[keemosabi]

So I was reading the below article:

How do we convert one odds format to another?

Knowing how to convert one form of odds to another can be helpful, especially if you have come into possession of a large amount of betting data that has odds formatted in an unfamiliar way.
To do this, we first need to convert any odds format to their implied probability. Once we have done this, the calculations are fairly straight forward.
Converting implied probability into decimal odds.





e.g. Implied probability of 75% would return decimal odds of 1.33.
Decimal odds = 100 / 75
Decimal odds = 1.33
Converting implied probability into fractional odds





So an example of 25% implied probability would be calculated as:
Fractional odds = (100 / 25) – 1
Fractional odds = 4 – 1
Fractional odds = 3, expressed as 3 to 1.
Converting implied probability into moneyline odds

This depends on whether the implied probability is above 50% or below.
If it is above, we make the following calculation.




So for example, the implied probability of 75%.
Moneyline odds = - (probability)/(100 – probability) * 100
Moneyline odds = - (75 / (100 – 75)) * 100
Moneyline odds = - (75 / 25) * 100
Moneyline odds = - 3 * 100
Moneyline odds = - 300.

If the implied probability is below 50%, the calculation is adjusted a little.




So for example, the implied probability of 25%.
Moneyline odds = ((100 - probability)/(probability) * 100)
Moneyline odds = ((75) / (25) * 100)
Moneyline odds = 3 * 100
Moneyline odds = + 300

I understand how to use the formulas, but where are they derived from?

[HUY]

So I was reading the below article:


I understand how to use the formulas, but where are they derived from?

Convention.

[keemosabi]

Convention.

What do you mean by that?

[HUY]

What do you mean by that?

I mean it's just the way that the odds are written. It's a notation system. Do you have any specific questions?

[matthew919]

I think what HUY is referring to is the the US odds format is just convention, and rather arbitrary. Logically, you can think of it as being derived from the implied probability as follows.

For a dog wager (though it's the same idea for a favorite):
Assume the event you are wagering on has a 1/4 probability of occurring. This means that out of 4 wagers for an event of this kind, you will win one and lose 3. So lets assume you make four wagers at the same size; you 'should' win one out of four (the 'should' implies a limit as your number of wagers goes to infinity, but you can ignore that). The vig-free odds should pay out 3 times your wager on your one expected win, to cover the the three expected losses.

I.e. you will lose 3 times as often as you win- this is the ( (1-pr)/pr) part of the equation, and symbolizes that you will win three times your wager.

The second half of the equation, where we multiply by 100, is just convention. Essentially this scales it up to a wager size of 100, so for every 100 dollars, how much do you win. For favorites, where the odds are negative, it's how many hundreds do you need to wager to win 100. It could have just as easily have been represented without the scaling factor, but for whatever reason that's the convention.

[Blax0r]

What do you mean by that?

Read up on Expected Value on wikipedia.

After that, given -500 or +500 odds (American), compute the implied probability of winning (solve for "p") after setting EV to 0.

You can repeat the exercise for Decimal odds.

Your results should more or less match the formulas you found.