Attn: Justin Re: "Sum of two distributions"

[MonkeyF0cker]

In a 16 game season, you take the sum of two distributions. 8 games, p+0.1, added to 8 games, p-0.1.

I'm talking about assigning a power ranking to each team. Give each team a ranking of 0 to 1, which is the probability of it beating an "average" team on a neutral field. The .1 adjustment (perhaps 0.09 is more accurate) is for HFA.

An average team with an average schedule have a distribution of Binom(8,0.6) + Binom(8,0.4). A good team (expected to win 12 games) would be Binom(8,0.85) + Binom(8,.65).

Perhaps, I'm a little novice in my distribution mathematics and maybe your way is more efficient. Anyway, I'd like to find out but from what you stated in the Season Win Totals thread, it's unclear to me how you work out the addition of two binomials. Perhaps, you could enlighten me a little. For the sake of simplicity, let's assume that you have an average team with an average schedule (50% neutral field win expectancy) and use your HFA adjustment. So, assuming that there are 8 games for a team with a 60% chance of winning at home and 8 games with a 40% chance of winning on the road and I'm trying to find the odds that the team wins 8 games or more throughout the season, how would I add the two binomials in Excel? Am I supposed to use 1-BINOMDIST(8, 16, 0.6, TRUE) and 1-BINOMDIST(8, 16, 0.4, TRUE)? Or would I use 1-BINOMDIST(4, 8, 0.6, TRUE) and 1-BINOMDIST(4, 8, 0.4, TRUE)? Do I then simply add the probabilities together? Do I average them? What do I do?

Thanks.

[Justin7]

Perhaps, I'm a little novice in my distribution mathematics and maybe your way is more efficient. Anyway, I'd like to find out but from what you stated in the Season Win Totals thread, it's unclear to me how you work out the addition of two binomials. Perhaps, you could enlighten me a little. For the sake of simplicity, let's assume that you have an average team with an average schedule (50% neutral field win expectancy) and use your HFA adjustment. So, assuming that there are 8 games for a team with a 60% chance of winning at home and 8 games with a 40% chance of winning on the road and I'm trying to find the odds that the team wins 8 games or more throughout the season, how would I add the two binomials in Excel? Am I supposed to use 1-BINOMDIST(8, 16, 0.6, TRUE) and 1-BINOMDIST(8, 16, 0.4, TRUE)? Or would I use 1-BINOMDIST(4, 8, 0.6, TRUE) and 1-BINOMDIST(4, 8, 0.4, TRUE)? Do I then simply add the probabilities together? Do I average them? What do I do?

Thanks.

I'm sure you need no help with this, but it is a decent question for other people.

You can calculate the odds of a team winning x games manually. P(win 0 games) = BinomDist(0,8,0.6,false) * BinomDist(0,8,0.4,false). P(win 1 game) will be the sum of 2 distributions (Home win 1 * road win 0, and home win 0 * road win 1). P(win 2 games) will be the sum of 3 distributions and so on, up to 9 terms for 8-8... and then 8 terms for 9-7, down to 1 term for 16-0. It's a pain in the ass to do it this way, and I'd probably make typos.

Another way to do it is to create a 9x9 table. On the vertical axis, you have the home wins, with the home win probability distribution. On the horizontal axis, you have the road wins, with the road win distribution probability. Each box of the grid is the product of the two probabilities.

I would create two more 9x9 tables, determining whether that distribution won or lost. For winners (assuming you bet over), it might be =if(roadwins+homewins>SeasonWinsOffer,1, 0) in the whole grid, their roadwins and homewins depends on the cell you are calculating. Almost easier to do than describe.

Add up all the distributions if you have a 1 in your winner grid via sumproduct. That is the p of winning. Add up the distributions if you have a 1 in your loser grid. That is your p of losing. Whatever is leftover is the probability of a push.

[Justin7]

Here's a quick example that took about 10 minutes. I wouldn't bet anything using this until I spent some time making sure everything was correct.

[MonkeyF0cker]

Do you realize that you're creating a combinatorical distribution? What happens when you need to find the probability for 8.5 or 9 wins for the next team? So you keep extending and contracting the matrices for each unique win total? How is that efficient? Do you know that it's possible to create a combinatorical function that includes that team's schedule for an NFL season that you'd never need to alter unless the season length changed? There's no way your way takes less time than mine, and it's certainly not accurate.

How much would you be willing to bet that I can't change the actual push rate for 8 wins (keeping an average win probability of 50% throughout the season with lines -600 < x < 600) by more than 2% simply through the schedule?

[Justin7]

Do you realize that you're creating a combinatorical distribution? What happens when you need to find the probability for 8.5 or 9 wins for the next team? So you keep extending and contracting the matrices for each unique win total? How is that efficient? Do you know that it's possible to create a combinatorical function that includes that team's schedule for an NFL season that you'd never need to alter unless the season length changed? There's no way your way takes less time than mine, and it's certainly not accurate.

If I want to find the p for 8.5 or 9 terms, I simply change change it in cell C6. Add 10 seconds (including load time) to the 10 minutes I already spent.

How much would you be willing to bet that I can't change the actual push rate for 8 wins (keeping an average win probability of 50% throughout the season with lines -600 < x < 600) by more than 2% simply through the schedule?

You can spend as much time as you like on a $500 prop. Unless your gains are extraordinary, you will lower your hourly wage to that of a burger flipper.

[MonkeyF0cker]

If I want to find the p for 8.5 or 9 terms, I simply change change it in cell C6. Add 10 seconds (including load time) to the 10 minutes I already spent.

So, you're saying that you can change all three matrices and input the data faster than I can copy and paste 16 lines and click a button?

You can spend as much time as you like on a $500 prop. Unless your gains are extraordinary, you will lower your hourly wage to that of a burger flipper.

Really? What if I told you that I can make a 4% edge with your way -EV simply due to the schedule with the exact same constraints that I outlined above? Who's flipping (coins) burgers exactly?

I think you're missing a key component here. Programs can be written and reused. The work is done once. Where are you not understanding this?

[Justin7]

So, you're saying that you can change all three matrices and input the data faster than I can copy and paste 16 lines and click a button?

I'll repeat myself, since you missed it. I can change one cell, and it changes all the matrices. So yes, that is faster than your cut/paste.

Really? What if I told you that I can make a 4% edge with your way -EV simply due to the schedule with the exact same constraints that I outlined above? Who's flipping (coins) burgers exactly?

I wouldn't be surprised. I'm sure I can find one season win total in 3 years that does the same. And (as I said earlier) the extra time you expend on this lowers your hourly rate. Do you actually bet this stuff?

I think you're missing a key component here. Programs can be written and reused. The work is done once. Where are you not understanding this?

I don't know why you believe this. There is the creation of a reusable program, and the importation of data. In a trivial problem like this, importing the data takes longer than the underlying program.

Monkey, you are like a bag of Doritos. I know better. I know I shouldn't. But oh, the combination of the ingredients with no redeeming values is so good, I just have to bite.

On a more important note than the trivialities of this thread, how do you prefer the pronunciation of your alias?

[MonkeyF0cker]

I'll repeat myself, since you missed it. I can change one cell, and it changes all the matrices. So yes, that is faster than your cut/paste.

Are you REALLY trying to compare this in nanoseconds?

I wouldn't be surprised. I'm sure I can find one season win total in 3 years that does the same. And (as I said earlier) the extra time you expend on this lowers your hourly rate. Do you actually bet this stuff?

Umm. So, you think that there's only ONE schedule (between -600 < x < 600) that alters the actual edge by 4%+? LOL. And what about all of the others from (1%, 4%)???? Insignificant I suppose. The reason I brought it up is to show that IT MATTERS.

I don't know why you believe this. There is the creation of a reusable program, and the importation of data. In a trivial problem like this, importing the data takes longer than the underlying program.

The creation takes a trivial amount of time more than creating your method and can be made to incorporate a variable number of games (i.e. It can be used for other sports as well.). So, while you're recreating yours for NCAAF, MLB, whatever, mine is already up and running.

Monkey, you are like a bag of Doritos. I know better. I know I shouldn't. But oh, the combination of the ingredients with no redeeming values is so good, I just have to bite.

On a more important note than the trivialities of this thread, how do you prefer the pronunciation of your alias?

No redeeming values? LOL. Projecting much?

[brettd]

From a neutral observer on the front line here, at least Justin gave us an example spreadsheet for us plebs to work with. Maybe Monkey could show us the superiority of his method by making an example spreadsheet for the rest of us to look at too.

[MonkeyF0cker]

From a neutral observer on the front line here, at least Justin gave us an example spreadsheet for us plebs to work with. Maybe Monkey could show us the superiority of his method by making an example spreadsheet for the rest of us to look at too.

I guess I should clarify that it's not MY method, per se. It's simply the proper way to calculate the true odds of all elements in the domain of a discrete, combinatorial distribution with the given information.

I won't be releasing anything. My work is almost exclusively done in a programming language - not Excel.

[mathdotcom]

I feel sorry for anyone who uses Excel daily

I find it even too clumsy to use for basic accounting. Slow/inefficient, frustrating, pretends to be user friendly but isn't, like all Microsoft products.

[HUY]

A spreadsheet is good for interactive functionality, like a calculator. It's also good for keeping track of your bet history. It's horrendous for research though.

[FreeFall]

A spreadsheet is good for interactive functionality, like a calculator. It's also good for keeping track of your bet history. It's horrendous for research though.

What happens when you have 10000 bets in your SS?

I prefer databases.

[calm]

I feel sorry for anyone who uses Excel daily

I find it even too clumsy to use for basic accounting. Slow/inefficient, frustrating, pretends to be user friendly but isn't, like all Microsoft products.

User error.

[evo34]

Perhaps, I'm a little novice in my distribution mathematics and maybe your way is more efficient. Anyway, I'd like to find out but from what you stated in the Season Win Totals thread, it's unclear to me how you work out the addition of two binomials. Perhaps, you could enlighten me a little. For the sake of simplicity, let's assume that you have an average team with an average schedule (50% neutral field win expectancy) and use your HFA adjustment. So, assuming that there are 8 games for a team with a 60% chance of winning at home and 8 games with a 40% chance of winning on the road and I'm trying to find the odds that the team wins 8 games or more throughout the season, how would I add the two binomials in Excel? Am I supposed to use 1-BINOMDIST(8, 16, 0.6, TRUE) and 1-BINOMDIST(8, 16, 0.4, TRUE)? Or would I use 1-BINOMDIST(4, 8, 0.6, TRUE) and 1-BINOMDIST(4, 8, 0.4, TRUE)? Do I then simply add the probabilities together? Do I average them? What do I do?

Thanks.

Why do you troll so obviously/desperately/frequently if you've already figured it all out and are sleeping on a mattress made of money? Sincere question.

[mathdotcom]

User error.

Yes it's my fault that it takes a long time to load and is not built to handle any real data analysis, and it's my incompetence that makes me prefer a much more bare bones and complicated command based program that 99% of people would not have any clue how to use...

[MonkeyF0cker]

Why do you troll so obviously/desperately/frequently if you've already figured it all out and are sleeping on a mattress made of money? Sincere question.

Apparently, trolling is letting people know that Justin's method has serious quantitative flaws and his stance on losing his precious time is meritless. Good to know.

You might not like my approach, but I'm right. That must be why it bothers you so much. If you think not, I would love for you to attempt to prove me wrong.

You should be seriously embarrassed by your post about Renaissance BTW. That's probably why you're in this thread though. Keep trying, guy. You'll get it right one of these times.

[MonkeyF0cker]

Here's what I will provide though...

An average team. A line is offered with a total of 8.5 wins at +155o/-175u. For Justin, this presents a 2.0171389% edge on the over.

With this schedule (in win %)...

0.649122807
0.565217391
0.722222222
0.761904762
0.733333333
0.454545455
0.795918367
0.722222222
0.357142857
0.238095238
0.25
0.3125
0.263157895
0.344827586
0.6
0.229789864

The actual edge on the over at +155 is -0.2037793%. The lines average to 50% through the course of the season. They are mostly comprised of ML's that equate to spreads of 3.5-8 (which is certainly not out of the ordinary) with all ML's between +336 and -390.

[mathdotcom]

fudge factor

[evo34]

Apparently, trolling is letting people know that Justin's method has serious quantitative flaws and his stance on losing his precious time is meritless. Good to know.

You might not like my approach, but I'm right. That must be why it bothers you so much. If you think not, I would love for you to attempt to prove me wrong.

You should be seriously embarrassed by your post about Renaissance BTW. That's probably why you're in this thread though. Keep trying, guy. You'll get it right one of these times.

My error trades in the past month are larger than what you've traded in your lifetime. But whatever.

[MonkeyF0cker]

My error trades in the past month are larger than what you've traded in your lifetime. But whatever.

Of course they are. That goes without saying.

Your dick is 8234 miles long too.

[MonkeyF0cker]

Who's trolling now, assbag?