math question and the effect on over/under percentages..please help

[ImBen]

This thread is such an absolute mess I wouldn't know where to begin even if I had the slightest interest in helping other people compete for my money.

[DrSues02]

[ QUOTE ]
This thread is such an absolute mess I wouldn't know where to begin even if I had the slightest interest in helping other people compete for my money.

[/ QUOTE ]

That's why I posted. Any help would be appreciated. It has taken me a long time to enter in all the season data...changing the formulas on the summary page is the easy part. Just need suggestions.

DrSues02

[MyTurn2Raise]

discrete verse continuous distributions

[DrSues02]

[ QUOTE ]
discrete verse continuous distributions

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No idea what this means.

DrSues02

[DrSues02]

I sent several people PM's but no replies. I would really like to discuss this with someone who believes there are errors in my math.

Any other thoughts.

DrSues02

[jelly]

To start with, I like threads like this so please do not get discouraged with my comments as they are not meant as an abuse. This is not a forum for ImBen style oneliners - we are here because we believe that EV(learning from each other)>EV(staying in the cave). Therefore I appreciate your interest.
Now lets face one thing. You are trying to put together a stat-analyzing system to beat sportsbetting, right? What do you know about statistics? Very little, I'd say. You cannot tell the diference in discrete vs. continuous distribution and you are sending around PMs asking to discuss "your math"? I know you mean well, but it is like discussing poker hand saying "I do not know what pot odds are, but please tell me, where my line is wrong." I hope you can see that this would not make sense.
Fundamental error in your math is that you believe that you can add up, multiply or average any two numbers that have the same "%" sign behind them. Now, do you think that people would be studying statistics at universities if things could be solved in this 9th grade way? Your numbers are approximations at best and this is not very useful with sportsbetting, where the edges are pretty slim.
As an example, do you think that those teams that cover OVER 55% of the time vs. random opponent would cover OVER only 55% of the time facing each other? Common sense says it is more. BTW, note for <font color="red"> adanthar </font> here: unlike NFL or NBA, the lines are usually the same across the card in NHL (especially when it comes to period total) - books only change odds because moving a line by half a point is huge in hockey, compared to high scoring sports. So actually this data is of some use (although it is not the best route).
Another spot - you multiply OVER percentage with sum of percentages assigned to both goalies. Obviously the only reason to add these up is to get an around-one-hunderd-number to multiply with. Anyway, multiplying UNDER with 109% makes no sense at all so let us do it "properly". You rate GKs by their "defensive contribution" which would be 1/your_number. So MacDonald would be 84% of the average in "stopping goals" and therefore UNDER is less likely. Leighton is 1/1.0018 so their average is around 92% and when I multiplied this with UNDER figure of 50.81% I got like 46.9 which does not add up with what you counted as OVER percentage by far more than rounding could explain. That should make obvious that this cannot be the right way.
To give you some pointers - scoring in hockey is basically a Poisson process so you ideally want to find intensities of scoring for both teams in the given match, calculate probabilities of each team scoring different number of goals and adding those up for different totals. You probably wont fully understand this so before you ask, please get some introductory text on statistics so that you become familiar with the basics first. I do not want to offend you but otherwise it is really difficult to speak about this.

[DrSues02]

[ QUOTE ]
To start with, I like threads like this so please do not get discouraged with my comments as they are not meant as an abuse. This is not a forum for ImBen style oneliners - we are here because we believe that EV(learning from each other)&gt;EV(staying in the cave). Therefore I appreciate your interest.
Now lets face one thing. You are trying to put together a stat-analyzing system to beat sportsbetting, right? What do you know about statistics? Very little, I'd say. You cannot tell the diference in discrete vs. continuous distribution and you are sending around PMs asking to discuss "your math"? I know you mean well, but it is like discussing poker hand saying "I do not know what pot odds are, but please tell me, where my line is wrong." I hope you can see that this would not make sense.
Fundamental error in your math is that you believe that you can add up, multiply or average any two numbers that have the same "%" sign behind them. Now, do you think that people would be studying statistics at universities if things could be solved in this 9th grade way? Your numbers are approximations at best and this is not very useful with sportsbetting, where the edges are pretty slim.
As an example, do you think that those teams that cover OVER 55% of the time vs. random opponent would cover OVER only 55% of the time facing each other? Common sense says it is more. BTW, note for <font color="red"> adanthar </font> here: unlike NFL or NBA, the lines are usually the same across the card in NHL (especially when it comes to period total) - books only change odds because moving a line by half a point is huge in hockey, compared to high scoring sports. So actually this data is of some use (although it is not the best route).
Another spot - you multiply OVER percentage with sum of percentages assigned to both goalies. Obviously the only reason to add these up is to get an around-one-hunderd-number to multiply with. Anyway, multiplying UNDER with 109% makes no sense at all so let us do it "properly". You rate GKs by their "defensive contribution" which would be 1/your_number. So MacDonald would be 84% of the average in "stopping goals" and therefore UNDER is less likely. Leighton is 1/1.0018 so their average is around 92% and when I multiplied this with UNDER figure of 50.81% I got like 46.9 which does not add up with what you counted as OVER percentage by far more than rounding could explain. That should make obvious that this cannot be the right way.
To give you some pointers - scoring in hockey is basically a Poisson process so you ideally want to find intensities of scoring for both teams in the given match, calculate probabilities of each team scoring different number of goals and adding those up for different totals. You probably wont fully understand this so before you ask, please get some introductory text on statistics so that you become familiar with the basics first. I do not want to offend you but otherwise it is really difficult to speak about this.

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Thank you for the reply. I was only hoping to generate some discussion on the topic and find it helpful that people point out my mistakes.

I've taken calculus and statistics at university level. I'm a straight A student on a full ride scholarship for grades. This definitely isnt a brag (since numerous people have pointed out how wrong I am), but to show I can understand what people are talking about....I just don't choose to "brush up" on my statistics every day.

As far as the goalies: I will just make seperate teams by goalies instead of working out the +/- % as compared to the other goalies on the squad. I've already gone through the data and added the goalies for each game so this should be relatively easy to do.

So back to my original problem: If one team that is 55% 1stP under plays another team that is 50% 1stP under, how would you calculate the odds of that this particular game goes under?

Keep in mind, that these percentages were derived from a sampling of ALL of that teams games vs a group of random opponents.

Thank you again for the reply. I hope we can discuss this further. I sent you a PM as well.

DrSues02

[jelly]

[ QUOTE ]

Thank you for the reply. I was only hoping to generate some discussion on the topic and find it helpful that people point out my mistakes.

I've taken calculus and statistics at university level. I'm a straight A student on a full ride scholarship for grades. This definitely isnt a brag (since numerous people have pointed out how wrong I am), but to show I can understand what people are talking about....I just don't choose to "brush up" on my statistics every day.


[/ QUOTE ]

You are welcome.
I expected you to understand what I wrote (otherwise there is no point writing it up, is it? [img]/images/graemlins/grin.gif[/img]) You might have taken statistics course but it (i) was one of really poor standard or (ii) you forgot a LOT since you passed it. If you want to take this mission seriously, you really should refresh/broaden your knowledge.

[ QUOTE ]

So back to my original problem: If one team that is 55% 1stP under plays another team that is 50% 1stP under, how would you calculate the odds of that this particular game goes under?

Keep in mind, that these percentages were derived from a sampling of ALL of that teams games vs a group of random opponents.


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You have your data. You start by discarding an awful lot of it. BOS 3 ANA 1 becomes TRUE. BOS 0 ANA 0 is FALSE. Then you decide you want some interactions and start working them kind of backwards. Sounds sub-optimal at best.
If you still want an answer to your question, you want to create function [0,100]x[0,100]-&gt;[0,100] that has a couple of common sense features like symmetry, continuity, non-decreasness and a couple of boundary conditions &lt;0,0&gt;=0, &lt;100,100&gt;=100, perhaps &lt;x,50&gt;=x (not so sure). Think of others, perhaps finetune it towards the data - I do not know it and I would not go this way.