Tough Math Problem

Are there any mathematicians or bookmakers who can share what should be a rather straightforward mathematical equation with me? Please bear with me the length of this post.

I have spent hours and hours on this supposedly simply mathematical calculation. :smoking:hno::smoking:

The preface: I have a list of events that have taken place over the past two years. Quite simply, there are over 10,000 events that I have listed in a file. While odds for basketball and football are easy to figure out, as they are normal straght-line bets for both Sides and Totals, they are easy to calculate and I need no help with them.

However, baseball and hockey shows a Moneyline bet.

Each event has exactly three lines of information. The title line contains the date/time and indicates a neutral site if not a normal away/home game. This line is discarded, leaving two lines.

The first line has the AWAY team, followed by odds. The odds can either be a moneyline amount or a totals number.

The second line has the HOME team, followed by odds. As above, the odds can either be a moneyline amount or a totals number.

Between the two odds, the Moneyline is very easy to determine, as that number is always shown as -110 or less (-111, -112, etc). The other number is the Totals number of which I do not need the calculation. I am only trying to figure out a calculation based on a Sides bet.

If one team is showing the moneyline bet, then that team is favored, and the other team is the underdog.

The totals (over/under) amount, therefore, is showing on the line of the underdog.

Here is a sample for a baseball event:

Boston -125
Cleveland 41

This shows that Boston is the visiting team, and Cleveland is the home team. As Boston has the moneyline total, it shows that Boston is the favorite, and the Totals number (next to Cleveland) is 41.

Discard the Totals number, as I don't need it for the calculation, and will suppress it from the rest of the process.

Now, if someone bets on Boston of one unit, if Boston wins, his winnings will be 100/125, or .8 won, plus the unit wagered for a total of 1.8 units returned. That part is easy.

Now, what isn't included in the calculation is the House vigorish. I believe this is what is causing some problems in the way I am trying to communicate the problem. So for now, let me defer to another example.

I am assuming that the HOUSE percentage is .0909 (or 100/110). In other words, if both teams are equal odds, then each team would be 100/110 on the payoff. Let me write it out:

Boston -110
Cleveland

Since the odds are the same for Boston as the vigorish odds for the house, then it could just as correctly be written as follows:

Boston
Cleveland -110

So at a vigorish of .0909, each team would be paid at 100/110, plus their unit back, on winning. Therefore, I can actually write it like this:

Boston -110
Cleveland -110


BACK TO THE ORIGINAL EXAMPLE

Boston -125
Cleveland ???

The question remains: What is the Moneyline for Cleveland, based upon a vigorish of .0909? More specifically, what is the mathematical equation for figuring out the odds?

If it makes it easier:

House vigorish: .0909

Boston win/unit: 0.8 (plus the original unit)
Cleveland win/unit: ???

What is Cleveland's win/unit based upon the line for Boston and the house vigorish given as shown?

I'm sorry for being so long, but I needed to be exact here. In short, I need the exact calculation based on my requirements. Note I don't need the actual moneyline answer as I can easily convert between decimals and moneyline displays. I just need the exact decimal answer rounded to 2 digits. Where can I ask this question if it can't be answered in this forum?

Thanks for ANY help! Once I can get this answer, I will be able to create some cool betting aids for everyone!

I'd say about Cleveland +115. I'm saying -115/+115 as a no vig line. I'm not sure if that is what you want ?

You seem to be dealing with 20 cent lines ( -110/-110). With Boston at -125, Cleveland would be +105. Change by 10 cents.

But this would differ with something far from a pickem, like a -400 game.

There is no vig on money lines.. Its built in... For example thre SB line: New Orleans is +180 and Indy is -210... You also seem to have it listed wrong... its 210 to win 100 in this example for Indy or 100 to win 180 for NO... In you example you have Boston -125.... You show 100/125.. You have to wager 125 to win a 100... you show 100/125

Doug,

First of all, I appreciate your input:toast:

What I am trying to do is to create a "retroactive betting simulator." I am using the -110 (0.0909) vigorish, or the "20-cent line." Although I'm reasonably affluent in "Americanese" (able to instantly figure out payouts from American odds), I find myself a bit on the ignorant side in true mathematical acumen.

You are correct in saying that a moneyline of -400 is not going to result in a +380 line for the opposition. Basically, it means that 400 units are being put at risk to win 100 units, or a 1.25 return on 1 unit. I believe there is a mathematical construct that I can...

A: Plug in the odds for Team One, and
B: Plug in the vigorish

...and obtain result C: the odds for Team Two.

To be honest, this should be the same as figuring out a pari-mutuel calculation for a two-horse race, with a house return of .0909. I am not mathematically savvy enough to create the equation, but once I have it I can easily program it into the system I am creating.

I'm thinking of trying to find a math forum for the calculation, but I was hoping someone who is actually associated with a bookmaking operation would have the information on this calculation.

Cleveland +105 then.

Not sure this is the simpliest formula, but I think the ML for the underdog would be as follows ----

MLu = 100 * ( (100 - MLf)/(100C + MLf * (1-C)) - 1)

where
MLf is the moneyline for the favorite
C is the "vig" (actually vig +1, or 1.04545454545 in the 20 cent line case).

The result will come out to be a number greater than 100, except in cases where both sides are negative (ex: -110, -110). In that casae, the MLu will calc to 91 -- divide that into -100*100 to get a true ML.

In case you care ---

in the non-vig case,
Prob(fav) = -MLf/(100-MLf)
Prob(dog) = 100/(100+MLu)

in this case, Prob(fav) + prob(dog) = 1.0

when you add vig, Prob(fav) + prob(dog) = 1 + vig

I'm calling vig 0.045454545, so probs add to 1.045454545 (i'm calling that "C")


The eqns then become
C * Prob(fav) = -MLf/(100-MLf)
C * Prob(dog) = 100/(100+MLu)

Then it's just substituting to isolate MLu.

onemwtheone said:

In case you care ---

in the non-vig case,
Prob(fav) = -MLf/(100-MLf)
Prob(dog) = 100/(100+MLu)

in this case, Prob(fav) + prob(dog) = 1.0

when you add vig, Prob(fav) + prob(dog) = 1 + vig

I'm calling vig 0.045454545, so probs add to 1.045454545 (i'm calling that "C")


The eqns then become
C * Prob(fav) = -MLf/(100-MLf)
C * Prob(dog) = 100/(100+MLu)

Then it's just substituting to isolate MLu.

Click to expand...

onemwtheone...Thanks! This is a good start :toast:

I am probably better off converting all American odds to decimal odds before doing the calculation. I'm going to play with your formula and figure it out.

Again, thanks...this is definitely in the right direction!

onemwtheone said:

Not sure this is the simpliest formula, but I think the ML for the underdog would be as follows ----

MLu = 100 * ( (100 - MLf)/(100C + MLf * (1-C)) - 1)

where
MLf is the moneyline for the favorite
C is the "vig" (actually vig +1, or 1.04545454545 in the 20 cent line case).

The result will come out to be a number greater than 100, except in cases where both sides are negative (ex: -110, -110). In that casae, the MLu will calc to 91 -- divide that into -100*100 to get a true ML.

Click to expand...

That dude is smart

defying said:

that dude is smart

Click to expand...

lol

Try this:

(Fav ML)*.909090=X
(Fav ML -X)*2=Y
Fav ML -Y

Your example:
125*.909090 = 113.63625
(125-113.63625)*2=22.7275
125-22.275=102.725
So it's -125/+102.725 as the equivalent of -110/-110

This is my 5 minute workup. I think this works but don't ask me for any proofs.

I'm still trying to figure out how the hell e=mc2.

onemwtheone said:

In case you care ---

in the non-vig case,
Prob(fav) = -MLf/(100-MLf)
Prob(dog) = 100/(100+MLu)

in this case, Prob(fav) + prob(dog) = 1.0

when you add vig, Prob(fav) + prob(dog) = 1 + vig

I'm calling vig 0.045454545, so probs add to 1.045454545 (i'm calling that "C")


The eqns then become
C * Prob(fav) = -MLf/(100-MLf)
C * Prob(dog) = 100/(100+MLu)

Then it's just substituting to isolate MLu.

Click to expand...

:monsters-

onemwtheone said:

Not sure this is the simpliest formula, but I think the ML for the underdog would be as follows ----

MLu = 100 * ( (100 - MLf)/(100C + MLf * (1-C)) - 1)

where
MLf is the moneyline for the favorite
C is the "vig" (actually vig +1, or 1.04545454545 in the 20 cent line case).

The result will come out to be a number greater than 100, except in cases where both sides are negative (ex: -110, -110). In that casae, the MLu will calc to 91 -- divide that into -100*100 to get a true ML.

Click to expand...

Here is an example of a real ML.

MLf = -200
C = 1.045

MLu = 100 * ( (100 - MLf)/(100C + MLf * (1-C)) - 1)

MLu = 100 * ( (100 + 200)/(104.5 - 200 * (1-1.045)) - 1)
MLu = 100 * ( (300)/(104.5 -200 * (-.045)) - 1)
MLu = 100 * ( (300)/(104.5 + 9) - 1)
MLu = 100 * ( (300)/(113.5) - 1)
MLu = 100 * ( 2.64 - 1)
MLu = 100 * 1.64
MLu = 164

I know that currently the Colts ML is -200, and on my site the Saints are +170.

uppy:

Furmanski said:

Here is an example of a real ML.

MLf = -200
C = 1.045

MLu = 100 * ( (100 - MLf)/(100C + MLf * (1-C)) - 1)

MLu = 100 * ( (100 + 200)/(104.5 - 200 * (1-1.045)) - 1)
MLu = 100 * ( (300)/(104.5 -200 * (-.045)) - 1)
MLu = 100 * ( (300)/(104.5 + 9) - 1)
MLu = 100 * ( (300)/(113.5) - 1)
MLu = 100 * ( 2.64 - 1)
MLu = 100 * 1.64
MLu = 164

I know that currently the Colts ML is -200, and on my site the Saints are +170.

Click to expand...

Yeah, the +164 is just the theoretical ML to have if the favorite is posted at -200 (and you want to get the same rate of return (from the books standpoint) on the wagers made based on -110 each side) ---

(at -110 each side, and exactly equals wagers made on each side the book would get a 4.545% return on the money wagered).

At -200 the favorite has a 63.768% chance of winning (assuming the book has adjusted up the line to get their 4.545% return). This would then correspond to prob of the dog winning at 36.232%, and the line set at +164. Assuming folks wager in this proportion (63.77 to 36.23) --

For every $100 wagered, 63.77 on the fav, 36.23 on the dog, ---

If the fav wins, book pays out 63.77 + 63.77/2 = 95.66, netting $4.34
If the dog wins, book pays out 36.23 + 36.23 * 1.64 = 95.65, netting $4.35.

What I posted was just a theortical exercise - I have no idea how the books set the lines exactly.

6

onemwtheone is the BOMB!!

The calculation works exactly as I need. Actually, I was able to hunt down the pari-mutuel calculation I was looking for, and one's formula is like a two horse race (before breakage), other than the conversion of decimal and American odd structures.

Thanks for breaking it down line by line as well; I did the same thing after I had converted it before. I do like your method, as I can just plug in the American odds directly, which makes it easy as I crunch tens of thousands of events.

Again, this is just what I need. Now I will be able to check out betting strategies based on historical opening lines for all six major sports this past decade...and I'm going to share every bit of it with you!

arty: