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You’re all so intelligent. I’ve noticed this before, punters are so good at maths. I’m usually stood there at bookies counting with fingers how many 2’s you can get into 15 for 15/2 and so on. And on that basis i can’t possibly comment on the suggestions made haha. Looks very good though
I’m not actually exactlysure what your proposal is RH other than it is based on the overround and the current R4.
How would it deal with this – as this is the sort of example that highlights the problems with applying it to winnings only
3 runner race – evs, evs, 100-1
Even money shot withdrawn. Current r4 would give you a 45p reduction on your winnings if you had backed the even money shot – clearly ludicrous.
My proposal is nothing to do with the current R4 which is flawed because it is based on price alone (see numerous previous postings !! ).
The mathematically correct reduction on your example would be approx 55.5p based on Even money withdrawal in a 101% market based on a grid approach (appled to profit not whole stake) . Is virtually the same as Even money example with the 5 9-1 shots posted above which is of course 100% market not 101%.
BTW I reckon the answers you should give based on your method to the three examples are 33%, 30% and 20%. As pointed out they will not be the same as mine which are expressed as % of profit therefore do not include the stake.
(appled to profit not whole stake)
So if I have a £1 on one even money shot and the other is withdrawn you are going to pay me £1.44 for beating a no-hoper?
Sorry was out walking the little one not deliberately stalling !!
Think in those circumstances you will always have a problem tbh but I take the point.
So to extend your BF example you would propose any even money 2.0 being subject to a 50% deduction to actually make it 1.0 so whilst you couldn;t win it would more accurately reflect the relative merits of the two horses that are left ?
That might be interesting to explain to a punter who thinks he has backed a winner but only gets his stake back though it would definitely be a more correct return in those circumstances.It itself still has problems however in terms of making the same deduction based solely on the price of one horse irrespective of the market overround.Say we have four runner race with Evens, 2-1,4-1 and 9-1 which is 113%.
After the withdrawal of the even money chance 2.0 leading to a 50% reduction in the decimal prices (3.0,5.0 and 10.0) the three left would be 1-2, 6-4 and 4-1 which gives a 127% market. The overround has doubled in favour of the bookmaker. ( My brain hurts too much to work out whether that increase is linear i.e it doubles because of the 2.0 as that could allow some market overround adjustment to bring it back to 113%.)Obviously where there are Even money chances withdrawn in markets with more runners and hence even greater overrounds this will increase even further.
So the correct solution would be a grid that has overrounds and odds but the latter expressed as a decimal so 50/113 = 44% to be applied to the decimal odds of the other four that remain. i.e 3.0,5.0,10.0 become 1.68,2.8 and 5.6 so say 4/6,7-4 and 9-2 = 114%.
That would incorporate both the overround and price and reflect the comparitive chances of the remaining runners and leave the market overround unchanged.
That is actually quite an easy grid to produce in terms of numbers but I need to take some time in a darkened room first.Can you check the logic The Dark Knight as it does seem to produce a correct grid IMO.
My example was deliberately an extreme one Richard, but basically the punter should be on at about 1.01/1.02 after the withdrawal. In reality there would be more overround built into such a situation anyway so the key would be getting the formula for the overround and the subsequent reduction in the reduction factor right (if that makes any sense -aaaargh)
You have provided a solution in your post above which looks quite nice. I too would need time in a darkened room to think about whether there are any problems with it!
(I think the key point is that it is based around the reduction factor model as opposed to the R4 model)
I think it is the fact that the by calling it a reduction factor you can apply it to the whole return (including stake) whereas it is the pence in £ profit which creates the anomalies you have identified.
Surely the answer lies in a fairly basic calculation.
Three runner race – A is 6/4, B is 6/4, C is 2/1
Horse A is withdrawn.
Percentages
A= 40%
B= 40%
C= 33.33%Remove over-rounds from probabilities
Proportional Over-round on horse A = 13.33*(40/113.33) = 4.7048
Horse B = 4.7048
Horse C = 3.9203(Don’t worry bookies – over-round gets added back in later!)
This means actual probablities at time of withdrawal =
A= 35.2951
B= 35.2951
C= 29.4130Ok – now we need to calculate probabilities in absence of Horse A. To do this we assign it’s probability to the other horses proportionally based on their price relative to the other remaining horses so.
Proportions (horses probability/sum of all the remaining horses probability expressed as a %)
Horse B = 32.2951/(39.251+29.413) = 54.54512%
Horse C = 29.413/(39.251+29.413) = 45.45488%So – we allocate the probability of Horse A (now withdrawn) to the probability of the remaining horses proportionally –
Horse B and C now have a probability which equals it’s original probability minus the over-round plus a proportion of Horse A’s probability (added in relative proportion to the other remaining runners based on their original prices)
Horse B = 40 (it’s original price) – 4.704844 (it’s proportion of the original over-round + 19.251 (it’s proprtion of Horse A’s chance) which all equates to
Horse B = 54.55%
Horse C = 45.45%We now have to add back the over-round (total over-round MINUS horse A’s part of it) which is 8.625%. We do this proportionally based on new prices so
Horse B gets 54.55% which is 4.705
Horse C gets 45.45% which is 3.920Meaning corrected probabilities in the absence of Horse A of
Horse B = 59.255%
Horse C = 49.37%And new prices of
Horse B = 0.687/1
Horse C = 1.025/1Logical?
In TDK’s example (two horses at evens and one at 100/1 with one of the even money shots withdrawn) new prices would be –
Horse A = 0.0147/1
Horse B = 50.248/1That is basically what I was getting at cormack – the reduction factor system is effectively based on the horses % chance of winning the race. Your system is taking account of the overround by stripping it out then adding it back it….
I think it is the fact that the by calling it a reduction factor you can apply it to the whole return (including stake) whereas it is the pence in £ profit which creates the anomalies you have identified.
Surely, you need to make sure the assumptions you make within any calculations you make are valid ones. For example, who exactly determined removing the o/r from the book in a proportional manner is the right™ thing to do?
You could make a decent case because of the favourite-longshot bias in bookmaker markets that a flat linear removal of the per horse o/r from each runner was a more accurate representation of what happens in practice to winning chances when compared to the results they yield. i.e. you take eg 2% off a 7/4 shot and a 16/1 shot regardless. (yes you couldn’t take 2% out of a 66/1).
You could indocine but, as you mention, as you get to longer prices then the over-round become dis-proportionate.
I don’t think anybody determined it was the ‘right’ thing to do. We’re just suggesting is all.
Sorry it has taken a while for me to take on board some of the points raised on this thread. A head full of flu did not help and as always you wake up suddenly with things a lot clearer so best to post whilst it is.
Here is my proposal for a new deductions method to replace R4.There are three steps to the calculation.
The first is the % of the runner withdrawn (i.e Evens 50%, 2-1 33% and so on).
The second is the total market overround at the time of withdrawal (can apply to a firm’s early prices as well as on course shows).
From these two figures you calculate a deduction percentage as follows :
(% of runner withdrawn) / ( Total market Overround) so Even money in a 100% market would be 50%, in a 110% market would be 45.5% (50/110) and so on.
The last step is to apply this deduction percentage to the total returns (including stake), so any payment on winning bets would be reduced by 50% in the first instance and 45.5% and so on.
To use thedarkknight’s example of two Even Money chances and a 100-1 shot (total market overround of 101%) the deduction for one of the even money withdrawals would a deduction percentage of 50/101 = 49.5%.
So a punter having a £100 on the even money chance that runs would have £98 deducted from his total return of £200 i.e a return of £102. This correctly reflects the fact that after one of the Even money chances is withdrawn the odds would indeed be 1-50 and 50-1 for the two remaining horses.
Similarly in a three runner race where all horses are 2-1 one withdrawal would lead to a 33% deduction percantage (33/100) from total stakes.
Therefore £100 win on one of the other 2-1 chances would lead to a total return on £300 less the 33% deduction (£100) to give a return of £200 which again is the correct return based on the fact that after one of the runners being withdrawn the market would of course be evens each of two.Hope that makes sense.
Obviously it is my belief that this provides a correct arithmetic solution to the problem of deductions but one area remains which favours the bookmakers and that is when the withdrawal leads to a change in the number of each way places. It is my opinion that this would no longer be justified now there is a correct deduction percentage so would alsos propose the following change.
Where a withdrawal occurs after either an early price or on course market has been formed that would reduce the number of each way places the original number of places are still paid on bets struck prior to withdrawal. They are of course subject to the above deduction.
In the new market the lower number of each way places would of course be paid. So any early price 16 runner handicap would still pay four places on any bets struck prior to withdrawal.
This to my mind is a nice by product of a more robust and arithmetically correct rule and as always all views welcome.
The place part would potentially get very messy indeed…
Let’s take an extreme example again – as they are the examples that best make a point…
16 runner handicap hurdle on a Sunday and we have 4 "contenders" each at 3-1 and 12 Milton Bradley sprinters turning up for appearance money priced at 100-1.
Sadly, Milton’s van breaks down on the way to the race track – are bookmakers going to be happy paying four places to those who placed their bets on the runners prior to the breakdown????
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