Calculating Season Wins Fair Odds

[rfr3sh]

Lets say I calculate the number of wins I think a team should win during the year, how do I calculate which lines I should bet

for instance:

Lets say I have Estimated the Bills wins total at 6 wins,

Pinny currently offers :

Over 5 - 136
Under 5 +116

Is this a good line for me to bet?
If so how would I calculate that?
What if Pinny had the line set at 6 instead of 5?

[Justin7]

Lets say I calculate the number of wins I think a team should win during the year, how do I calculate which lines I should bet

for instance:

Lets say I have Estimated the Bills wins total at 6 wins,

Pinny currently offers :

Over 5 - 136
Under 5 +116

Is this a good line for me to bet?
If so how would I calculate that?
What if Pinny had the line set at 6 instead of 5?

Do a binomial distribution. A quick rule of thumb is that a half-game in NFL season wins is worth 50 cents at the "8", and less as you get further away.

If 6 is the fair number, I would bomb away on over 5 -136.

[rfr3sh]

Do a binomial distribution. A quick rule of thumb is that a half-game in NFL season wins is worth 50 cents at the "8", and less as you get further away.

If 6 is the fair number, I would bomb away on over 5 -136.

Not familiar with binomial distribution will have to google search it

[Ganchrow]

Well the first consideration, of course, would be the texture of the team in question's games.

To illustrate, imagine two hypothetical scenarios:

1. The Bills had 10 games with opponents against whom they had exactly 0% probability of winning, and 6 games with opponents against whom they had a 100% probability of winning.
2. The Bills had 16 games with opponents against all of whom they had exactly 6 16 = 37.5% probability of winning.

Now in both in cases expected win total is 6 games, but obviously the two distributions would be entirely different. In the first case you'd take the under 6.5 at ANY price as you would with the over 5.5. (While in the second scenario fair values on the overs would be o5 -267, o5.5 -146, o6 +104, o6.5 +156.)

Obviously this is a particularly pathological example, but I think you get the point.

An inextricably related issue is that of home versus away games. Even if you were to assume the Bills equally likely to win against all opponents on neutral ground, HFA would still come in to play.

With those caveats aside (and several others glossed over for the sake of brevity), were we to assume equal win probabilities for each game then the fair value for any given season win total can easily be calculated via the Binomial distribution.

Let S = Total games played = 16
Let W = Expected number of wins

Then for integer X:

The probability of Over X½ seasons wins would be given in Excel by:

=1-BINOMDIST(X, 16, W/S, 1)

And the conditional probability of Over X seasons wins would be given in Excel by:

=(1-BINOMDIST(X, 16, W/S, 1)) / (1-BINOMDIST(X, 16, W/S, 0))

So for over 5.5, this would yield a probability of =1-BINOMDIST(5, 16, 6/16, 1) ≈ 59.3268%, which at a line of -136 would an expected edge of 2.95%.

Note, however, that this simple single-parameter analysis, while potentially valuable versus a rec-style bookmaker that sets its own lines, is most assuredly not going to beat Pinnacle.

[Ganchrow]

Not familiar with binomial distribution will have to google search it

The binomial distribution simply computes the probability of winning W out of N trials of an event, each one individually with win probability p.


Specifically:

Pr(W wins out of N trials | single trial win probability = p) = _NC_W * p ^W * (1-p) ^W-N

Where _NC[sub]W[/sub is the combinatorial function given by N! W! * (N-W)! , and N! represents N factorial, which is N * (N-1) * (N-2) * ... . The combinatorial function is given in excel by:

=COMBIN(W, N)

The binomial distribution is also given in Excel:

=BINOMDIST(W, N, p, 0)

If you wanted to calculate the probability of W or fewer wins then the Excel formula would be:

=BINOMDIST(W, N, p, 1)

And if you wanted to calculate the probability of W or more wins then the Excel formula would be:

=1 - BINOMDIST(W-1, N, p, 1)

[Ganchrow]

With respect to a couple of the problems with using the binomial distribution for calculating (MLB) win totals, I posted the following way back in the Spring of '07 (nope, can't get there from here):

1. There are almost certainly different probabilities associated with winning home and away games. It's not the case that in general that the sum of two independent binomial random variables is distributed binomially, so as such it isn't appropriate to just look at the average win rate across home and road designations.
   
   Nevertheless, for home home/away win rates that are fairly close, results should be rather similar. For example, for a home win rate of 60% and an away win rate of 80%, the true probability of winning 121 or fewer game would be 49.407%; while using the binomial and the average win rate of 75%, results are 49.395%, a difference of 0.012%.
   
   This objection could further be extended with the realization that win rates aren't constant between opponents either. However, because each team plays a fairly large number of opponents, this issue will in most cases carries even less weight than the home/away issue.
   
   
2. Results between games are probably not independent. I'm not talking in reference to unexplained, generic streaks, which most statistical literature tends to discount, but in reference to specific events such as injuries, trades, and play-off contention. In other words, mathematically speaking, the data probably possesses some auto-correlation, meaning that the deviation from expected results of a given game is correlated with the deviation from expected results results of other games.
   
   In this manner autocorrelation will tend to widen the tails of a distribution, increasing the likelihood of extreme results. For example, given a team with a roughly 62% win prob (the probability associated with a team that you expect to win 100 games in the regular season), the probability of that team winning 75 games or fewer, is according to the binomial only about 0.00482%. In reality the true probability is likely several orders of magnitude higher.

[Justin7]

Note, however, that this simple single-parameter analysis, while potentially valuable versus a rec-style bookmaker that sets its own lines, is most assuredly not going to beat Pinnacle.

For perhaps the first time ever, I will respectfully disagree with Ganchrow.

Pinnacle's openers on NFL season wins, or anything else with $500 limits or less at open, are very beatable. Props and futures are loss-leaders. Pinnacle doesn't care if you get the best of it on a $500 bet. They're paying you a consulting fee for your opinion. In exchange, they will make their earn when limits go up to 5k, and the not-so-sharps bet in volume.

[IrishTim]

I would be a lot smarter gambler if Ganch and Justin would argue more often.

[IrishTim]

Oh, and before I forget - you two disagreed on the value of the 2 in college basketball a few years ago. I'm not a stalker, I swear, just made a habit out of reading archived Think Tank threads.

[rfr3sh]

yeah . this thread has turned into something great.

much appreciated you two I have a lot to learn and I am glad both of you are available resources



Justin: do you know when the limits increase? I want to place some wagers on this with a small bankroll before the lines move to much

[Wrecktangle]

Oh, and before I forget - you two disagreed on the value of the 2 in college basketball a few years ago. I'm not a stalker, I swear, just made a habit out of reading archived Think Tank threads.

Perhaps Irish is running a conflict matrix on everyone who posts in the Tank? I hope I agree with myself on all my posts.

[mathdotcom]

For perhaps the first time ever, I will respectfully disagree with Ganchrow.

Pinnacle's openers on NFL season wins, or anything else with $500 limits or less at open, are very beatable. Props and futures are loss-leaders. Pinnacle doesn't care if you get the best of it on a $500 bet. They're paying you a consulting fee for your opinion. In exchange, they will make their earn when limits go up to 5k, and the not-so-sharps bet in volume.

A+ post from Justin7

There I said it.

[Ganchrow]

Pinnacle's openers on NFL season wins, or anything else with $500 limits or less at open, are very beatable. Props and futures are loss-leaders. Pinnacle doesn't care if you get the best of it on a $500 bet. They're paying you a consulting fee for your opinion. In exchange, they will make their earn when limits go up to 5k, and the not-so-sharps bet in volume.

I'm certainly in agreement with your assessment that in general low-limit wagers at Pinnacle are readily beatable ... I just contend that this particular elementary binomial analysis, that assumes equal win probabilities across all season games (be they home or away) is just way too simplistic even for a $500 limit.

Although of course as always ... I may well be wrong.

[rfr3sh]

under 5.5 would yield a probability of =1-BINOMDIST(10, 16, 11/16, 1)

is that correct?

[Ganchrow]

under 5.5 would yield a probability of =1-BINOMDIST(10, 16, 11/16, 1)

is that correct?

Pr(Under 5.5) = 1 - Pr(over 5.5)
If you expect 6 wins then:

Pr(Under 5.5) = 1 - Pr(over 5.5) = BINOMDIST(5, 16, 5/16, 1) ≈ 40.673%

Which also happens to equal:

=1-BINOMDIST(10, 16, 10/16, 1)

[Ganchrow]

Pr(Under 5.5) = 1 - Pr(over 5.5) = BINOMDIST(5, 16, 5/16, 1) ≈ 40.673%

Above should read: = BINOMDIST(5, 16, 6/16, 1) ≈ 40.673%

[rfr3sh]

Thanks for your help,

im working on a spreadsheet right now to see which lines to bet for the season,
am going to start off will a small Bankroll,

do you think I should use Half kelly, or just flat bet all of the games if it is my first season doing this

[Justin7]

Thanks for your help,

im working on a spreadsheet right now to see which lines to bet for the season,
am going to start off will a small Bankroll,

do you think I should use Half kelly, or just flat bet all of the games if it is my first season doing this

For your first year, flat bet 1% of your bankroll per bet. After 1 year, you'll have a better idea of your edge (or the house edge).

[rfr3sh]

Thanks Justin, hopefully this works out for me

[rfr3sh]

Placed some small wagers thanks guys

[Data]

Note, however, that this simple single-parameter analysis, while potentially valuable versus a rec-style bookmaker that sets its own lines, is most assuredly not going to beat Pinnacle.

For perhaps the first time ever, I will respectfully disagree with Ganchrow.

Pinnacle's openers on NFL season wins, or anything else with $500 limits or less at open, are very beatable. Props and futures are loss-leaders. Pinnacle doesn't care if you get the best of it on a $500 bet. They're paying you a consulting fee for your opinion. In exchange, they will make their earn when limits go up to 5k, and the not-so-sharps bet in volume.

These two statements do not contradict with each other.

[Data]

A+ post from Justin7

There I said it.

Never understood why you were giving him so much grief.

[rfr3sh]

Generally How many team totals should I find to have an edge? I'm assuming there should be more totals with no edge then the other way around

[LegitBet]

how does this factor into the math?

I've often thought these early prop and future bets had insidiously more value to the book, as they get the advantage of holding your money all season long, win or lose.
what do you think?
btw highly impressive you guys are (who says degenerate gamblers aren't sometimes geniuses! )
meant with levity and great respect!

Andrew

[durito]

I've often thought these early prop and future bets had insidiously more value to the book, as they get the advantage of holding your money all season long, win or lose.
what do you think?
btw highly impressive you guys are (who says degenerate gamblers aren't sometimes geniuses! )
meant with levity and great respect!

Andrew

Who is betting?

The book would probably prefer that a +ev player bet the future, even one with substantial ev (and yes finding 15% edges on these is not hard) as opposed to having that cash to bet over and over again all season (assuming the player could find daily/weekly +ev opportunities). For the losing player, I think they'd prefer them to bet and lose weekly. Which, is of course, why many ap don't bet futures at all except on credit. Even on credit I don't bet them anymore.

[rfr3sh]

Who is betting? The book would probably prefer that a +ev player bet the future, even one with substantial ev (and yes finding 15% edges on these is not hard) as opposed to having that cash to bet over and over again all season (assuming the player could find daily/weekly +ev opportunities). For the losing player, I think they'd prefer them to bet and lose weekly. Which, is of course, why many ap don't bet futures at all except on credit. Even on credit I don't bet them anymore.

thanks for confirming, when calculating my edge I had some pretty high %'s at some of them and I thought I was just being retarded and miscalculated, but I guess with the low limits it makes sense that you can find some good +EV bets