New Method: Tier Racing System (Sorting Method)

[MathGuy]

A method that I am serious thinking about trying is a TIER racing system. I know all about the Sterns, PN, CPN, PPN. (In fact, as Mathguy, I have done the work to confirm those methods, and even took it far enough to see that Stan & Corey answers of the PPN, 5 lane 20 and 22 racer situations are not the best answer possible, but that is a topic for another post.)

I like the Perfect N solutions (PN,PPN,CPN) for the criteria given: Accuracy, have each racer race on each track the same number of times, against each racer the same number of times, in an efficient way.

I wasn't happy with that critera though. That criteria serves 1 to 3 boys in the group very well, and others somewhat well. Because the boys raced more, it is definitely better than an elimination method.
I wanted to add this criteria, have as many different boys race and "win" as possible. Thus if there are 16 boys racing, I don't want only 4 to 6 boys actually winning a race, I would want to have almost all of them winning a race. This would increase more of the boys having a positive experience with PWD, not just a few of them.

This seems like a imposible criteria, you can't have every boy win a race, but it is a worthy criteria. Nothing destroys a boys self-esteem more than racing a PWD, and not winning a single race.

Tier racing system would move the better racers to higher tiers, and the lessor racers to a lower tiers as the rounds progress. Thus the average and below average boys will eventually race against each other, and WIN some races, and I believe make the pinewood derby a lifetime "good" memory, rather than a memory of always coming in 3rd place or worst.

The first round would start with the boys arranged in Tiers randomly, then as each round takes place, the winners would move up a tier, and the losers would move down a tier. And then you would race the next round.
The scheduling would be done (edited) physically setting up the board for the next race. Note cards on two large boards work well.

Yes, Lane assignment would be random draw. You can add some twists or PN or CPN for a finals round that assures accuracy for the top tiers.

More details to come (what to do for each number of boys), but the goal her is to sacrafice a little bit of accuracy for the top few, for a more fun and satisfaction for everyone. Just not us nutty PWD dads.

[Stan Pope]

Good points, good goals!

Have a look at no-chart multiple elimination - http://members.aol.com/standcmr/nelim.html. Running a quintuple elim 2 at a time results in about 5 percent exiting without a win. Running quintuple ellim 3 at a time increases the winless exits to about 12%. Already follows most of the requirements. You can juggle the percentage up or down by adjusting the elimination count.

Top-5 place accuracy stays good. Time to run is excellent, partly because there is virtually no paperwork and partly because the boys are managed in bunches rather than one at a time.

[ExtremePWD]

Our district race uses a format similar to what you are describing. All of the scouts start in one large pool and race each other randomly. The winners stay in the "no loss" group and all others move down to the "one loss" group. The next round goes through the "no loss" group with random assignments followed by the "one loss" group with random assignments. After the second round a third group with "two losses" is created. This can be run without charts and gives more opportunity for the "slower" cars to race other "slower" cars and increase their chances of registering a win. The number of maximum losses can be picked to match the number of scouts to the time available. Theoretically you can continue this method until there is only one boy in each group and only one boy out of the entire group has no wins. One of the problems is that the top groups sort out to single racers fairly quickly. I have a spreadsheet that I have used to automatically calculate the pool sizes per round. To achieve accuracy in the finals I would suggest taking the top 7 arrived at by this method and run them through a Perfect 7 to award the top 4 trophies. In our pack we will be running a partial perfect to pick out the top 7 who will run off in a Perfect 7. We then will take the remaining group and run a partial perfect for best gas mileage (slowest car, details in another thread). This method would also help satisfy your criteria of more scouts winning a race.

[ExtremePWD]

Stan and I must have been typing at the same time. We are from the same district and that is why the responses have similar content.

[Stan Pope]

Our district race uses a format similar to what you are describing. All of the scouts start in one large pool and race each other randomly. The winners stay in the "no loss" group and all others move down to the "one loss" group. The next round goes through the "no loss" group with random assignments followed by the "one loss" group with random assignments.

Actually, they reace "from the bottom up" to eliminate ambiguity about group content.

Spreadsheet??? What, you don't like the Javascript???

[Darin McGrew]

I wanted to add this criteria, have as many different boys race and "win" as possible.

Hmmm... In a 2-lane round-robin schedule, only one entrant can come up completely winless.

The "edge case" for a tier racing schedule is when a tier contains only as many cars as your track has lanes. So for a 16-car derby and a 4-lane track, it makes sense to have at most 4 tiers.

Thinking this through, after everyone's had one race, you could create 4 tiers: the first-place finishers are in tier 1, the second-place finishers are in tier 2, and so on. From this point on, you need to move as many cars into a tier as move out of a tier. So if the basic idea is that the first-place finisher moves up a tier and the last-place finisher moves down a tier, then you're swapping two cars between tier 1 and tier 2, two cars between tier 2 and tier 3, and two cars between tier 3 and tier 4. So the third round looks a lot like the second round, at least for tier 1 and tier 4 (where 3 of the 4 cars are the same). And the fourth round is probably going to look a lot like the second and third rounds. And so on.

I think it would be better to have different cars racing against each other more.

What if we move more than one car each time? If we move first and second up, and third and fourth down, then tier 2 and tier 3 are much more dynamic. Basically, you end up approximating a bubble-sort. And maybe round n and round (n+1) don't look much alike, but round n and round (n+2) probably look a lot alike, especially as the derby goes on.

What if we have fewer tiers? Let's say we start the second round with 2 tiers (the top tier with the first- and second-place cars, and the bottom tier with the third- and fourth-place cars). If you move the two first-place cars from the bottom tier up, and the two fourth-place cars from the top tier down, and if you mix up the 8 cars now in each tier, then the third round could look quite different from the second round. There's a fair chance that those cars would switch back to their original tiers the next round, but the ability to mix up which cars race against which other cars could help avoid having round n and round (n+2) looking the same.

I'd be curious to see an analysis of the number of winless cars in a tier-based schedule vs. a system that simply tries to schedule each car against as many different opponents as possible.

[ExtremePWD]

Actually, they reace "from the bottom up" to eliminate ambiguity about group content.

Spreadsheet??? What, you don't like the Javascript???

I wrote the spreadsheet before I new the Javascript existed. It actually creates a map of the entire process so that the trends can be visually examined. This makes it easy to identify ways to customize the race program.

[ExtremePWD]

You had told me before that the Javascript existed but I never checked it out since I had a spreadsheet that satisfied my needs. I just took a look out of curiosity and the two are nearly identical in function and output. I could have saved 30 minutes of developing and writing equations if I had known sooner. Nice work, Stan.

[Stan Pope]

You had told me before that the Javascript existed but I never checked it out since I had a spreadsheet that satisfied my needs. I just took a look out of curiosity and the two are nearly identical in function and output. I could have saved 30 minutes of developing and writing equations if I had known sooner. Nice work, Stan.

Thank you. From your description, I suspected they might have a lot of similarities.

I threw that together in Sept 1999, about the same time the district began running no-chart quintuple elim.

The plan had been on my website since 1997, but had not stirred any interest amongst the locals until CM from the Eureka Pack asked me how to run his races ... his situation was sufficiently unique that no-chart fit best, so I gave him a 10 minute instruction course over the phone. He used it, loved it and suggested it to that year's distr. PW chair. Chair asked how to do it for a district race ... gave hime the 20 minute instruction, provided the necessary tools and we ran it for the Tiger track.

The reception was good, boys got a lot more racing than prior years (and in about the same amount of time) and the chairman appreciated not having to spend the night before the races drawing up that 128-car DE chart and filling in all the numbers. The next year he wanted to do all 5 tracks that way! We are still there! I don't know how to make it better except to get the track staffs so well trained that they can consistently maintain 34 second cycle times!

[MathGuy]

I am going to investigate this system also. It sounds like it accomplishes the goal of sending as many boys home with "wins" as possible. Merry Christmas to all.

[Stan Pope]

Good idea! I'm still interested to see how your original idea shakes out.

One of the characteristics I like about our "no chart" operation is that a youngster who arrives late is not "out of luck." With charted methods, it is difficult to fit a late comer into the competition, let alone fit him in fairly.

In a district race in central Illinois, many folks are traveling an hour or more in winter weather. It doesn't take much to cause folks to arrive late.

We can insert the late comer in, recording losses for missed rounds. It is still a penalty, but the penalty fits the infraction better. And, late arriving "top 5" cars will still tend to perculate to the top 5, although their margin for error is reduced as tardiness increases.

[Stan Pope]

Tier could be approached by the "manage boys in groups" method as described on my "No-Chart" page. We manage the boys, not the cars, because the boys race their own cars, and getting the boys where they need to be is potentially much more time consuming than getting the cars there. The result is that the pace of racing is excellent, even though the boys are staging and retrieving their own cars.

There is a complication distinguishing tiers in the current round from tiers being formed for the next round. For example, while racing tier 2 (of four), members of new tiers 1, 2 and 3 are being created. Those racers need to be kept separate from the tiers 1, 2 and/or 3 that are waiting to race. "No-Chart" simplifies the management problem by lining up a group to race (after mixing) so that the "racing" group is no longer among the seated groups. Since we start each round "at the bottom", and intergroup movement is only "toward the bottom," ambiguity is avoided.

Keep us involved and informed, MG!

[Darin McGrew]

I'd be curious to see an analysis of the number of winless cars in a tier-based schedule vs. a system that simply tries to schedule each car against as many different opponents as possible.

I just took a look at a PPN chart (16 cars, 4 lanes, cars race twice in each lane). Ignoring lane bias (i.e., the "fastest" car always wins), half the cars (8) won at least one race, and three-fourths of the cars (12) came in first or second place in at least one race.

[MathGuy]

I created a simulation model for this 16 racer derby.
Car Time = Racer Base + Lane Bias + Random Error
Racer Base Time is Normal Mean 2.500 , Std Devition of .05
Lane Bias is Normal Mean 0, Std Deviation of .017
Random Error is Normal Mean 0, Std Deviation of .02 (staging variation)

32 Race based on PPN chart (2 rounds, 4 lanes, 16 racers)
Average Number of Racers wining at least one race is 10.2 or 64%

32 Race based on Tier system (8 rounds, 4 tiers, 16 racers, random lane assignment).
Average Number of Racers winning at least one race is 13.4 or 84%.

The randomness of my model gives more victories based on lane bias and stageing and random error.

I think we can improve the PPN method by have a final round race for the tiers, thus 13-16 would race, 9-12 would race, and 5-8 would race, then do a Perfect N. By ending the PPN method with this, we would like increase the number of winners by at least one to 11.2 and 70%+.

The Tier system would need to have a PN method at the end anways to improve select the top 3 racers.

[MathGuy]

We are racing on 2/28, and I am fairly well set on a Tier racing method with the following modifications.

1. We will have an initial round be registration order (or by den) to sort the initial tiers better, then place cars into tiers for the 2nd round based on finish (as suggested above). Thus first place cars are place in the top tier(s), etc.
2. We will race each round after that with the winners moving up a tier, and the losers moving down a tier.
3. We will have a few turtle cars to populate the lowest tier to be raced by the den leaders. Thus the slowest scout cars will eventually be staged againt the slow turtle cars. This allows all the scouts to have wins (or 2nd's).
4. The number of rounds will be established, and enough so that a car that is initially placed in the lowest tier, can make a run to the top tier if they move up every time. (The staging should be very fast)
5. We will run a 4 car finals round using a lane rotation method. The finals round will be populated by the results of the final tier round, with the top 3 finishers of the Top Tier race, and the top finisher of 2nd Tier race.

As for the "TURTLE CARS", they will have maximum weight of 4.0 ounces, and No lubrication applied. At the end of the day, we will have an open "TURTLE RACE", where we will apply graphite to the cars that leaders or parents made and have a quick race. These turtles will allow Parents, Sibs, and Leaders to have a bit of fun too. Thus these cars are going to be competive against themselves, but slow against any scout car.

This methods percision is going to be slightly worst than other methods, but my hope that even the slowest boy has a great time.

This method is thought out for our rank races with sizes of 8 to 25. It could work for larger group, but it depends on how many rounds you have, the logic that I have is that you do want enough rounds so that a car can move up to a top tier, if they started had a bad first draw, and had to make it from bottom to top. If you have an group of 64 kids raceing at the same time, its not going to work. (We have each rank schedule at a different time so that no group is waiting around.)

I will report on the results.