain meticulous power ratings on every team for home and away. I only have one power rating for each team but have to then modify for location and other affects (did they play last night, are there time zone issues, injuries, etc).

But, apparently this was all a simply question of what the answer was in a Bayesian methodology, and I already provided the answer and the method for getting it previously.

Straw man my ass.

[Ganchrow]

The two other answers are "Albuquerque" or Bugs Bunny lines. Let's look at the case of two average teams facing each other such that the home team wins 61% of the time. using the method I outlined above we get the road team as approx .4444 and the home team approx .5556. Applying the 1/7 team as facing these teams at home or away gives +480 and +750 lines respectively.

How is this reasoning at all mathematically sound?

[Wheell]

The Bayesian answer isn't mathematically sound either, the question is do you have a fix.

For the record stepping from the .39 to .4444 to the +453 +795 methodology both shows the problems with and offers solutions to the Bayesian methodology.

And I'm the guy swinging at straw men?

[Wheell]

I guess the Bayesian methodology is mathematically sound if all you want to do is do math. If you are interested in making the occasional wager...

[Ganchrow]

The Bayesian answer isn't mathematically sound either, the question is do you have a fix.

For the record stepping from the .39 to .4444 to the +453 +795 methodology both shows the problems with and offers solutions to the Bayesian methodology.

And I'm the guy swinging at straw men?

No ... what you're saying is just nonsense. Probability has certain rules. Bayesian inference tells us how to update prior probability estimates based on new information. You're just messing around with numbers and not in any manner backing it up with any mathematical reasoning.

Now maybe some reasoning does exist and I'm just not seeing it, but you're certainly not making even the most meager of attempts to provide it.

I mean why not just take the cube root of the home probability multiply it by 6 and call that your answer? You're just declaring, "No my 'math' is right, the Bayesian method is wrong but I won't explain why."

[Wheell]

I answered your Bayesian question. I showed my work.

Now, I am trying to help people make money without giving away information that quite frankly should not be given away on a public forum.

If we only want to stay inside the world of Bayesian math you've got your answer for 61, you got your answer for 90, and if you want answers elsewhere I can provide them.

Ganchrow... take a few moments to think about what I am doing. Think about how basketball games exist in reality and think about this:

What lines would you post on an NBA game that was +600 on a neutral court? You have a database of NBA games, you should be able to get a good grasp of HCA.

[Ganchrow]

You didn't "show your work" .... you copied the log5 formula, plugged in the data, and came up with an answer.

Then you declared that answer wrong but still adamantly refuse to provide any mathematical reasoning as to why you believe it so.

So are you claiming this methodology applies only to the NBA ... or does it apply to any game of chance where a HCA may be inferred?

It's pretty hard to argue with a declaration of "I'm right and you're wrong."

[reno cool]

still working on the simple question here. So I was thinking about the ping pong ball example.
so if I take the prob of drawing a with home .08714 and compare to b with road .33428 you get the 3.84-1 Is this a right way of looking at it?

I'm just getting lost trying to figure the reasoning for the formula as written.

[Wheell]

I'm not saying your wrong. I'm saying the Bayesian methodology doesn't work in the NBA, and it REALLY doesn't work in NCAAB. I use the LOG5 in a lot of sports but I also understand the real world is a messy place.

The log5 gets the wrong answer because reality disagrees with it, not because I like or dislike it. However, log5 is an EXCELLENT tool.

I ask again, what lines would you post on an NBA game that was +600 on a neutral court?

[Ganchrow]

still working on the simple question here. So I was thinking about the ping pong ball example.
so if I take the prob of drawing a with home .08714 and compare to b with road .33428 you get the 3.84-1 Is this a right way of looking at it?

I'm just getting lost trying to figure the reasoning for the formula as written.

I'm not sure I'm understaing you here.

Are you saying that A has 8.714% probability of winning against B on a neutral court and that road teams in general win with 33.428% probability?

If so then the answer is 15.97%.

[Wheell]

still working on the simple question here. So I was thinking about the ping pong ball example.
so if I take the prob of drawing a with home .08714 and compare to b with road .33428 you get the 3.84-1 Is this a right way of looking at it?

I'm just getting lost trying to figure the reasoning for the formula as written.

If I am reading you correctly the answer would be 5.26-1.

[Ganchrow]

I'm not saying your wrong. I'm saying the Bayesian methodology doesn't work in the NBA, and it REALLY doesn't work in NCAAB. I use the LOG5 in a lot of sports but I also understand the real world is a messy place.

The log5 gets the wrong answer because reality disagrees with it, not because I like or dislike it. However, log5 is an EXCELLENT tool.

So to address this you've chosen to present an ad hoc methodology that you refuse to back up with any mathematical reasoning whatsoever?

As I've stated (in different forms) repeatedly throughout this thread:

One very important consideration is the degree to which home field advantage (technically, we're talking about advantage expressed in terms of the log of the fair odds ratio) is evenly spread across all ranges of relative home/away team quality, which is the implicit assumption of the original question.

No argument here that this underlying assumption will deviate to varying extents across various sports and odds ranges but the point of this question is to illustrate the underlying math.

[reno cool]

no, I'm not sure what those # represent. 8.71% of the time you would draw team A along with Home from the other sack. 33.4% of the time you would draw team B with road. The rest of the time the other 2 options.

[Wheell]

So you've chosen to present an ad hoc methodology that you refuse to back up with any mathematical reasoning?

As I've stated (in different forms) repeatedly throughout this thread:

It is the ad hoc method that I use in real life, but I'm not posting the explicit details to the second part of it because that formula is proprietary. However, the steps one takes to get to the point I listed do lead you down the correct path.

I also note that you are declining to answer my question. You haven't even acknowledged my question to the point of declining to answer.

Are we here to educate and elucidate or are we here to do math and show how smart we are?

[Wheell]

no, I'm not sure what those # represent. 8.71% of the time you would draw team A along with Home from the other sack. 33.4% of the time you would draw team B with road. The rest of the time the other 2 options.

Ah, yes, I see what you mean, and yes, that is correct.

[Ganchrow]

Mine is not ad hoc methodology ... it's based on first principles of probability and applies equally well to all areas of chance provided the underlying assumptions are correct and the model inputs are valid. That's pretty much the opposite of ad hoc.

But your posting an ad hoc method that you claim to use in real life (and knowing and trusting you in real life I'm sure you do) but without providing even the most meager of logical justifications for it is hardly education -- it's just showing off.

I'm not answering your question because it's not at all the point of this thread.

I'm here in this thread to educate and elucidate by both demonstrating and explaining the Bayesian math underpinning this type of analysis so that people may then refine and hone the analysis to fit their own needs based both upon additional posterior knowledge along with analysis of the sport in question's historical record. The point is that until one sufficiently understands the basic and generic principles of a given sports betting modality, one will have a difficult time building upon it to a creative an effective and predictive model of their own.

[Ganchrow]

no, I'm not sure what those # represent. 8.71% of the time you would draw team A along with Home from the other sack. 33.4% of the time you would draw team B with road. The rest of the time the other 2 options.

Yeah:

(8.71% + 33.40%) 8.71% - 1 ≈ 3.835.

[reno cool]

Alright, I think I'm beginning to get the principle here. Seemed like a simple question at first. Thnx

[Wheell]

Mine is not ad hoc methodology ... it's based on first principles of probability and applies equally well to all areas of chance provided the underlying assumptions are correct and the model inputs are valid. That's pretty much the opposite of ad hoc.

But your posting an ad hoc method that you claim to use in real life (and knowing and trusting you in real life I'm sure you do) but without providing even the most meager of logical justifications for it is hardly education. It's just showing off.

I'm not answering your question because it's not at all the point of this thread.

I'm here in this thread to educate and elucidate by demonstrating and explaining the Bayesian math underpinning this type of analysis so that people may then refine and hone the analysis to fit their own needs based both upon posterior knowledge along with analysis of the sport in question's historical record. The point is that until one sufficiently understands the basic and generic principles of a given sports betting modality, one will have a difficult time effectively building upon it to a creative an effective and predictive model of their own.

I never meant to accuse you of using an ad hoc method, I just don't know how to snip parts of a post. I was attempting to directly answer your point.

The assumptions in the Bayesian model might work in a lab but in real life modifications are necessary in every sport I have encountered.

I'm not going to provide the directions for the left turn past Albuquerque but if you look at the numbers and the method I listed someone who aced the math part of the SAT's like yourself should be able to figure out where to go next.

As for not answering my question of what lines you would set, should I create another post where that IS the point? If I do will you answer the question?

[Ganchrow]

I never meant to accuse you of using an ad hoc method, I just don't know how to snip parts of a post. I was attempting to directly answer your point.

My apologies for my misunderstanding then.

The assumptions in the Bayesian model might work in a lab but in real life modifications are necessary in every sport I have encountered.

Of course modifications are necessary ... but if you don't understand the Bayesian model in the first place how can you intelligently make such modifications?

Step 1: Learn basic theory
Step 2: Understand implications basic theory
Step 3: Compare theory with historical record
Step 4: Look for existing systematic bias
Step 5: Refine model assumptions to adjust for said biases
Step 6: Understand implications of refined thoery
Step 7: Continue with Step 3

I'm not going to provide the directions for the left turn past Albuquerque but if you look at the numbers and the method I listed someone who aced the math part of the SAT's like yourself should be able to figure out where to go next.

I'm not after your models. You know that quite well. Nor am I interested in the mechanics of the process. It's not enough to me (and I think also to most regular contributors to the Think Tank, including obviously you) to know which buttons to push, but rather to know what each button actually does and why they should all be pressed in the first place.

As for not answering my question of what lines you would set, should I create another post where that IS the point? If I do will you answer the question?

At this point it's just a loaded question, isn't it?

I think you realize why I'm not answering it, anyway ... but as I keep saying ... that reason is besides the point of this thread.

Anyway, we can talk about it next time we go out and get drunk. Asshole.

[Wheell]

Anyway, we can talk about it next time we go out and get drunk. Asshole.



And here is what I think of you:
Link Not Working - Removed-)

[Ganchrow]

The two other answers are "Albuquerque" or Bugs Bunny lines. Let's look at the case of two average teams facing each other such that the home team wins 61% of the time. using the method I outlined above we get the road team as approx .4444 and the home team approx .5556. Applying the 1/7 team as facing these teams at home or away gives +480 and +750 lines respectively.

OK. So to put this in familiar terms, here's what you've proposed:

Let P = Team X wins next game at home
Let X = Probability Team X wins next game on neutral field
Let H = Probability that an average team wins at home against average opponent

p = ^{(X * √H)} / _{(X * √H + (1 - X) * √1 - H )}

Or more simply stated using the logit() function:

lg(P) = lg(X) + lg(H) 2

To the extent it works ... great.

[reno cool]

Yeah:

(8.71% + 33.40%) 8.71% - 1 ≈ 3.835.

ok what does this mean? why not just:

.334/.0871= 3.835