AFL

OK guys, this is the formula for AFL starts/odds. You can use this formula to calculate the expected start from the odds on the favourite. It was quite different from the NRL formula, which looked more like a distribution. The AFL formula is kind of a modified exponential, with quite a bit of fudging from the line makers. I suspect the line is moved to try and maximize bookie profits, as it would be more subjective in a high-scoring game like AFL over NRL.

It seems that in AFL the bookies are a LOT more liberal with the relationship between starts and odds than the NRL. For instance, odds of $1.66 can vary from a start of -9.5 to -13.5. There is about a 3 point either-side shift in the lower starts, and in some places a 6 point movement in the higher starts.


ODDS = a / [ 1 + b * e^(-c * START) ]

OR

START = -Ln[(a / ODDS - 1) / b] / c

Where
a = 0.95
b = -0.58
c = -0.033

So for example, if the odds were 1.46

START = -Ln[ (0.95 / 1.46 - 1) / -0.58] / -0.033
= -Ln[ (0.65 - 1) / -0.58 ] / -0.033
= -Ln[ -0.35 / -0.58 ] / -0.033
= -Ln[ 0.60 ] / -0.033
= 0.51 / -0.033
= 15.55

The expected start is 15.5 +/- 3



This will work from about 1.01 to 1.90.

You might find it easier to copy this to a Excel SpreadSheet.

Jake.

Well done Jakelee,but I'm a bit lost.
Is e,that epsilon Naperian log thing?
And Ln,is that the log to the base e.

Hello Moeee,

e is the exponential function. Read boffin stuff here: http://en.wikipedia.org/wiki/Exponential_function

Most calculators have one, and it's usually labled "Exp". In excel you use the function exp(...). Basically, it's just a special number that has an infinite number of decimal places, but lucky for us the calculator has a good approximation!

So to do e^7, on the calculator you would do EXP -> 7.

And yes, Ln is Log to the base of e. Also known as the natural log.

Jakelee.
How you showed an example of working out the start from odds,Can you do an example of a margin.Say if I thought a team would win by 15 points,could you do this example step by step to show the ODDS.

Like this:


ODDS = a / [ 1 + b * e^(-c * START) ]

Where
a = 0.95
b = -0.58
c = -0.033

ODDS = 0.95 / [ 1 - 0.58 * e^(0.033 * -15) ]
= 0.95 / [ 1 - 0.58 * e^(-0.495) ]
= 0.95 / [ 1 - 0.58 * 0.61 ]
= 0.95 / [ 1 - 0.353 ]
= 0.95 / 0.64
= 1.48



Thank you Jakelee.

And if you played around with the values b and c,could it then work with the base ten?

Don't understand how e came into it.
Wasn't it supposed to be following a graph of tan?