NRL Starts Conversion Graph

[jakelee]

The following chart converts from Starts to Odds for the favorite.

http://pics.xs.to/pics/04072/nrlstarts.GIF
http://pics.xs.to/pics/04072/nrlstarts.GIF


I am working on a calculator for roll-your owns and starts.

Jake.

<font size=-1>[ This Message was edited by: jakelee on 2004-07-27 11:52 ]</font>

[moeee]

Is it too much trouble to get you to put the margins on the y axis,and the prices on the x axis.
Why?.I don't see the resemblance between this curve and your earlier one.

[moeee]

You went to all this trouble and then abandoned it.
Where are you Jakelee?

[jakelee]

Hi Guys,

Been away... no internet for a week!

Anyhow, I have put together a website for NRL starts/Odds conversions.

here (http://www.horologe.com.au/econtrafama/starts/)
http://www.horologe.com.au/econtrafama/starts/

The season's almost over though! But might be useful for next season.

Jake.

<font size=-1>[ This Message was edited by: jakelee on 2004-08-23 11:02 ]</font>

[moeee]

I know jack shit about NRL.
What data do you need for an AFL chart?

[jakelee]

To do an AFL conversion (I already have the formula, just need the paramters). I don't follow AFL, so I'm not sure what range the starts go from (would you see a +80.5 handicap?):

I would need:

<blockquote>
- Opening Fav/Dog Start and Opening Fav/Dog To Win Odds for quite a few values from equal favs (ie, +0.5) to a big difference (ie, +80.5). I also need the starting odds for the line (it's always 1.85 for NSW SportsTAB) Like this:
<code>
Line Odds: $1.85
Start Win Odds
-10.5 $1.70
-50.5 $1.21
+5.5 $2.00
... etc
</code>
I don't need every value, just enough so I can fill in the gaps.

If someone can provide this data for the TAB, I can calculate the
</blockquote>

JL.

<font size=-1>[ This Message was edited by: jakelee on 2004-08-24 09:01 ]</font>

[Mr J]

The most I've seen is +54.5. I doubt there has ever been anything over 60.

[moeee]

Jakelee.Is this any good?
With lines at $1.90

1.90 -4.5
1.80 -5.5
1.75 -4.5,-5.5
1.70 -5.5,-6.5,-7.5,-8.5
1.65 -7.5,-8.5,-9.5,-13.5
1.60 -9.5,-10.5,-11.5,-12.5,-13.5
1.55 -10.5,-13.5
1.50 -12.5,-15.5,-17.5
1.45 -15.5,-17.5,-18.5
1.40 -18.5,-20.5
1.35 -22.5
1.33 -22.5,-23.5,-24.5
1.30 -20.5,-23.5,-24.5
1.28 -24.5,-27.5
1.25 -24.5,-26.5,-27.5,-28.5
1.22 -29.5,-30.5
1.20 -31.5
1.18 -32.5
1.16 -34.5,-36.5
1.14 -36.5,-39.5,-40.5
1.12 -39.5,-42.5
1.11 -35.5
1.10 -40.5,-42.5,-43.5
1.08 -42.5,-46.5
1.06 -46.5
1.02 -71.5

Seems to be mistakes made by bookies,or more likely,minor differences due to who is playing who.

[jakelee]

That's what I need. Give me a few days.

[moeee]

Come on Jakelee.
Just need the mathematical formula.
Margins to percentages.
No fancy webpage necessary.Something I could do on my calculator is fine.

[jakelee]

<h4>AFL</h4>

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.

<code>
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

</code>

This will work from about 1.01 to 1.90.

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

Jake.

[moeee]

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.

[jakelee]

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.

[moeee]

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.

[jakelee]

On 2004-09-02 11:44, moeee wrote:
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:

<code>
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

</code>

[moeee]

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?