Another Season Come and Gone....

[CuriousGeorge]

Well another season has come and gone here in Western KY . At District, my kids took 2nd in Webelos II, 4 Overall and 3rd in Bears, 5th Overall. We had 130 kids at district this year, a new record. My oldest sons single run track record (from his 2007 car) was broken by the second place Overall car. My son's time was 3.008 and the new record is 3.006. He really hated to see that get beat. The Overall winner was the same car that beat us at the pack level, but at districts it was even faster, they seemed to have worked on their wheels some more. All in all, my boys were very happy with the outcome. Our Pack took the 1st, 2nd (built a new car and it was smokin), 4th, and 5th place Overall spots. The 1st and 2nd overall cars only had 5/10,00th of a second difference. It seems that at least a few people didn't fall asleep at my PWD Clinic. My kids worked hard and "did their best" and I'm very, very proud of them. I'll try and post some pictures later on of the cars.

As far as our Awana's race My oldest son was the Grand Champion and my youngest son finished 4th. He should have been 3rd but I couldn't figure out the bracket system they used, When I asked, they said it was an elimination system with a twist .

I'm not sure what happened though. In their second heats they raced each other and only the 'electronic eye' (the ones that have the lights that blink or stay on) could tell who won, it was the closest race the whole night. My youngest boys car seemed to be slowing down the more it raced... either that or my oldest boys car picked up some serious speed the more it raced . It took almost two hours to race just 20 kids.

[frontosacam311]

Congrats on Districts! I had the same thing happen to me one year with the double elimination. My car placed 4th overall- yet it had beaten the third place car. My car had been double eliminated before his had. So from what I have gathered the double elimination works great for placing the two fastest accurately but anything after that is up in the air.

[CuriousGeorge]

That's a pretty accurate description.... I still never figured out their 'twist' though.

Another thing they did was run only 2 out the 3 lanes the track had. They raced lanes 1 and 3. Lane 1 was without a doubt the hot lane.

They raced two cars at a time, one in lane 1 and 1 in lane 3.... then they ran the same to cars again, only switching lanes. If a car won both times they went on to the next bracket but.... if each car won once, they reversed the cars again and ran a best 2 out of 3. Well, there was no big surprise (to me) when lane 1 won every 2 out 3 they had. Totally not fair. There were other problems also, I'm going to post more about the District and Awana race in the Planning, Preps & Running the Race forum.

But needless to say, I'm going to offer my packs track, me, and my computer for next years race. The track has an actual timer, and with the GPRM Software they should be able to run 5 times the amount of races (in three lanes instead of two) and have accurate standings at the end of the Grand Prix. I know the kids would love to have their cars raced a lot more and for the action to more continuous instead of waiting on the guys to try and figure out how to make the brackets (which is a whole other story).

[Stan Pope]

A few years ago, I wrote about this "interesting form" of double elimination racing. It acts slightly to reduce the effect of variance between runs of a car. The cost is more than doubling the number of heats.

Look at the outcomes from a "best 2 out of 3 heat":

1. Cars are more different than the lanes:
In this case the faster car wins both heats almost all the time. Once in a while the run variances will add up poorly on one of the heats and the third heat actually corrects for the variance. This third heat reduces the "luck factor" slightly. The vast majority of time, the result is the same as if one heat were run on randomly assigned lanes.

2. Cars are more equal than the lanes:
In this case the car in the faster lane wins almost all the time. Then the decision of which car to run in the faster lane determines the winner most of the time. Depending on how the occupant of the fast lane is chosen, this increases the "luck factor" (if the lanes are assigned by lot) or the "manipulation factor" (if a person decides which car to run there.)

Once in a while, the run variances will add up poorly on one of the first two heats and the third heat will not be run. This increases the "luck factor" slightly. The vast majority of time, the result is the same as if one heat were run on randomly assigned lanes.


In the same amount of time (or maybe less time) a Quadruple Elimination race can be run, with each heat being one run on randomly assigned lanes. The "luck factor" is present to about the same degree (assuming that there was no "manipulation factor" before!)

Here are stats for 20 cars:
Double Elimination (DE): 80 "heats" at 2.5 runs per heat = 200 runs.
Quadruple Elimination (QE): 162 "heats" at 1 run per heat = 162 runs, plus optional 3 to 6 run ladder to rank the remaining 4 cars for 1st -4th place.

In this form of DE, each car that is eliminated has lost 4 heats to each of two other racers (except for the #2 car which has lost 4 heats to the first place car.

In the QE above, each car that is eliminated has lost 4 heats to (most of the time) each of four different racers.

The error rate in identifying 1st and 2nd place is comparable. QE does a much better job for 3rd and 4th place.

Timing removes the lane variance almost entirely. However, for accuracy, the number of runs should be sufficient to reduce the best car's run-to-run cumulative variance below the variance between cars. If pack winners progress to district or council racing, this requirement is more difficult to meet for the district and council racing. Of course, you don't need to satisfy that criteria if you don't care if luck plays an increased role in deciding who gets the award trophies!

[Stan Pope]

What I did not say above is that I wrote about that DE scheme to the Council PWD Chairman of a nearby council which I visit from time to time to watch grandson's race. They divided the council race entrants into four groups and ran this best 2 of 3 format DE in each of the groups. Then the top two (sic) from each group meet in another DE, same format. Turns out the last year my Grandson raced there, the #2 racer went 0 and 8 against grandson! Poor kid lost 8 races all day ... all to my grandson! Still, he got a nice trophy!

I have another concern with their method... they gave 4 speed trophies (somehow) There is nearly a 50% chance that either #3 or #4 was in the same group as grandson and #2 and did not get to vie for #3 and #4 trophies in the finals!

Yes, I know it doesn't sound like it should be that high, but you can compute it yourself by computing the probability that neither #3 nor #4 shared group with #1 and #2:
P(#3 not in group with #1 and #2) = 0.75
P(#4 not in group with #1 and #2) = 0.75
P(#3 not in group with #1 and #2 AND #4 not in group with #1 and #2) = 0.75*0.75 = 0.56.
P(#3 or #4 in same group with #1 and #2) = 1 - 0.56 = 0.44

The fact that Grandson and #2 were in the same group is a lower probability event, about 0.25, i.e. happens, on average 1 year out of 4. So #3 or #4 missing a deserved trophy is about a 11% chance, or, on average, one year out of 9!

Okay, anybody got that glassy-eyed stare yet?

[woodworx]

We run a double elimination format also but with 3 lanes, all three cars getting to run in all three lanes. It for the most part seems very fair. But this year i noticed something that made me wonder how fair it really is. Having an uneven amount of boys in my sons den he was given a first round bye. After winning his race in the second round he was automatically placed in the finals, since by the third round everyone already had one loss. He was guaranteed a first or second place finish but did not get much racing in. It turned out he got first in his den and was also the pack champion with only losing one heat races when his car left the track. I can see though now that a slower car could of been in the finals just by getting a bye by having the luck of the draw.

[GravityRacer]

What I did not say above is that I wrote about that DE scheme to the Council PWD Chairman of a nearby council which I visit from time to time to watch grandson's race. They divided the council race entrants into four groups and ran this best 2 of 3 format DE in each of the groups. Then the top two (sic) from each group meet in another DE, same format. Turns out the last year my Grandson raced there, the #2 racer went 0 and 8 against grandson! Poor kid lost 8 races all day ... all to my grandson! Still, he got a nice trophy!

I have another concern with their method... they gave 4 speed trophies (somehow) There is nearly a 50% chance that either #3 or #4 was in the same group as grandson and #2 and did not get to vie for #3 and #4 trophies in the finals!

Yes, I know it doesn't sound like it should be that high, but you can compute it yourself by computing the probability that neither #3 nor #4 shared group with #1 and #2:
P(#3 not in group with #1 and #2) = 0.75
P(#4 not in group with #1 and #2) = 0.75
P(#3 not in group with #1 and #2 AND #4 not in group with #1 and #2) = 0.75*0.75 = 0.56.
P(#3 or #4 in same group with #1 and #2) = 1 - 0.56 = 0.44

The fact that Grandson and #2 were in the same group is a lower probability event, about 0.25, i.e. happens, on average 1 year out of 4. So #3 or #4 missing a deserved trophy is about a 11% chance, or, on average, one year out of 9!

Okay, anybody got that glassy-eyed stare yet?

So, the answer is...no double elimination. I'll go look at your schema in the other forum. I didn't get glassy-eyed, but that's because I was wearing my super-impervious high-density polycarbonate goggles.

[Stan Pope]

I'll go look at your schema in the other forum.

That was a "snail mail" critique that accompanied a CD full of pictures that I send down. (Lotsa pics of Cub Scouts holding up their cars with huge proud smiles.

I didn't get glassy-eyed, but that's because I was wearing my super-impervious high-density polycarbonate goggles.

Good plan!

[CM924]

We run double elimination as well. What I didn't get was my son raced the Pack champion and won, yet somehow ended up in 4th place??? I am going to suggest some changes for next year, not sure how far I will get as the man who has been putting on the races has done it for 35 years.

[Stan Pope]

We run double elimination as well. What I didn't get was my son raced the Pack champion and won, yet somehow ended up in 4th place??? I am going to suggest some changes for next year, not sure how far I will get as the man who has been putting on the races has done it for 35 years.

DE results derive not from whom you beat or lose to, but when you lose. I'm guessing that the track "has some serious issues with lane equality." Even the 2nd place trophy, not to mention 4th, is up for grabs in that situation!

If the old guy has been doing it for free, then you have been getting your money's worth. If he charges for the service, challenge him to learn other elimination methods, e.g. quad-elim because you would like the 4th fastest car to get the 4th place trophy, or timed or points racing. Accuracy with DE after 2nd is poor. If you would like to get a clearer picture of DE method accuracy, Cory Young has built some nice simulation software and makes it available for free at http://www.pack146.nova.org/pinewood/software.html. It is "truly free", i.e. no adware, etc, is included!

Or, build the fastest car (with enough margin to overcome track issues) and let others worry about accuracy below 1st place.