The Virtual Grand National

For the Virtual Grand National you can see quite a big overround built into the win price (144% - fair is 100%), the overround on the place is not as big proportionally speaking (595% - fair is 500%).

Will this give us an opportunity to find value in the each way market?

First we have to decide how we believe the places are decided. For the win it is the consensus that the prices are fair.  A simulation/algorithm based on the horses form and strengths will determine the probability of each horse winning.  The prices will then directly represent this probability with a bit of margin built in.  This works.

For placing it is a bit more complicated. You can't have both a realistic simulation to generate the places probablities/prices and each way prices that represent the actual place price.

Here is how the racingpost describes the simulation:

The simulation itself is made up of mathematical algorithms using data taken from the horses' previous performances. The race's outcome uses a number of factors such as age, weight, form and weather conditions but also contains details such as fallers, unseated riders and collapsing fences.

This tells me that the place prices will be based on a simulation of the real event, rather than a RNG picking 1/5 odds.  This is controversial as it probably goes against the Bookies licencing conditions.  If they offer a virtual event then the price (for placing in an each way bet) should be as accurate as possible to the actual probability of placing ie should be 1/5 odds.

So lets say the places are decided by an accurate simulation of a real event. We know from people like Henery/Lo/Bacon-Shone who studied place probabilities and Bill Benter who applied some of the theory to winning that the place is related to the win probabilities of all horses in the race based on the Discounted Harville Formula. There are obviously exceptions, but it gives a rough guide as to what on average you could expect the place probability to be. 

Lets not mess around, applying a version of Discounted Harville to the win prices with margin removed gives the table below for place probabilities and Expected Value of an each way bet.

EV for win and Each Way bets based on a Discounted Harville formula

So there is no obvious each way value to be had.  The longer priced horses have better EV but still -EV by this simple calculation.  Also, going by this guide you are better off betting win only unless you are picking one of the 66/1 or bigger chances.

However the Discounted Harville formula should be seen as just a guide. All horses are not the same.  For example for a fast, high stamina horse but very poor at jumping you might think if he gets around he will win - but highly likely to fall. In this case the table above will overestimate the chance of that horse placing.

On the other hand a solid jumper the table may be underestimating the chance of placing so you may use judgement to push the EV's listed a little higher and who knows you may judge one or two of the big priced horses are value.

Discounted Harville.

I wanted to get to the point quickly so skipped the details.

Harville described a simple model for estimating place probabilities in 1973. For example a three horse race where the horses have probabilities of 50%, 30% and 20%. He said if the favourite (50%) wins then you would scale the remaining probabilities to 100% again to pick the 2nd place horse.  So horse two (the 30% horse) would be 30/(100-50) or 60% chance to come 2nd.  You can repeat this for all the possible combinations of 1st, 2nd, 3rd etc to calculate probabilities for trifectas and places etc.

This turned out accurate enough in some cases.  Especially when applied with bookie odds (which suffer from a favourite long shot bias).  This bias actually went someway to cancelling out the inherent bias in Harville's formula.  Harville's formula actually overestimated significantly the favourites, and underestimated the long shots when compared with real world results.

Henery developed a much more complicated equation (so complicated that it was practically unusable) which was much more accurate at predicting the probabilities.

Lo/Bacon-Shone added a couple of discount parameters about 1995 to the Harville formula to deal with the bias so that you dont reduce the probabilities as fully at each step, but rather reduce them by a power.  The paper provided parameter values which approximated Henery's equation and these are the values that I have used above.

Overrounds

I have been using a chrome extension to display the win and place overrounds on the top of the oddschecker table.  You can see it here.

chrome extension displaying the market overrounds