An extension of this is to use the points to develop a prospective dividend for each horse. These can then be used in comparison to TAB and Fixed odds dividends in order to highlight horses that are overpriced in relation to their chances of winning.
The most common method of doing this is to add up the total number of points in the race and divide each of the individual horse points into the total. The resulting percentage for each horse is then used to determine its desirable dividend.
Traditional method of working out prospective dividends from ratings points.
Lets look at 2 examples. Note that because Horse F and Horse L have zero points, their chances are estimated at 2%.
Note: Because Horse F has 2% chance, we add 61 points to the total. 3000 divided by 98% equals 3061
Note: 2100 = divided by 98% equals 2142
At first glance, these framed markets seem OK. So what is the problem? There are 4 problems :
1. The calculations fail to take into account the relative strength of the points rating system. What is the systems top pick strike rate? The top pick strike rate affects the overall distribution of winning chances.
2. How good is 1000 points in relation to the system points scale?
3. A points allocation of 500, 400, 300, 200, 100 and 0 for Race 1 will give exactly the same dividend distribution, using the traditional method, when in reality they should be more compact, if the same ratings system is used. A top pick, which is 1000 points ahead of the bottom pick, should have greater chance of winning compared to a top pick only 500 points ahead.
4. In cases where the systems long-term strike rate is above about 22%, the percentage chances of the top few picks under this method are almost always under-estimated and the chances of the lower rated runners are almost always over-estimated.
From the experience of developing a points system for rating NZ horse races that has achieved a strike rate of 26% over 20,000 races, I have developed an equation that better represents the chances of each horse.
The equation only applies where the top pick of the ratings system achieves a long-term strike rate of at least 22%, the higher the better. It is based on the following:
1. When framing a horse racing market from a selection system based on points using the traditional method of dividing individual points by the total race points, and when the long-term strike rate for the top pick is at least about 22%, the percentage chances for the top few picks are almost always under-estimated and the percentage chances for the bottom few picks are almost always over-estimated.
2. In reality, the percentage chances, and therefore dividend approximations, are not linear, in relation to the points, but exponential. In other words if Horse A has twice the score of Horse B (provided the lowest rated runner has a score of zero) then Horse As chances are more than twice those of Horse B.
3. As the top pick long-term strike rate increases, the correct allocation of approximate dividends gets more exponential in relation to the points.
4. As the top pick long-term strike rate increases, if the prospective dividends are calculated correctly, the dividend estimates become more accurate.
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
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.
Now, lets recalculate the prospective dividends for Race 1 after 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 :
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 Fs 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))
= 1000 + (1000000/1000)
= 1000 + 1000
Horse B adjusted score
= 800 + ((800x800x1)/(2000-1000))
= 800 + (640000/1000)
= 800 + 640 = 1440
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
I contend that the above market is a more accurate assessment of the winning chances of each runner for Race 1 compared to the one worked out at the start of this article.
Recalculating Race 2 should result in a prospective dividend of $1.80 for the top pick. This is more realistic considering its impressive score and the differential to the 2nd pick.
Consider a points system with a highest possible difference between top pick and last pick of 20 points. Strike rate for top pick is 25%.
The Theorem adjusted score for Horse A
= 15 + (15x15x1)/(20-15)
= 15 + (225/5)
For Horse B
= 11 + (11x11x1)/(20-15)
= 11 + (121/5)
= 11 + 24.2
The dividend for Horse A is relatively low because its score (15) is close to the highest possible (20) meaning that there is a wide class difference between the top and bottom rated runners.
Now, lets assume that the highest possible score (after 1st adjustment) is 40 and not 20. This indicates a smaller spread of class between the horses. Horse As prospective dividend under this scenario increases to $2.95. Horse Gs dividend decreases to $45, dividends that are indicative of a lower class spread.
This Theorem is not necessarily the best way of assessing a horses chance. But it is more accurate than the traditional method, of assessment from raw point distribution, in cases of medium to high top pick strike rate.
Long-term strike rate in all cases refers to strike rate for the top rated runner on all races before any filtering of races takes place.
The term about 22%, in reference to strike rate, is used because of the uncertainty of exactly when the exponential component kicks in.
RaceBase, Hamilton, NZ, September 2005