Limitations on Number of Heats per Entrant in Racing

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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FatSebastian
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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Thu Aug 18, 2011 3:13 pm

Stan Pope wrote:I believe that it was mentioned in the 15th Burlington web site (though it might have been in emails that I exchanged with the organizers there.)
Okay, I was able to find it with that clue. Thanks.
Stan Pope wrote:On the suggested scoring ... the "passages" through the Track N::1 gate must be plussed and minused for each racer...
Agreed - I had noted that "rollovers" must be annotated as "positive" or "negative". Bookkeeping for a kid who happens to find himself being knocked back and forth between the "Gold" and "Silver" tracks could get confusing though. :/



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Thu Aug 18, 2011 7:33 pm

FatSebastian wrote:Agreed - I had noted that "rollovers" must be annotated as "positive" or "negative". Bookkeeping for a kid who happens to find himself being knocked back and forth between the "Gold" and "Silver" tracks could get confusing though. :/
I thought that it was at least implicit in your statement. I commented to be sure that more casual readers didn't miss the implications. :)


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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Thu Aug 18, 2011 8:02 pm

Carrying forward the "ring structure" analysis, as FS noted, fastest cars rotate about the ring in the "Plus" direction with their average speed of rotation proportional to their ranking between the median and fastest cars. Similarly, the slowest cars rotate about the ring in the "Minus" direction with their average speed of rotation proportional to their ranking between the median and the slowest cars.

This from my "mental simulation" of racing the method:

In between, the cluster of cars which rank near the median tend to "stay close to where they started racing." Some oscillation is expected since the original distribution of racers was not homogeneous. Since the original locations of those median-bunch cars are randomly distributed around the ring, there is no "central location" about which the median-bunch cars gravitate.

Since the "ring" method does not tend to cause head-to-head races between similarly matched cars, it is probably slower at ranking the cars than would the original terminated line of tracks.


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Thu Aug 18, 2011 9:12 pm

Stan Pope wrote:...the cluster of cars which rank near the median tend to "stay close to where they started racing." Some oscillation is expected since the original distribution of racers was not homogeneous.
:nod: I might have also said that they tend to "end up close to where they started."
Stan Pope wrote:Since the original locations of those median-bunch cars are randomly distributed around the ring, there is no "central location" about which the median-bunch cars gravitate.
Yes, it seems that one might be able to make conclusions based only on how far away one traveled from their starting location.
Stan Pope wrote:Since the "ring" method does not tend to cause head-to-head races between similarly matched cars, it is probably slower at ranking the cars than would the original terminated line of tracks.
Probably. It would be an interesting thing to simulate.

The distribution of race scores might also be an interesting data set for analysis. Might the outcome resemble the results of something like a Galton box and have a predictable distribution? Could race officials thereby detect cheating by a statistical hypothesis test of the distribution of scores? For example, one might expect that ~1/2 the cars end up toward the right of their original location, and ~1/2 end up toward the left. This would not necessarily identify individual cheaters, but it might suggest anomalous activity within the population of race outcomes, say, if the population of scores were highly asymmetrical.



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Thu Aug 18, 2011 9:38 pm

FatSebastian wrote:
Stan Pope wrote:Since the "ring" method does not tend to cause head-to-head races between similarly matched cars, it is probably slower at ranking the cars than would the original terminated line of tracks.
Probably. It would be an interesting thing to simulate.

The distribution of race scores might also be an interesting data set for analysis. Might the outcome resemble the results of something like a Galton box and have a predictable distribution? Could race officials thereby detect cheating by a statistical hypothesis test of the distribution of scores? For example, one might expect that ~1/2 the cars end up toward the right of their original location, and ~1/2 end up toward the left. This would not necessarily identify individual cheaters, but it might suggest anomalous activity within the population of race outcomes, say, if the population of scores were highly asymmetrical.
I think I would describe that which is detected differently: "failure to follow the process rules". This could be intentional or unintentional.

The expression of "left or right of their original location" requires clarification ... left or right on a doubly connected 1 dimensional structure (ring) doesn't have intrinsic meaning.


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Thu Aug 18, 2011 9:56 pm

Stan Pope wrote:I think I would describe that which is detected differently...
A reasonable clarification - at least "anomalous activity" IMO does not imply intention. ;)
Stan Pope wrote:The expression of "left or right of their original location" requires clarification ...
"Final score is positive or negative."



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Thu Aug 18, 2011 11:09 pm

FatSebastian wrote:
Stan Pope wrote:The expression of "left or right of their original location" requires clarification ...
"Final score is positive or negative."
:)


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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Fri Aug 19, 2011 4:07 pm

I have also looked, briefly, at utilizing tracks with other lane counts, should the population of 3-lane tracks be insufficient.

It appears that two-lane tracks could be stuffed in among the 3-lane tracks (between the Gold and Silver Tracks) if the number of racers assigned were reduced to about 2/3 of those on the 3-lane tracks. The race dispositions would be 1st: up one; 2nd: down one.

It also appears that four-lane tracks could also be used, either leaving one lane unused, or using all 4 lanes, increasing the assigned racers to about 4/3 of those assigned to the 3-lane tracks and disposing 1st: up two; 2nd: up one; 3rd: down one; 4th: down two. Or could dispose 1st: up one; 2nd and 3rd: same track; 4th: down one.


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