I was reading the article linked below last night which revisits the idea that when creating a set of ratings for horse racing one can gather a set of horse features for a given race. For example the Jockey strike rate of each mount along with the draw position along with … you get the picture. Now the the difference between a one step and a two step created model is that with a one step you include as a feature of each horse it’s starting price be that bookmaker or Betfair. The problem with this approach is that the SP can swamp the attention of your chosen model building algorithm. Not surprising really given the well documented effect on winning SP has. Short priced horses win more often and even shorter priced horses horses win more often than simple short priced horses and so on.

The two step approach chooses to get round this by building the model using only what is called the fundamental features, in other words we take out the SP and focus on the characteristics of the horse. Once we have built this model and produced a set of ratings for a given race we then proceed to step two. In step two the SP is introduced to the results of step 1 in order to build a final model, this means the SP has not had a chance to bully the fundamental features as they were examined in step 1.

All this can lead to producing an evaluation of the chance of each horse winning and hence a betting strategy based on backing those with longer odds than their predicted chance according to the model. For many people using there own ratings or someone else’s the odds line production can be a daunting problem, but do we really need to worry about that stage. Can we just forget the oddsline component ?.

If a set of ratings is profitable to top or top two rated do we need to oddsline it, perhaps not. Creating an oddsline may well create fewer bets and perhaps a more impressive ROI% but what if backing the top two had created pretty much the same profit but from twice or three times as many bets ?. I am suggesting that the non oddsline approach can have its merits in our UK set up. In the US where a 17% takeout has to be overcome along with no facility to take a price an oddsline is an essential tool as I see it but here in the UK we bet to a 1% takeout (OK a little more if you are paying 5% commission on Betfair). Furthermore the dreaded premium charge looms over us if we get successful on Betfair and here is where the non oddsline approach has some merit. The larger number of bets generated and fluctuations in the profit rate will offer some safeguard against premium charges. that higher ROI% from fewer bets will in time be more likely to change a non premium charge account into a PC one. A slower burning larger turnover account will have a much grater chance of avoiding PC. In fact I would encourage all break even type bets to be left in your betting portfolio to add extra protection.

Here is the link to the paper, comments welcome as usual.

http://www.bjll.org/index.php/jpm/article/viewFile/419/450

Peter Jansen

said:Hi Mark,

Thanks for the interesting discussion!

One comment in the paper was of particular interest viz:

The two-step modelling procedure, on the other hand, requires that

the training sample is split in two, one for each step; this is required in order to

overcome the potential problem of over-fitting (Benter, 1994).

I would have thought that simply developing the fundamental model and the market-based model on the same training set was OK but it appears not to be so.

Any comments?

I have replicated the models as per the paper in R and found that the two stage model shows that the fundamental model contributes about 60% to the final model prediction whilst the market model about 40%. Including more than one track seems OK provided some variables reflect this. I avoided races with little revealed form or low prizemoney.

The use of ‘exploded’ data I have not properly investigated. It appears to be useful according to the paper. My feeling is that it may be worthwhile where winning margins were small: if say a horse wins with a large margin then making it second or third in an ‘exploded’ race looks to me to merely introduce noise but am willing to be convinced otherwise!

Cheers, Peter

smartersig

said:Hi Peter

I think the second step involves taking the first step outputs and then attaching the log of the odd chances according to SP. The final model is then derived from this second set of parameters. If you used the data used in the first step you would be reusing the same data the fundamental model was based on which would be big no no. You seem to be thinking that the fundamental model and the SP included model are two distinct models, they are not the step two is the first model plus the SP added.

I thin exploding the data would still be fine down to second place even if they are beaten a long way as the remaining field are still fighting for second place due to the prize money. the key question is when does competition cease to be due to no incentive to make a place or two. One could argue that the researchers should have looked at deeper explosion further down the field on high value races as there is plenty of good prize money in 4th place.

Peter Jansen

said:Hi Mark,

“I think the second step involves taking the first step outputs and then attaching the log of the odd chances according to SP. The final model is then derived from this second set of parameters.”

Ah! That makes more sense, my smarts have deserted me once again.

What I did was make two models from the same training set: first model had the fundamental features, second model had just two market features. The market features I used were the log of normalized sp probability (log.sp_n) and the normalized rank order of sp (sp_n.rank). The t-values were typically of the order of 17 and -19. I wish all features had such huge t-values! For my fundamental models the highest t-values were for features related to the ability of the horse at the distance and a feature related to the breeding capability for this distance.

“I thin exploding the data would still be fine down to second place even if they are beaten a long way as the remaining field are still fighting for second place due to the prize money. the key question is when does competition cease to be due to no incentive to make a place or two. One could argue that the researchers should have looked at deeper explosion further down the field on high value races as there is plenty of good prize money in 4th place.”

You make some excellent points here.

I had used exploded data but used a beaten margin cutoff of 1 length ie only considered using 2nd and 3rd placegetters if they were within 1 length of the winner.

I will have a further look at relaxing this condition.

High prizemoney races can have 4th place prizemoney greater than many winner’s purses in lesser races so perhaps there is further research needed here.

Cheers, Peter

smartersig

said:Also be aware Peter that the author also suggests using the natural log of the probability produced by step 1, the fundamental model only, as well as the log of step 2 the sp’s, quote below

” Consequently, a second-step is required, incorporating the

natural logarithm of the fundamental model probability, ln ðp f

ijÞ, as well as the natural logarithm of the normalised closing odds probability, ln ðps

ijÞ, based on a second set of races.”

Peter Jansen

said:Thanks for the heads up, I will ensure both use the log function.

I am interested in exploring two cases related to ‘exploded’ data.

Case 1:

The winner is discarded and the remaining runners constitute a new race.

The response variable (finish position) is re-ranked as are any other variables that have within-race characteristics.

Repeat this process, discard both the winner and second place.

Case2:

Where the winning margin is small the finishing positions of first and second are reversed. The rationale here is that for close beaten margins a minor random occurrence in the race could well have determined the specific outcome so include the alternative outcome.

I do not include any of the ‘exploded’ data in my test (hold-out) set, they are only used to boost the size of the training set.

Any comments welcome!

smartersig

said:Try both, your out of sample test data will tell you if one is significantly better than the other. My other question would be, do you not have enough back data to not even worry about data explosion which is usually deployed when data is scarce.

Peter Jansen

said:The Sung and Johnson paper asserted, in reference to ‘exploded’ data:

“. This is clearly a valuable process as it increases the number of independent choice sets, which results in more precise parameter estimates. ”

This seems a good enough reason to try the method: no definite answer is given by them as to what constitutes sufficient races ie when it is not useful to add in the extra ‘exploded’ races.

I will have a look at adapting my CLR model to see if it is worthwhile to include the ‘exploded’ data and report back.

Mark, thanks for your input.

Peter Jansen

said:Back again!

data wsrFund roiFund wsrBack roiBack roiKelly wsrLay roiLay

raw 27.78 +5.31 33.46 +8.25 +2.78 11.10 +38.17

exploded 28.01 +2.29 34.20 +4.87 -5.56 13.04 +26.60

The wsrFund and roiFund figures refer to the top-ranked selection in each race from a Fundamental model using CLR.

The wsrBack and roiBack refer to Back bets placed on any predicted probabilities that are greater than or equal to the mean predicted probabilities +2*stdev of predicted probabilities.

The figures for Back bets are pessimistic in that prices are winsorized to mean price plus 1.5*sd so that a few big outsiders do not create a false dawn.

The wsrLay and roiLay refer to Lay bets placed on any predicted odds that are less than or equal to the median predicted probabilities -2*stdev of predicted probabilities.

The figures for Lay bets are likely optimistic as they assume Lays are struck at 1.25*sp only.

The roiKelly figures are for half-Kelly bets restricted to prices <= $21 ie 20/1.

The above figures are averaged over 9 datasets each with different tracks.

My figures do not support the use of 'exploded' data.

Win strike rates for the raw plus 'exploded' data are improved a little but the ROI for Back and Lay bets is quite a bit worse.