New Method: Tier Racing System (Sorting Method)

[MathGuy]

Darrin said.

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

I have set up a designed a few different charts so that we can move winners up and drop losers down, but not in pairs for a 4 person chart. I would have at least two turtle cars in this config. The idea is that a winner will move up multiple tiers so that a faster car can climb to the top quicker, it also mixes up the race a bit more. I would want at least one turtle car in every race, maybe up to 4 of them. For a 4 lane race, assuming 24 boys and turtles. There are few different Tier charts that can be divised for 6 tiers, but I am thinking this can work.

24 Finish/Next Tier
Tier 1st 2nd 3rd 4th
A::: A A B C
B::: A B C D
C::: A C D E
D::: B D E F
E::: B D E F
F::: C E F F

The boys want to make it and stay in the top tier. In this set up, a boy who is initially place in Tier F can jump to Tier A in two races. The finals I would do a 5 car Lane Rotation base on the last round top 3 from A, winners of B and C.

I am thinking that I might have some smaller groups, and I am going to move it to a 3 lane race. Again, I want boys to have fun and win races.

[Stan Pope]

24 Finish/Next Tier
Tier 1st 2nd 3rd 4th
A::: A A B C
B::: A B C D
C::: A C D E
D::: B D E F
E::: B D E F
F::: C E F F

Hmmm... Missing some symmetry that I expected to see in tiers D, E and F. (Am I expecting symmetry when there should be none?)

[MathGuy]

Hmmm... Missing some symmetry that I expected to see in tiers D, E and F. (Am I expecting symmetry when there should be none?)

For a larger group, say 60, I made a chart like this(Movement):
Tier 1st 2nd 3rd 4th
A:::: A A B C
B:::: A B C D
C:::: A C D E
D:::: B D E F
E:::: B E F G
F:::: C F G H
G:::: D G H I
H:::: E H I J
I:::: F I J K
J:::: G J K L
K:::: H K L M
L:::: I L M N
M:::: J M N O
N:::: K M N O
O:::: L N O O

There is some symetry, but once you get to the top or bottom you lose it.
At F, winner moves up 3, 2nd stays, and 3rd moves down 1, 4th moves down 2. There is no rule though, the chart movement just has to make sense, and is designed with the idea that there will be some "Turtle" cars to dominate the bottom tiers. Because I was looking at smaller numbers less than 25, I saw that there a few different movement charts feasible. A am also thinking that we have a 6 lane track, but our group sizes might be between 10-20, and for small groups I will want to go to a 3 lane chart.

I will have to have a chart ready for 8 to 22 for our derby, I am going to lean toward racing 3 lanes for the smaller numbers. I will probably have the race be organized with a person on a table with index cards to keep track of who will be racing in what tier and a movement chart infront of them. Who needs computers.

[Stan Pope]

Hmmm... Missing some symmetry that I expected to see in tiers D, E and F. (Am I expecting symmetry when there should be none?)

There is some symetry, but once you get to the top or bottom you lose it.

I'm talking about a different symmetry ...

24 Finish/Next Tier
Tier 1st 2nd 3rd 4th
A::: A A B C
B::: A B C D
C::: A C D E
D::: B D E F
E::: B D E F
F::: C E F F

A different way of expressing this is
A::: 0 0 -1 -2
B::: 1 0 -1 -2
C::: 2 0 -1 -2
D::: 2 0 -1 -2
E::: 3 1 0 -1
F::: 3 1 0 0

The symmetry that i expected was that diagonal components would be negative of each other.

[MathGuy]

I believe the numbers go to the ad-hoc design, (nothing wrong with that). Edited message, see below.

[MathGuy]

Stan, I think this is what you were getting at.

24 Finish/Next Tier
Tier 1st 2nd 3rd 4th
A:::: A A B C
B:::: A B C D
C:::: A B D E
D:::: B C E F
E:::: C D E F
F:::: D E F F
Tier 1st 2nd 3rd 4th
A:::: 0 0 -1 -2
B:::: 1 0 -1 -2
C:::: 2 1 -1 -2
D:::: 2 1 -1 -2
E:::: 2 1 0 -1
F:::: 2 1 0 0

I like the movement, seems easy now.

[Darin McGrew]

24 Finish/Next Tier
Tier 1st 2nd 3rd 4th
A:::: A A B C
B:::: A B C D
C:::: A B D E
D:::: B C E F
E:::: C D E F
F:::: D E F F
Tier 1st 2nd 3rd 4th
A:::: 0 0 -1 -2
B:::: 1 0 -1 -2
C:::: 2 1 -1 -2
D:::: 2 1 -1 -2
E:::: 2 1 0 -1
F:::: 2 1 0 0

I like the movement, seems easy now.

Looking at this mechanism, I can see it reaching a state where the fastest two cars stay in positions A1 and A2, where two cars alternate between A3 and B1, where two different cars alternate between A4 and C1, and where one car stays in B2.

Given this state, and assuming no lane bias, it's easy to rank 1st (A1) and 2nd (A2). You need a runoff to determine 3rd (A3 or B1), 4th (A3, A4, B1, or C1), and 5th (A3, A4, B1, B2, or C1).

[Cory]

... and even took it far enough to see that Stan & Cory 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.)

Do you have generators for these two cases? If you do and you would send them to us, we could make them generally available.

[Cory]

Maximizing the number of positive experiences is a worthy goal.

On the other hand, there is no such thing as a free lunch.

All these wins for the slower cars don't come out of thin air. They are coming from two sources: (1) Introducing "turtle cars" into the mix, and (2) Taking away wins from faster cars by having the faster cars beat up on each other.

You can introduce "turtle cars" into any racing system with this effect. I've been doing it for years whenever I have a group of six boys, because I'd rather use a PN chart than a PPN chart. Therefore, this technique is really not specific to the "tiered method" -- it's a technique in and of itself.

[Just an aside: I'm a fan of turtle cars. We've had two of them over the years, a Batgirl car and a Troll car. They definitely provide entertainment value. And for many kids with slow cars, they improve the win-loss "experience". There are kids, though, who see right through it, muttering, "The only car I beat was the Troll car." But overall, I think they're a good thing.]

Back to the tiered system. Assume a larger group, 4 lanes, 40 or so cars:

I would expect the system to produce bad cars with so-so records. If you start in a bottom tier with the 6th slowest car, you'll likely bounce around the bottom 2 or 3 tiers and finish 2-3 or 3-2.

I would expect the system to produce good cars with so-so records. If you start in the top tier with the 6th fastest car, you'll likely bounce around the top 2 or 3 tiers and finish 2-3 or 3-2.

Assume for a moment that the two boys in the above scenarios built their own cars with little or no help. Neither of them wins a trophy. Both finish with the same record. A really fast car that would usually have won all but one of its races in a PPN chart ends up with a losing record.

I also think that for a good car that starts in the bottom and bubbles its way to the top, there will likely be a crucial race somewhere along the way where a lane assignment could make the difference between reaching the finals or not reaching the finals.

I saw something like this in a double-elim several years ago. A particular car lost its first race because of a bad lane. It then came up through the loser's bracket and had to face the same car again, and there was nothing in their system to keep him from getting the same bad lane again. Your system seems vulnerable to this sort of thing.

MathGuy, your "tiered system" is a really good idea, but I'm still wrestling with these particular issues.

[Stan Pope]

Cory,

I have received the generators in question ... but just for the first round. No second round generators. When I get past the District Derby (in 8 days!) I'll pursue this with you.

The Tier method is not aimed at creating records, but at creating a final arrangement of cars. An interesting aspect is that early results don't play a significant role in the final state. Running more rounds doesn't help create more accurate results.

I am a bit concerned that the process does not converge well. It oscillates, at best.

[Cory]

I have received the generators in question...

Terrific. The only thing harder to find than generators is people who are good at finding generators. Props to MathGuy!

The Tier method is not aimed at creating records, but at creating a final arrangement of cars.

Understood. My issue is that many kids (and parents) are concerned with creating records.

[MathGuy]

One advantage I have for myself to apply this is that we have a 6 lane track, and I will likely only be using 3 or 4 lanes, thus I need to test the track to figure out which combination has the least bias.

I don't think this is appropriate for highly competitve race at district or council.

The record doesn't matter, you just need to finish in one of the top tiers, thus the mind set will hopefully change to what group or tier are you racing in. Some relatively less sophisticated folks will think about wins and losses, and won't even realize there is a sorting routine going on.

[Stan Pope]

As an alternative to Darin's suggestions on ranking, which depended on absence of lane bias, consider using "Who occupied rank A (maybe ranks A and B) during the last N rounds" to select finalists. If N > 1, then A-C oscillations are compensated for. This can probably reduce the effects of a single "bad run" late in the racing.

Some simulations are needed to prove whether this does a good job of putting the objectively fastest cars into the finals.

For finals, you can run precision charts without worrying about anyone spending the day without a win.

[Cory]

Some relatively less sophisticated folks will think about wins and losses, and won't even realize there is a sorting routine going on.

I've learned that someone will be unsatisfied no matter what you do. One parent this year commented that he wished the lanes on our track WEREN'T so even, because it caused his son to never get the edge he needed to win a race.

They might have been happier with your new system, so keep at it.

[MathGuy]

Well, we have got it done. I think it was a great success. It took allot of preparation for the method to work well. Lots of comments were that the races moved quickly and I didn't see as many boys upset about the outcome. I will ask some others that weren't involved in running it for their feed back.

It is a good thing that we had prepared non computer based method, because we had planned on using a race software to show the finish times, but we had a few computer problems that prevented this. The race was ran on two large boards with index cards with the boys names on them.

Our "leader" turtle cars worked great. The crowd really got excited when a boy's car beat the leader's cars by 4 lengths. This had to build the boys self esteem. (By the way, we didn't mention "turtle" cars.)

I think we accomplished our goal, with 85% of the boys winning a race. After a one or two rounds the races got very close, which made them allot more exciting. There is also perceived fairness when you race head to head.

The other thing that happened was that all the races got very close after a few rounds. This made the races more exciting. Lots of wow's when you have 4 cars racing within a half of car length.

I will write something this method (via PDF). I do believe it is a great method for a pack level race. I will generate some instructions explaining the method, how to run the method, and a complete set of movement charts for each set of boys and lane configurations. I think this might take a few weeks, but I love to share.