30 Cars, 3 lane track, no timer,need top 4 finishers...

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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Go Bubba Go
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30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Go Bubba Go » Thu Oct 16, 2008 11:47 am

Any thoughts on how best to arrive at the top 4 fastest cars under these circumstances:

1) Using 3 lane track with no timer (eyeball 1st, 2nd, and 3rd place).

2) 30 cars total vying for top 4 positions.

3) Entrants are "aware" of lane variation and may wish to utilize a method that helps mitigate that as an issue.

This is an "adult race" setup for a donor, with the top 4 finishers going on to compete as the donor's entries for a local charity event.

Any input welcome...

Bubba

p.s. My initial thoughts (either in single races, or in heats of 3 if lane variation is an "issue" for them).

Round 1: Run cars once in 10 groups of 3, placing the cars from each group in 3 "loss count" trays according to those that have been identified as being slower than no other cars so far (i.e. 1st place in initial race / heat), slower than at least one other car (i.e. 2nd place in initial race / heat), and slower than at least two other cars (i.e. 3rd place in initial race / heat). Now race only the 10 cars in the "slower than no other cars so far" tray according to the same methodology, repeating the process until there is only one car left in the "slower than no other cars" tray. That is the first place car.

Round 2: Run cars from the "slower than at least one other" tray similar to Round 1 above, with the 1st place cars remaining in the "slower than at least one other" bucket, 2nd place going to the "slower than at least two others" tray, and 3rd place going to a fourth "slower than at least three others" tray. Continue on with the cars from the "slower than at least one other" bucket until only one car remains. That is the second place car.

Round 3: Similar to above, racing the "slower than only two others so far" cars to identify the one car that is finally "slower than only two others" i.e. third place car...

Round 4: Similar to above to identify the "slower than only three others" i.e. fourth place car...

There may be a nomenclature for this method already, if so I apologize for my ignorance in not utilizing it.


"Who's Grandpa's neighbor?"... Phil Davis, Down and Derby

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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Thu Oct 16, 2008 2:07 pm

A scheme like this was incorporated in one early commercial product. Don't know if it is still being sold.

Accuracy should be comparable to n-elim and maybe comparable to PPN.

Watch out for in-group match-ups after round 2: A car can be matched with a prior opponent unless care is taken, because they took different loss paths to that group. For instance the group with 2 "beaten by points" contains cars that finished 1st in rnd 1 and 3rd in rnd 2, 2nd in rnd 1 and 2nd in rnd 2, and 3rd in rnd 1 and 1st in rnd 2.

In any case, the results you have should then be fed into a ladder of the first 4 or 5 place finishers to "confirm" ... 4&5 race, 4 needs one win and 5 needs 2 wins to progress. Before each run, draw for lane between the two best matched lanes. Survivor progresses against #3 in the same manner. If you don't do the pre0heat draw and just "swap lanes", then the initial draw (back in round 1) can be the determiner.

Another advantage is that this makes the last race of the day for first place! What you have places an early round race as the race for first place.


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Thu Oct 16, 2008 6:50 pm

An important aspect of this scheme is that the concept of lane equity just doesn't apply. It doesn't matter if each car raced in each lane the same number of times, because what matters is WHO was raced during each of best lane and worst lane runs!

The best you can do is to allocate all lane advantage and disadvantage in a purely random fashon and let the good matches and the bad matches average out. (Note that "the order an official picks cars out of a tray" is NOT random ... don't get caught in that one.)

I've been trying to think through the similarities and differences between the scheme and the n-elim method. The critical difference seems to me to be the effect of lane inequities. They may negate the application of transitivity in the evaluation. (That is, is the difference between 2nd and 3rd place ) If the track has two nearly equal lanes and one poor lane, and the difference often exceeds the difference between the competitors, then I think the differentiation between 2nd and 3rd place does not give better results.


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by TAL » Mon Dec 15, 2008 9:52 pm

We had 24 cars with a 3 lane home made track , no timer and did 3 full races. One race at 32 feet , once at 40 feet and the last race was 48 feet.

Results were the same at the end of all 3 races. All was completed in well under 2 hours.

We Numbered the cars 1, 2, 3, 4, etc... as they sign in at the race.

They are then grouped 1 2 3 , 4 5 6 , 7 8 9 , 10 11 12 , etc. and so on in the orders numbered.

Cars 123 run once in each of the 3 lanes ; Lane order 123, 312, 231.
Car in the 3rd lane moves far left to lane one, and the other 2 cars move right to the next lanes.

Any of the 3 cars that has a first place finish in the 3 runs of the heat advances to round 2.
If 2 or 3 of the cars have a first place finish they will be seperated as the start of the next groups of the cars for the up coming round 2.

Any car that does not have a 1st place finish in the first round are seperated for a wild card round (second part of the first round) to race in groups of three again to race against other cars that did not have a first place finish in round one for their last chance to advance to round 2 .

Again any car that has a first place finish in the 3 run heat in the wild card part of the race will be allowed to advance to round 2.

Bottom line; of the 3 run heat you must have a first place finish in a single run of the 3 run heat to advance to round 2.

Now in round 2 ; Again, groups of three and you must have at least 2 first place finishes in the 3 run heat to advance to round 3. Any car in the groups that do not have 2 first place finishes in there group 3 run heat will be staggered back in groups of 3 to run again (2nd round wild card) in other groups that also did'nt have 2 first place finishes.

Now in round 3 you have to win all three runs of the group heat to advance to round 4 .

We never made it to round 4 , winners were determined.

Quik run down to explain to participants ,
Groups of three run once in each lane in round 1, you must have at least a first place finish in the 3 run heat to advance to round 2 .
(All rounds have the second part wild card groups for the cars that did not meet required amount of finishes to advance).

Round 2, you have to have at least 2 first place finishes in the 3 run heat to advance.

Round 3 , you must win all 3 runs to advance to next round.

In the end all were satisfied and clearly recognized the winners.



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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Tue Dec 16, 2008 2:44 am

TAL wrote:We had 24 cars with a 3 lane home made track , no timer and did 3 full races. One race at 32 feet , once at 40 feet and the last race was 48 feet.

Results were the same at the end of all 3 races. All was completed in well under 2 hours.
Cool, TAL! Thank you for sharing that! Is it correct that cars that don't progress during Wild Card heats are eliminated? OTOH, it appears that many will progress in the first Wild Card heat. (I like to see as many youngsters as possible win at least one heat during the races! Best scheme I've seen for handling a racer counts of 50 to 100 sends approx 87.5% of racers home with at least one heat win!)

Have you conducted a formal accuracy analysis or simulation on the method? If so, what were the results?


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by TAL » Tue Dec 16, 2008 11:59 am

Stan Pope wrote: Is it correct that cars that don't progress during Wild Card heats are eliminated?
Yes , you have to meet the number of first place finishes required for the designated round in the wild car heats or you are eliminated.



Have you conducted a formal accuracy analysis or simulation on the method? If so, what were the results?
No , we just used that method that series of races and it seemed to work really well .

All seemed to be very satisfied with the results and all racers got at least 6 runs on the track.



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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Tue Dec 16, 2008 2:32 pm

Thanks, TAL.

It wasn't immediately clear how finish places (1st, 2nd, ...) are determined. Perhaps that will be more clear when I run a full walk-through. So far, I just graphed the racer flow.

The algorithm does not fit any of the Evaluation Simulation programs that Cory Young put up on his website, so I have hauled out my Developer's Hat and started a Sim for this procedure, using concepts described in http://www.stanpope.net/pwmeval.html and as improved upon by Cory in his programs. It will take a while to get to the other side, but I'll share when/if.

Meanwhile, I'm working on routines to produce random numbers with Poisson and Gaussian distributions! :)


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by TAL » Tue Dec 16, 2008 3:17 pm

Wow! I'm really happy you see possible potential in the method. :D


Possible senerio: If in round 1 each of the 3 cars in the group accomplish a first place win in the 3 run heat we just staggered them into different groups in round 2 being each of the 3 cars have a first place finish in their 3 run heat.

In round 2 if noone meets the 2 first place requirements, again we just staggered all 3 of them to different groups in the next round.



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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Tue Dec 16, 2008 3:32 pm

Yes, got that part ... missing determination of "top 4" and "ranking thereof."

It seems likely that at some point e.g. in round 3, the "still alive group" reduces to about 5 or 6 racers, then in the next round, it drops to, for instance, 2 racers. Three or four were eliminated in the same round, but two of those should be included in the "top 4". (The order of elimination within the round should not be a factor, since that was determined by the race crew arbitrarily.)


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by TAL » Tue Dec 16, 2008 4:05 pm

What would be a good way to determine the finish order?
Right , I agree order of elimination cannot determine finish order, what about a second wild card group for the eliminated from the last round?

Maybe last 5 or 6 cars have some type of head to head action?



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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Tue Dec 16, 2008 4:26 pm

TAL wrote:What would be a good way to determine the finish order?
Right , I agree order of elimination cannot determine finish order, what about a second wild card group for the eliminated from the last round?

Maybe last 5 or 6 cars have some type of head to head action?
:)

I was hoping that you had defined that stuff already and that all I would have to do is to use that defined algorithm in the simulation!

I'll get out a deck of cars, shuffle them up, and walk through a few rounds to see what I learn from the process.


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Thu Dec 18, 2008 10:22 pm

Haven't done much with the ranking mechanism, but finished coding the Gaussian Random Number Generator this afternoon. Next is a Poisson Distribution generator, which will be a bit more difficult. Then, I've gotta bear down and understand the method and identify possible schemes for ranking. :) What fun! :)


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Re: 30 Cars, 3 lane track, no timer,need top 4 finishers...

Post by Stan Pope » Sun Dec 28, 2008 2:27 pm

Lacking a racer ranking method for the method, the usual accuracy depiction doesn't work. (See Cory's DerbySim program on his web site) so "summary results" are hard to show. Instead I listed the last few rounds survivors from each of 99 trials (trying to show the "top 4" racers from, each trial) and passed them on to TAL off-line.

The results, although preliminary, seem really mixed. That, combined with the lack of a clear ranking algorithm, lead me to conclude that except to test this simulation program context, I won't pursue the method any farther.

The positive results are that I have built routines to create and scale random numbers with both Gaussian (Normal) and Poisson-like distributions and I have some of the necessary density distribution factors for the various types of races: pack race (cars built almost always get raced), pack finals, open district (or council) race (many guys with cars which were slow in the pack races don't bother entering), moderately selective district races, highly selective district races, and district finals.


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