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

I'm working with an NHL database to come up with some over/under percentages for various periods. I have all of the games from this current season for every time broken down by period.

I then have these calculated to determine that teams Over or Under 1.5 percentage, a line that is commonly offered for each period.

Then, I have a summary page where I can average the values for two teams who will be playing that day:

Example: Detroit goes under 54.55% of the time and PHI goes under 43.64% of the time.
If they are playing each other, that becomes an average of 49.09% on the under.

I hope everyone can follow me so far. Everything seem logical up to this point?

Then, since many NHL teams use various goalies, I have an average of each teams goals allowed per game. Det might give up 2.61 goals per game...this number is an average of ALL the goaltenders they might use during the season.

I want to use the goaltender for THAT particular game. If Goalie #1 gives up 3.09 goals per game, he would be 118.39% ABOVE the average for the team.

Therefore, the team would theoretically give up more shots and the game would go OVER more often than average.

Everyone following this?

My problem: How do I incorporate this goalie number into the averages I have for the OVER/Under?

I've tried taking the average of the two goalies (say its 105% above their teams averages), then multiplying that by the current over/under percentage.

An example:

Goalies:
DET MACDONALD 118.39%
PHI LEIGHTON 100.18%
Average for the combined goalies:
109.28%

O/U:
49.09% 50.91%

Weighted by Goalies:
O/U:
53.65% 55.64%

Basically, multiplying 109.28% by the O/U numbers adds 9.28% to the total. However, as u can see, the %'s no longer add up to 100%.

Anyone have any ideas or thoughts on where I'm going with this?

Please let me know. I've spent a very long time working on this.

Thanks.

DrSues02

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

[ QUOTE ]
I want to use the goaltender for THAT particular game. If Goalie #1 gives up 3.09 goals per game, he would be 118.39% ABOVE the average for the team.

Therefore, the team would theoretically give up more shots and the game would go OVER more often than average.

[/ QUOTE ]

This is not necessarily true. The goalie could (and most likely ) just gives up more goals with an equal # of shots because he is not as good. Your point on the game going over more is valid though.

This would be a VERY time consuming process, but can't you just look up the goalie for each game and use all those games as the average for the team, instead of saying that he gives up x% more then the total average.

I know you're using a variant of my system, but IMO you're making it WAY too complicated. You're on a slippery slope here, if you're going to break the games down so far as each goalie being used, why don't u consider the quality of the ice at game time, the referees in the game, and other IMO not so important factors that play into each game.

I understand that different goalies will effect the outcome, but for all that work you have to do to come up with these stats, I don't think it will raise your ROI enough to justify the extra work.

Re: math question and the effect on over/under percentages..please hel
 

I agree with 139 - The only exception might be teams that specifically employ a 60/40 split or smaller in goalie duties. I can only think of 1 such team: San Jose.

Perhaps Tampa as well.

Re: math question and the effect on over/under percentages..please hel
 

I'm not knocking the OP, but I REALLY HATE this forum's software. One misstep and a lot of writing is lost. This will probably be the last long post I'll reply to with proper context.

[ QUOTE ]
I'm working with an NHL database to come up with some over/under percentages for various periods. I have all of the games from this current season for every time broken down by period.

...

Example: Detroit goes under 54.55% of the time and PHI goes under 43.64% of the time.
If they are playing each other, that becomes an average of 49.09% on the under.

I hope everyone can follow me so far. Everything seem logical up to this point?

[/ QUOTE ]

As long as one opponent is above average and one is below average, this is fine. If both are above or below average this method is badly flawed. I hope you can see why.

[ QUOTE ]

My problem: How do I incorporate this goalie number into the averages I have for the OVER/Under?

[/ QUOTE ]

Here's how I'd do it (and how I've done it for baseball totals). I'd record who the goalie is for each game and treat each "team:goalie" combination individually. This eliminates your problem.

I haven't carefully analyzed your results, but I'm guessing that your math problem is due to the fact that each goalie hasn't played half of all games. So, no matter what, you have to track how many games are played by each goalie so you know how to weight your percentages, so you may as well break their stats out separately.

Make sense?

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

[ QUOTE ]
, if you're going to break the games down so far as each goalie being used, why don't u consider the quality of the ice at game time, the referees in the game, and other IMO not so important factors that play into each game.

I understand that different goalies will effect the outcome, but for all that work you have to do to come up with these stats, I don't think it will raise your ROI enough to justify the extra work.

[/ QUOTE ]


because goalie in net probably has a significant effect of decent magnitude and is easily obtained
whereas the other factors mentioned don't line up that easily.

Re: math question and the effect on over/under percentages..please hel
 

[ QUOTE ]

I'm not knocking the OP, but I REALLY HATE this forum's software. One misstep and a lot of writing is lost. This will probably be the last long post I'll reply to with proper context.

[ QUOTE ]
I'm working with an NHL database to come up with some over/under percentages for various periods. I have all of the games from this current season for every time broken down by period.

...

Example: Detroit goes under 54.55% of the time and PHI goes under 43.64% of the time.
If they are playing each other, that becomes an average of 49.09% on the under.

I hope everyone can follow me so far. Everything seem logical up to this point?

[/ QUOTE ]

As long as one opponent is above average and one is below average, this is fine. If both are above or below average this method is badly flawed. I hope you can see why.

[ QUOTE ]

My problem: How do I incorporate this goalie number into the averages I have for the OVER/Under?

[/ QUOTE ]

Here's how I'd do it (and how I've done it for baseball totals). I'd record who the goalie is for each game and treat each "team:goalie" combination individually. This eliminates your problem.

I haven't carefully analyzed your results, but I'm guessing that your math problem is due to the fact that each goalie hasn't played half of all games. So, no matter what, you have to track how many games are played by each goalie so you know how to weight your percentages, so you may as well break their stats out separately.

Make sense?

[/ QUOTE ]

Honestly, I don't see why where my math is flawed in the original average. If there is a better way to average them both..not taking into account the goalie factor, how would u go about the math?

Re: math question and the effect on over/under percentages..please hel
 

[ QUOTE ]
Honestly, I don't see why where my math is flawed in the original average. If there is a better way to average them both..not taking into account the goalie factor, how would u go about the math?

[/ QUOTE ]

If DET goes under 55% of the time and so does PHI, you assume that a DET-PHI game will be under 55% of the time, as well. But chances are that this is already factored into the line.

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

[ QUOTE ]
[ QUOTE ]
, if you're going to break the games down so far as each goalie being used, why don't u consider the quality of the ice at game time, the referees in the game, and other IMO not so important factors that play into each game.

I understand that different goalies will effect the outcome, but for all that work you have to do to come up with these stats, I don't think it will raise your ROI enough to justify the extra work.

[/ QUOTE ]


because goalie in net probably has a significant effect of decent magnitude and is easily obtained
whereas the other factors mentioned don't line up that easily.

[/ QUOTE ]

you are right and I guess I exaggerated a little when I compared it to those other factors. The goalie in net has a much greater impact on over/under totals then the quality of ice or referees. I was just trying to make a point that there are a basically unlimited # of factors that go into each and every game and to try to analyze them all is very unlikely.

Re: math question and the effect on over/under percentages..please hel
 

[ QUOTE ]
[ QUOTE ]
Honestly, I don't see why where my math is flawed in the original average. If there is a better way to average them both..not taking into account the goalie factor, how would u go about the math?

[/ QUOTE ]

If DET goes under 55% of the time and so does PHI, you assume that a DET-PHI game will be under 55% of the time, as well. But chances are that this is already factored into the line.

[/ QUOTE ]

What I'm looking for is when it ISNT factored into the line. If they are both going under 55% of the time, then the average between the 2 teams is 55% U. The fair line for this is -122.

If i can find a line at +100 for this bet, wouldn't there be value there?

Please let me know if you think my math is flawed.

DrSues02

Re: math question and the effect on over/under percentages..please hel
 

You're making a couple of important math mistakes throughout.

The first is that you're not recognizing the difference between median and mean. When working with small numbers (such as goals in a period) this can be a significant mistake. For example, a team that scores an average of 4 goals a game may seem like a good bet to score more than 2.5 goals in their next game. However if that team has scored 2, 2, 2, 2, and 12 goals in the five games they've played they have been under the 2.5 line four out of the five times.


This is a median based calculation:
[ QUOTE ]
Detroit goes under 54.55% of the time and PHI goes under 43.64% of the time.

[/ QUOTE ]

This is a mean based calculation:
[ QUOTE ]
If Goalie #1 gives up 3.09 goals per game, he would be 118.39% ABOVE the average for the team.

[/ QUOTE ]

You cannot calculate a weighted O/U % from these two statistics alone.


The second math mistake is related. In your final calculation you attempt to multiply % O/U and % goals. These two units don't match. You're attempting to factor in the goalkeeper way to late in your calculation. As npc suggested a good solution would be too keep your data separated by team:goalie then do the calculations from there.

Re: math question and the effect on over/under percentages..please hel
 

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.

Re: math question and the effect on over/under percentages..please hel
 

[ 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

Re: math question and the effect on over/under percentages..please hel
 

discrete verse continuous distributions

Re: math question and the effect on over/under percentages..please hel
 

[ QUOTE ]
discrete verse continuous distributions

[/ QUOTE ]

No idea what this means.

DrSues02

Re: math question and the effect on over/under percentages..please hel
 

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

Re: math question and the effect on over/under percentages..please hel
 

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.

Re: math question and the effect on over/under percentages..please hel
 

[ 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.

[/ 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.

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

Re: math question and the effect on over/under percentages..please hel
 

[ 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.


[/ QUOTE ]

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.