Minimum vs. Cumulative vs. Average times for outcome

Debates and discussions on the various race scheduling methods that can be used and their fairness and accuracy in determining the winners.
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Rod Turnbull
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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by Rod Turnbull » Tue May 12, 2009 7:30 am

Stan Pope wrote:Does CMA have a set of competition methods from which local organizers are encouraged or required to select for sanctioned events? Or does each local organizer get to "do his own thing" in selecting or concocting a scheme?
Kind of depending on what type of event you are holding... here are a few examples:

A national flat track event will have up to 15 or so classes with 100-200 riders some entering more than one class... before the event is added to the schedule the promoter has to guaranty a certain amount of prize money for each class and pay back a certain number of positions... a JR class may only have to pay back 3 positions and the promoter may only have to give out trophies... where the 500cc Expert class is required to pay back 15 places and 60% of the prize money goes to this single class... now as for rules we have how many paces we have to score back, sometimes it states that the rider gets more than one chance to make the final event... but the methods are dictated by the head CMA official on race day... it generally follows the same theme week after week... I can ask the official how many bikes he will let on the track for the final race and make a complete program from that information, show him what we have laid out, have it approved by him and posted in the pits in no time at all. Lets say for this National event the track was only a short track (1/4 mile), it's a clay track that is a little wet with rain a strong possibility later in the race program... there are 32 riders in the 500 expert class and the ref only wants 10 bikes on the track at a time for this class... 4 heat races (we know the riders so we try to spread them out and not get all the faster bikes in the same heat race), 1st and 2nd place transfers directly to the front row of the finals, 3rd-7th go to the semi-finals, 2 semi-final races with 1st and 2 place transferring to the back row of the final, 3rd-6th to the consolation race... then we take the top two finishers from the consolation race an put them in the 3rd row of the final... (now the ref only wanted 10 in each race but since this is the premier class and these guys now what they are doing and not likely to run each other over, plus we have started them on 3 different rows which makes for less congestion going into the first turn, the ref will OK the 14 riders which makes the promoter happy because it makes for a more exciting race for the crowd)... now as the evening draws to a close, by the looks of the clouds rolling in, it looks like we will not get all the races in... so we scrap the consolation race and run the 500 experts first in the final and save the JR classes for last... the rain comes and the last few races are not run. Now the top 15 riders for the 500 Experts are 1-10 as they finished in the final race... 11-14 are the top 2 riders from each of the semis (the semis are timed and the fastest race winner would get 11th and then the slower race winner would get 12th and so on), 15th place goes to the 3rd place finisher in the faster of the 2 semis... the JR class only had 4 riders and they where paid from their finishing order in the heat race. Next week then number of riders, track conditions, weather... is all different, so is the program.

Now Speedway racing on an average night in Canada is run with the flat track bikes and scored in much the same way... However Speedway National events have a rigid structure where the top riders move up a ladder and the slower riders move down the ladder and the whole event is score on a points system where you get say 4 points for a win, 3 for 2nd, 2 for 3rd... you get the idea. Now this would be a great way to do a PWD cars but with only a few dozen riders you are looking at 30 some odd races and it's a pain to keep track off... run 4 races, post the results, calculate who is racing who in the next 4 races and post that, repeat 6 or 7 times... it makes for lots of little intermissions.



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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by FatSebastian » Sat Jun 27, 2009 9:45 pm

gravityboy wrote:I personally prefer a system that rewards the 'good' car vs. the 'sprint' car, but I'd like to see what others think...
Re: Minimum vs. Cumulative vs. Average times, may I suggest a fourth possibility? :idea: The median is the central value of an odd number of outcomes (or the average of the two central values for an even number of outcomes). As an estimator of performance, the median time tends to be less sensitive to aberrant results (both low and high) compared to average (or cumulative) time.



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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by Stan Pope » Sat Jun 27, 2009 11:25 pm

FatSebastian wrote:
gravityboy wrote:I personally prefer a system that rewards the 'good' car vs. the 'sprint' car, but I'd like to see what others think...
Re: Minimum vs. Cumulative vs. Average times, may I suggest a fourth possibility? :idea: The median is the central value of an odd number of outcomes (or the average of the two central values for an even number of outcomes). As an estimator of performance, the median time tends to be less sensitive to aberrant results (both low and high) compared to average (or cumulative) time.
A real plus for your suggestion is that a car's times tend to have a skewed distribution rather than a normal distribution. So the average of the several times is skewed toward the slow end.

A possible negative is that it may induce some to "really run the ragged edge", i.e. build a car that runs fast or wipes out with little middle ground. If he "runs fast" one more time than he "wipes out", your suggestion gives him a great time. The average of all runs leaves him an "also ran." I'd have to think a lot about this extreme case before I'd conclude that giving him a great time would be consistent with the program goals. Thoughts?


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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by FatSebastian » Sun Jun 28, 2009 7:33 pm

Stan Pope wrote:A real plus for your suggestion is that a car's times tend to have a skewed distribution rather than a normal distribution. So the average of the several times is skewed toward the slow end.
I am fascinated by the suggestion that observed race times may be abnormally distributed. Is the distribution of race times discussed / analyzed elsewhere in DerbyTalk? (I did not find an earlier thread addressing this.)
Stan Pope wrote:A possible negative is that it may induce some to "really run the ragged edge", i.e. build a car that runs fast or wipes out with little middle ground. If he "runs fast" one more time than he "wipes out", your suggestion gives him a great time. The average of all runs leaves him an "also ran." I'd have to think a lot about this extreme case before I'd conclude that giving him a great time would be consistent with the program goals. Thoughts?
If by "wipe out" we mean that the car leaves the track / guide, it is not uncommon to rule that if a car repeatedly leaves the track, it must be removed from competition. Also, I'm not sure how one could calculate a meaningful average/accumulated time if some runs have no finish (other than infinite time = last place). May I therefore presume that we are discussing a car that can alternately be either really fast or really slow? If so, my lack of experience keeps me from envisioning how a "no-middle-ground" (highly bimodal) design might be intentionally accomplished, although it is a very interesting proposition.

Minimum time involves no mathematical evaluation and most folks seem to value it for the sake of simplicity. I think the bigger obstacle might be trying to convince / explain / use the median time as a performance indicator.



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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by Stan Pope » Sun Jun 28, 2009 11:55 pm

FatSebastian wrote:
Stan Pope wrote:A real plus for your suggestion is that a car's times tend to have a skewed distribution rather than a normal distribution. So the average of the several times is skewed toward the slow end.
I am fascinated by the suggestion that observed race times may be abnormally distributed. Is the distribution of race times discussed / analyzed elsewhere in DerbyTalk? (I did not find an earlier thread addressing this.)
Likely not! Most folks eyes glass over when anybody talks about that stuff. But, since you asked ... :) The assumption of normal distribution is close enough for most purposes. I can only give you the underlying concepts of my assertion, but formal proof or even experimental proof is not something I can give at this time.

Very simply stated, car's times have a firm lower bound and only an artificially selected upper bound. Run times tend to be pretty close to the lower bound, and that is where the median will be found. The average time will tend to be above the median. "Flyers" tend to be high times rather than low times.

If you look at typical car's times, you see that they are usually not too far away from the theoretical minimum time possible on that track on that day. With a bit of a "blip" during a run, the time can go much greater. Part of the reason is that the time measure is a result of other factors and I think that it is inversely related to those factors. So, while the factors involved may have normal distributions, their inverses (that add time to the runs) would not have normal distributions. If that description is difficult to grasp, think about the numbers 0.1, 0.4, 0.5, 0.6, and 0.9 which have (very approximately) a normal distribution about their mean of 0.5. Then consider the distribution of their inverses: 10.0, 2.5, 2.0, 1.7, and 1.1.

That is as far as my intuition can carry the explanation for now.
FatSebastian wrote:
If by "wipe out" we mean that the car leaves the track / guide, it is not uncommon to rule that if a car repeatedly leaves the track, it must be removed from competition. Also, I'm not sure how one could calculate a meaningful average/accumulated time if some runs have no finish (other than infinite time = last place). May I therefore presume that we are discussing a car that can alternately be either really fast or really slow? If so, my lack of experience keeps me from envisioning how a "no-middle-ground" (highly bimodal) design might be intentionally accomplished, although it is a very interesting proposition.

Minimum time involves no mathematical evaluation and most folks seem to value it for the sake of simplicity. I think the bigger obstacle might be trying to convince / explain / use the median time as a performance indicator.
Well, it was a bad choice of words. What I was thinking about when I used the word "wipe-out" was not such a dramatic event as launching off the track. Rather I was thinking of a car that part of the time was able to stay straight and true, and part of the time developed a severe case of the "wiggles". I think that is not uncommon as one approaches too closely the "bleeding edge" of energy extraction.

Curiously, "median time" is easy to think about but more difficult to actually "compute" than average time".


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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by FatSebastian » Mon Jun 29, 2009 2:27 pm

Stan Pope wrote:Very simply stated, car's times have a firm lower bound and only an artificially selected upper bound. Run times tend to be pretty close to the lower bound...
I was anticipating an explanation that times might operationally tend to skew toward slower speeds over time because of lubrication losses, dirt on the track, etc.
Stan Pope wrote:If you look at typical car's times, you see that they are usually not too far away from the theoretical minimum time possible on that track on that day. With a bit of a "blip" during a run, the time can go much greater.
I once collected a very limited set of timing data while optimizing COM placement for a particular (RR) design configuration. My recollection is that the distribution of times were grouped in "batches" or "clusters". My presumption at the time was that the car encountered certain small track defects, or experienced small wobbles, on various runs that knocked the time into a slightly different population. Had I collected a much larger sample, perhaps the convolution of these clusters would have resulted in a population that would have appeared more continuously distributed, I don't know. (With normally distributed data, the probability of getting an unusually fast or unusually slow run increases with sample size; this might appear as a "blip" in a small but normal population.)
Stan Pope wrote:Part of the reason is that the time measure is a result of other factors and I think that it is inversely related to those factors. So, while the factors involved may have normal distributions, their inverses (that add time to the runs) would not have normal distributions. If that description is difficult to grasp...
The description is not difficult to grasp, but I'm not quite sure why normally-distributed factors that effect time to finish would be inversely proportional to time of finish versus some other relationship. Regardless, this hypothesis seems to support the argument that the normal distribution in an inadequate model for run times.



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Re: Minimum vs. Cumulative vs. Average times for outcome

Post by Stan Pope » Mon Jun 29, 2009 3:56 pm

Good info, FS! I think your tests showing time clusters would be instructive to revisit! Your description of the observations lends credence.


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