[AusRace] Exponentialality - another way

Sun Jun 24 12:24:03 AEST 2018

The Equation

If you have a points system for rating horse races where the top pick
has a long-term strike rate of at least 22%, and provided that the
points are adjusted so that 

the bottom pick has zero points, using the equation

a=b+((b*b*c)/(d-e))

to further adjust the points will provide a better approximation of
the chances of each horse in a race in relation to the other runners.

Where :

a = Horses adjusted points

b = Horses allocated points (after making bottom pick zero)

c = Skewing Coefficient

d = Highest possible score attainable (after making bottom pick zero)
+ 10%

e = Top pick score (after making bottom pick zero)

Now, let's recalculate the prospective dividends for a race applying
the equation.

Step 1 Make sure the bottom rated runner has a score of zero. In our
case it already has, so no further adjustments are necessary. But if
Horse F had say a score of  

-200, then we would add 200 points to each of the horse scores. If
Horse F had a score of +200, then we would subtract 200 points from
each score.

The scores for Race 1 are therefore :

Race 1

Points

Horse A

1000.00

Horse B

800.00

Horse C

600.00

Horse D

400.00

Horse E

200.00

Horse F

0.00

Use these scores as b in the equation.

Step 2 Estimate the lowest rated runners chances of winning. In fields
of 11 runners OR MORE, this should almost always be 1%. As Race 1 is
only a 6 horse field, 

but the scores are widespread, Horse F's chances could be estimated at
2%.

Step 3 Determine the highest possible score a horse may obtain (after
the adjustment to make the lowest score zero). And add another 10%.
Assume in our case 

this is 2000 points. This is the highest possible difference between
the top pick and last pick and is d in the equation.

Step 4 Take the top pick score (after the zero score adjustment). In
Race 1 this is 1000 and is e in the equation.

Step 5 Decide on the skewing coefficient (c in the equation). This is
set according to the long-term system top pick strike rate. A setting
of 0.5 would be about 

right for a 23% strike rate and perhaps 2 or 3 for around 28%. We
shall use 1. The skewing coefficient determines the amount of
exponentialality. This is why it is 

increased as the strike rate improves. You may have to experiment with
the setting as both the coefficient and the chosen figure for highest
possible score 

affect the amount of skew.

Step 6 Calculate the adjusted scores by applying the equation to each
score.

Horse A adjusted score

= 1000 + ((1000x1000x1)/(2000-1000))

2000

2000

2000

Horse B adjusted score

= 800 + ((800x800x1)/(2000-1000))

1440

Race 1

Raw Score

Adjusted Score

Horse A

1000.00

2000

Horse B

800.00

1440

Horse C

600.00

960

Horse D

400.00

560

Horse E

200.00

222

Horse F

0.00

0

Step 7 Now add up all the adjusted scores.

2000 + 1440 + 960 + 560 + 222 + 0 = 5182. To take in the estimated 2%
chance for Horse F, divide this total by 98% (i.e. 100% - 2%). 5182 /
98% = 5287

Step 8 Divide each horses adjusted score into the adjusted total to
calculate an estimate of the percentage winning chance for each horse.

Horse A Chances = (2000/5287)x100 = 37.8%

Divide 100 by the percentage chance for the desired dividend. 100 /
37.8 = $2.65

Race 1

Adjusted Score

% Chance

Calculated Dividend

Horse A

2000.00

37.8

2.65

Horse B

1440.00

27.2

3.70

Horse C

960.00

18.2

5.5

Horse D

560.00

10.6

9.45

Horse E

222.00

4.2

23.8

Horse F

0.00

2

50

Another way

<http://www.avg.com/email-signature?utm_medium=email&utm_source=link&u
tm_campaign=sig-email&utm_content=emailclient> 

Virus-free.
<http://www.avg.com/email-signature?utm_medium=email&utm_source=link&u
tm_campaign=sig-email&utm_content=emailclient> www.avg.com 

---
This email has been checked for viruses by AVG.
https://www.avg.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://ausrace.com/pipermail/racing_ausrace.com/attachments/20180624/bb37e642/attachment.html>