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BGonline.org Forums
Nigel Merrigan's new race formula
Posted By: Bob Koca In Response To: Nigel Merrigan's new race formula (Timothy Chow)
Date: Saturday, 7 May 2011, at 1:06 a.m.
I think some of the modeling and math is not sound and in particular I have the following questions,comments and criticisms.
1) On page 2: "Another feature of the Keith Count that could prove useful is the 1/7 added to the leaders count. 1/7 or 14.28% divided by 10 (1.428) is the maximum wastage per average roll."
The paper focuses on long races so a given roll will not be bearing anything off. What is meant be the wastage of a roll? A POSITION has a wastage ((49/6) times expected number of rolls to bear off minus the pipcount) and not a roll.
2) On page 2, crossover rate and "efficiency" (in quotes) are mentioned but not yet defined. A table of efficencies and crossover rates is given on page 3. Then a definition is given as Point Efficiency = 100(11q)/11N where q is quadrant (with being born off as quadrant 1, homeboard as 2 ...). and N is the point.
OK, but what is the motivation for this definition? Also is there a reason why a cancellable 11 is in both the numerator and denominator?
3) A definition then is given for crossover rate as (11X)q/11Y where Y is defined as location to bearoff and X is defined as "Let X be the location to first point of bear-in (in all cases the 6-pt)"
I would replace location with distance. Also is there a reason why N has changed to Y? So the equation is actually (Y-6)q/Y Right? OK, but again why define it in that way?
4) On page 4: "The decision to disengage in minimal contact races can often be a potential mind field. Breaking with 13/7 13/11 after rolling a 62 for instance will gain 4% on the „2‟ but lose a massive 12% on the „6‟ for an overall loss of 8%"
I agree that the bar point is not the best place for a checker. I wonder though about those %ages. 8% of what? Is it 8% of win chances? 8% of an effective pip? 8% of something else? In this calculation the locations of the other checkers are totally ignored. For example suppose that you have 10 checkers on the 8 point. If given the choice would you wish to move 1 to the 7 point and 1 to the 9 point? The inefficiency of the 7 point depends on what else is going on. If there are many checkers on various high points to bear in, a single checker on the 7 gives an efficient way to play an ace. If there are many checkers there already and few on higher points then it will likely lead to being forced to play large numbers to low points.
5) On page 4 the following appears and is highlighted: "The sum of E-Pips is 21% of the pip lead plus 0.5 for each extra crossover the leader/trailer has in the outfield."
What was done was the ratio for each point was totaled and rounded off to get the 21%. No particular reason why that should give something useful but that doesn't mean it will not work.
6) On page 5 a method of converting a pip lead to a win chance is given using the point of last take as obtained from either Trices 62 rule or Nack's N32 rule. This is not the final answer though. The E-pips effect must also be added in. An example is given in which the XG rollout matches the estimated winning chance. Since the win chance is the issue it should be done at DMP instead of for money. Also I think that XG's bearin technique in races is subpar making the race effectively slightly longer for both sides so the win% may be slightly too high.
7) On page 6 a position is given in which white has 13 checkers on the 5 lowest points and two stragglers. It is written "Wastage is one key factor and the Keith Count estimates white has 6 pips worth."
Wastage is normally defined as the EPC minus actual pipcount. The Keith count adjustments are certainly not estimating that. Those adjustments are accounting for how much worse one side is than the other in terms of wastage.
8) He then goes on to write "To punish white for all that wastage seems unfair, so the question then is: by what means is a fair penalty?"
Why is that unfair? A one sided rollout with gnubg shows that white has a greater wastage than black of 5.4 pips. So the value of 6 is close. A value of 22/72(6) = 1.83 pips is calculated for the "wastage" for white but why should the ratio 22/72 of bearin pips to total pips be so important. White will still have at least 3 checkers on the ace point, at least 2 on the two and at least 3 on the 3 when the bearoff begins.
A rollout showing 69.8% win chance is shown and the 2 pip adjustment is justified by pointing out how the Kleinmann formula would have calculated a value of 77% using the 6 pip adjustment but gives 73% using the 2 pip adustment which becomes 69.22% when E-pips are factored in.
But the values he gives for the Kleinmann adjustments are very wrong. If a 6 pip adjustment is made then we have 78-81. Subtracting four for being on roll gives 74 - 81 giving D^2/S = .32 giving 65% and NOT the 77% value stated. (As a sidenote the Kleinmann technique gave a low answer here for two reasons. First is that the adjustment is not fully 6 pips, secondly with many checkers on low points the variability in number of turns white needs to bear off is lowered which helps him as the race leader).
9) The suggested use of the metric he proposes along with the additional adjustment of 21% of the pip lead plus .5 per crossover may have something to it. There are many ways to get a value of 21%. His first four pages get to it by throwing together a bunch of stuff and a bunch of calculations that obtain it but I see know reason why apriori they should give something useful. To me the paper would be improved by just eliminating those first 4 pages and just basically saying: "Here is an equation that seems to work. The values were chosen empirically."
He suggests that the method is superior to other methods based on the samples considered but he misapplied the Kleinmann count mathematically in one of the positions and also didn't realize the effect of checkers on low points. The estimation for that position of approximately 2 pips seems like a huge fudge.
There is a technique that was not included in the analysis. If you can get the point of last take as is assumed for his technique you can see how many pips the actual position is from that and do a per pip adjustment.
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