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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Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Mon Aug 15, 2011 11:00 am

This is a rather simple and obvious observation, but seems overlooked when scheduling methods are considered:

Number of Heats per entrant = (Racers per heat * Event duration * Number of tracks) / (Average time per heat * Number of entrants)

That is to say, the biggest limiting factor in how many heats a racer can run is how much track time is available for racing. Improving the Average time per heat is really difficult unless one tosses important factors such as "the owner stages the car"! (Some groups have adults stage the cars in order to save time, but that is not an option for me.) Reducing the Number of entrants is (or at least should be) a non-starter. It is an event in which we should be trying to serve as many of the membership as possible.

But, if the competition rule is amenable, Heats per entrant is linear with the Number of tracks! If the number of tracks is multiplied by 7, so also is the number of heats for each entrant. It would be necessary to multiply the event duration by 7 in order to accomplish a similar increase in the Number of heats per entrant!


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Mon Aug 15, 2011 12:20 pm

Stan Pope wrote:This is a rather simple and obvious observation, but seems overlooked when scheduling methods are considered:
More than one track may not be a consideration in scheduling because that option is not available or practical for most units?

Just to be clear, what is meant by "heats per entrant" in this situation? Is it the number of times each individual car is staged and allowed to go down the track to the finish line?

What advantages can be realized by having multiple tracks with fewer lanes versus a single track with more lanes? Should one schedule two 3-lane tracks as if it were a one 6-lane track?



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Mon Aug 15, 2011 7:08 pm

FatSebastian wrote:
Stan Pope wrote:This is a rather simple and obvious observation, but seems overlooked when scheduling methods are considered:
More than one track may not be a consideration in scheduling because that option is not available or practical for most units?

Just to be clear, what is meant by "heats per entrant" in this situation? Is it the number of times each individual car is staged and allowed to go down the track to the finish line?

What advantages can be realized by having multiple tracks with fewer lanes versus a single track with more lanes? Should one schedule two 3-lane tracks as if it were a one 6-lane track?
"Heats per entrant" ... yes, a contested run on the track for one racer. One heat on a three lane track results in 1 heat per entrant for the involved racers. Perhaps "runs per entrant" would be less ambiguous.

First, as the formula indicates, the greatest benefits accrue when a large number of racers are involved, such as at a district or council race.

The formula assumes that the tracks can operate independently. If not, the benefits are less. For instance, in our district races using no-chart quintuple elimination with heats alternating on two or more tracks from a single queue of racers, the ability of staff and racers to perform lane draw and feed the trios of racers to the tracks fast enough determines how well the multiple tracks can fulfill their potential.

I think that the suggestion to use 2 3-lane tracks in place of a single 6-lane track fits this latter case as well.

Separate tracks run heats totally independently in the 15th Burlington (bubblesort) method which accounts for that method's ability to produce large heats per racer numbers.


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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Mon Aug 15, 2011 9:04 pm

There is a companion measure that organizers should consider, too. It is "runs per entrant per hour". For a given heats per minute capability for a track/staff, as the number of racers increases, then runs per entrant per hour decreases.

The "flip side" of that measure is how much time the racers spend waiting for their turn to race.
As the number of racers increases (as it does for district and council races), the percent of each racer's time spent waiting increases!

In planning a district or council race, selecting a method of competition which produces lots of racing for each entrant usually makes for a better experience than if the youngsters sit and wait for 95% of the time. In my experience, Cub Scouts make much better participants than spectators.

Another consideration is "How much time spent racing (as opposed to watching/waiting) by each entrant" vs "the total time commitment by each entrant". For a racer in a rural midwest district, the racer might spend 1 to 2 hours commuting to and from the event, 1 hour getting through inspection, and 2 hours of competition. If the entrant runs in 4 heats during that time (at for instance, 1-1/2 minutes a piece, and is doing another half minute of "racing things" (such as drawing for lane or retrieving his car from the pit), he is an active participant for 8 minutes. The remaining 112 minutes he is a spectator. If I can increase each participant's heats to 20 in that same 2 hours, then each is an active participant for 40 minutes and a spectator for 80 minutes. I think that 40 minutes of active competition can make the experience better for each youngster (win or lose), and make the "overhead time" (commuting and inspection) seem much more worthwhile. What remains is to assure that the "active competition" is structured so as to be meaningful and productive, such as "each race contributing to the final standings" and "a low percentage of heats in which one racer 'blows the doors off' the others".

In the analysis that I've done, "62% active during the competition" is about a high as I've been able to push the 15th Burlington method. This assumes 7 racers per 3-lane track, 1/2 minute for 4-racer lane draw, and 1-1/2 minute heat cycle time. (Fewer than 7 racers per track causes the track utilization to degrade because the next heat lane draw awaits a racer who are still racing.)


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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Mon Aug 15, 2011 9:23 pm

FatSebastian wrote:
Stan Pope wrote:This is a rather simple and obvious observation, but seems overlooked when scheduling methods are considered:
What advantages can be realized by having multiple tracks with fewer lanes versus a single track with more lanes? Should one schedule two 3-lane tracks as if it were a one 6-lane track?
If the competition algorithm were PN family points final standings, then "no". The result does not satisfy the PN family criteria.

I suspect that the Cub Scout management inefficiencies would swamp the inefficiencies in managing twice as many Scouts on one track. What is harder than getting 6 specific Cub Scouts to gather at one 6-lane track? Getting 6 specific Cub Scouts to gather correctly at two specific 3-lane tracks!


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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Mon Aug 15, 2011 9:40 pm

Part of what this thread is trying to point out is that some racing methods that work splendidly for den-size groups have some serious drawbacks if applied to much larger groups.

For instance ...
If I use GPRM to schedule 6 runs per racer on a three lane track for my 12 member Wolf age group, then each member participates in 6 of the 24 heats, or 25%, with 75% waiting time.
If I use GPRM to schedule 6 runs per racer on a three lane track for my 40-member pack, then each member participates in 6 of the 80 heats, or 7.5% with 92.5% waiting time.
If I use GPRM to schedule 6 runs per racer on a three lane track for my 100-member district age group, then each member participates in 6 of 200 heats, or 3% with 97% waiting time.

The accuracy of the result is still excellent, but the waiting time dulls the experience!


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Mon Aug 15, 2011 10:45 pm

Stan Pope wrote:Number of Heats per entrant = (Racers per heat * Event duration * Number of tracks) / (Average time per heat * Number of entrants)
It was not obvious to me is why the formula should include Number of tracks. I would have thought that is part of Racers per heat , which seemed like a synonym for total number of lanes. Wouldn't Racers per heat equal number of lanes per track * Number of tracks? So I guess we are assuming that a "heat" is limited to a single track, which is why I asked what "heat" means here...

Heats per entrant is linear with the Number of tracks, but it would also seem linear to number of lanes? Is there a presumption in this formulation that all tracks have the same number of lanes?



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Tue Aug 16, 2011 7:22 am

FatSebastian wrote:
Stan Pope wrote:Number of Heats per entrant = (Racers per heat * Event duration * Number of tracks) / (Average time per heat * Number of entrants)
It was not obvious to me is why the formula should include Number of tracks. I would have thought that is part of Racers per heat , which seemed like a synonym for total number of lanes. Wouldn't Racers per heat equal number of lanes per track * Number of tracks? So I guess we are assuming that a "heat" is limited to a single track, which is why I asked what "heat" means here...
Now I see the source of concern. To interpret Racers per heat equal number of lanes per track * Number of tracks would seem to assume, maybe even require, that the tracks ran in lock-step. That seems a tight constraint.
FatSebastian wrote:Is there a presumption in this formulation that all tracks have the same number of lanes?
Yes, good point. That assumption derived from my thought context.


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Tue Aug 16, 2011 10:07 am

Stan Pope wrote:To interpret Racers per heat equal number of lanes per track * Number of tracks would seem to assume, maybe even require, that the tracks ran in lock-step. That seems a tight constraint.
Agreed. But it was not obvious (to me) how "scheduling methods" are suppose to fairly consider multiple tracks without a constraint like this. (Bubble sorting across multiple tracks really don't seem to employ a "scheduling method" in the traditional sense, as car placements from heat to heat are mostly determined by previous performance outcomes.)



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Tue Aug 16, 2011 11:43 am

Yes, Bubble sort and N-Elim use "adaptive scheduling" rather than "fixed scheduling" such as PPN. For pure time racing, fixed scheduling can be very effective. In fact, I don't think I'd like to try timed racing with adaptive scheduling.

Adaptive scheduling can be very strong for producing lots of close races. So long as the competitors understand that the criteria involve "who you win against" rather than "how many times you won", it produces good results.

One of the reasons that I'm digging around in this is that when larger groups are racing, as in our district races, participants spend an inordinate amout of time being (bored) spectators and not very much time actually "doing racing activities." Since one track can hold only so many heats per hour and our PWD Chairman insists that our event be a ONE DAY event and we need to hold races for 5 age groups with a total nose count of 300 to 400 Cub Scouts (I'd love to have more!), I'm looking at all of the limiting factors that I can to try to get more racing in less time. From 1 to 1-1/2 hour per age group seems a reasonable time, if we can get enough actual racing packed into that interval.


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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Wed Aug 17, 2011 10:46 am

The discussion leads me to believe that there might be other forms of adaptive scheduling which could operate easily and effectively on multiple, independent tracks. I am interested to hear of other concepts which could both rank racers and provide frequent races for each entrant.

For instance, the 15th Burlington method sorts racers along a single row of tracks. It does so with minimal record keeping because "sorting" (moves between tracks) is based on "local" criteria (i.e. the results of the last race on one track.) Are there other geometric structures, e.g. a circle, a figure 8, which could also function smoothly and provide similar benefits? Or are there other "local sorting rules" which also function well and, perhaps, assure that racers get to run on more of the tracks.


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Wed Aug 17, 2011 5:00 pm

Stan Pope wrote:For instance, the 15th Burlington method sorts racers along a single row of tracks. It does so with minimal record keeping because "sorting" (moves between tracks) is based on "local" criteria (i.e. the results of the last race on one track.) Are there other geometric structures, e.g. a circle, a figure 8, which could also function smoothly and provide similar benefits?
When you say "geometric structures", is this a reference to the organization / layout of adjacent tracks? If so, does "circle" imply a radial arrangement (like the spokes of a wheel) or a start-to-end arrangement (like the tread of a tire)?

Bubble sorting is notorious for being perhaps the most inefficient way to sort. However, this inefficiency would seem to be an advantage if the goal is to maintain activity. With that said, I suppose that as fast cars migrate one direction and slow cars migrate the other direction, eventually only the fastest cars compete against each other and slowest cars compete against each other. This would seem to make for many close races. The advantage is that this could lend to the excitement. Yet I wonder if issues of lane equity might become more noticeable as cars of the same caliber start to face off. Also, without an electronic timer for every track, sight judging might result in a lot of visual ties, with boys not being able to advance, or else advancing by twos, depending on how ties are treated. Could an inexperienced line judge cause a traffic jam?

I have not thought through the following suggestion very far, but to keep boys moving across all the tracks, and to mix things up a little in terms of competition, I wonder if there is merit in having the racers that win on the fast ("gold") track go down to the slow ("silver") track, and those who lose on the slow track go up to the fast track. As a racer moves off either end, the racer might get his hand stamped with "gold" or "silver" to signify that he made to the end traveling a certain direction (winning or losing), and the boys with the greatest number of winning "gold" stamps qualify for the finals. (Losing "silver" stamps might run off for a turtle award, or some other kind of fun award, to keep them interested in participating.)



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Wed Aug 17, 2011 9:45 pm

Some excellent thinking in there, FS! Thank you.

I'm thinking "generalized geometry", i.e. topology and connectedness. Your alternative of the "tire" and subsequent observation about Gold Track winners going to the Silver track, and vice versa (even if the tracks are still arrayed in a line) are consistent with my intent.

While avoiding an evolution toward running the fastest against the fastest would hurt the effectiveness of methods like 15th Burlington, there may be some value in breaking the Preliminary Racing into two parts ... a period of 4 or 5 heats apiece running as a ring with 1st place moving clockwise and 3rd place moving anticlockwise, then a period of 8 or 10 heats apiece running a "line" with 1st place moving toward (or staying on) the Gold Track, etc.

I considered this as I was typing the prior post because it would give more racers runs on more tracks without hurting the accuracy of the method. (Fast racers who start near the Gold Track and slow racers who start near the Silver track probably run on only a fraction of the tracks. This does not hurt accuracy, but might seem to some to be an unfair arrangement. I'm sensitive to both the fact and the appearance of unfairness.)

Early on I considered "counting appearances" on the Gold Track as a means of selecting Finalists. Apart from the extra bookkeeping needed, I was never able to convince myself that it would assure those deserving of the trophies would actually be finalists. (Bookkeeping also complicates the ability of the audience to validate the selection process. I think that "winning off the Gold Track" during Finalist Selection is really transparent... even the most casual observer can tell if it is being done fairly and correctly.) None-the-less, there is a beauty in rating the racers in terms of how quickly they can rotate around the wheel of tracks!


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Re: Limitations on Number of Heats per Entrant in Racing

Post by FatSebastian » Thu Aug 18, 2011 2:10 pm

Stan Pope wrote:None-the-less, there is a beauty in rating the racers in terms of how quickly they can rotate around the wheel of tracks!
Assume that there are N tracks, where the "Gold" track is Nth and the "Silver" track is first. Define a variable R which is number of "rollovers" (positive if receiving a "gold" stamp and negative if receiving a "silver" stamp). For a "circular" racing strategy, where winners perpetually move one direction and losers the other direction, the amount a racer ascends or descends is Ending Track - Starting Track + (R * N). With a record of starting track line, ending track line, and no. of rollovers for each racer, a score could be created for each racer.

Let's say there are N = 10 tracks. Tyler started in line for track 3 and ended in line for track 6, and he ascended past the "Gold" track twice. His final score score would be 6 - 3 + 2*10 = 23.

There's probably a lot of room for issues with such a system, including concerns over bookkeeping mistakes or boys inadvertently heading in the wrong direction.
Stan Pope wrote:(Bookkeeping also complicates the ability of the audience to validate the selection process. I think that "winning off the Gold Track" during Finalist Selection is really transparent... even the most casual observer can tell if it is being done fairly and correctly.)
I wonder if this is also one of the disadvantages, as it becomes obvious which cars are outstandingly good and (perhaps more painfully) obvious which cars are outstandingly bad. There is a stigma associated with being on the "slower" tracks which tempts the boys to advance themselves undeservedly. (I seem to recall that undeserved self-promotions were actually occurring at one race practicing bubble sorting, but don't recall where I noticed this.)



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Re: Limitations on Number of Heats per Entrant in Racing

Post by Stan Pope » Thu Aug 18, 2011 2:51 pm

FatSebastian wrote:(I seem to recall that undeserved self-promotions were actually occurring at one race practicing bubble sorting, but don't recall where I noticed this.)
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.)

If "self-promotions" occurred only a few times during the competition, then it is only a significant issue if precise records are kept as a basis for competition. We can detect that it has occurred by observing imbalance among the tracks' queues. As competition nears the end, then the staff on the critical tracks must heighten their vigilance. Unless such "self-promotion" were methodical, incorrect standings due to occasional errors during the first 3/4 of racing get corrected. (Fault tolerance is one of the positive aspects of the method!)

On the suggested scoring ... the "passages" through the Track N::1 gate must be plussed and minused for each racer so that oscillations across that border are not mistaken for full rotations! A "good car" could win on Track N on merit and lose on Track 1 intentionally to make a + passage once every two times he raced versus making a + passage once every N (or more) times he raced by winning every chance.

Scorekeeping for this style of racing would be easy if heat participants and results were tracked mechanically, e.g. by bar code or rfid readers at the starting and/or finish lines. (Could rfid readers distinguish the lane a car is in?) Such hardware would be good even for fixed schedule racing as verification that the race was being run in compliance with the schedule!


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