Why Less is More.

Debates and discussions on the various race scheduling methods that can be used and their fairness and accuracy in determining the winners.
Post Reply
User avatar
MathGuy
Master Pine Head
Master Pine Head
Posts: 178
Joined: Tue Dec 16, 2003 11:33 am
Location: NW burb of Chicago

Why Less is More.

Post by MathGuy »

I posted this in another thread, but it fits here also.

Less lanes have an advantage that people might not realize. Increasing the number of boys winning a race. A derby day is greatly more enjoyable if a boy win's a single race, then if they race several times and don't win any. The less lanes, mean the the less boys competing each race, thus a boy has a higher chance of winning at least one race.

Lets assume you have a group of 12 boys, and each boy races in each lane once for this example. That works out to 12 races, regardless if it is a 6,5,4,3, or 2 lane track. I will look at the PPN charts from the Cory Young charts, and use a simplistic assumption that car 1 beats car 2, car 2 beats car 3, etc. And count the number of unique winners using each track configuration. Answers:

2 lanes, each boy racing 2 times, 7 out of 12 boys wins at least one race.
3 lanes, each boy racing 3 times, 7 out of 12 boys wins at least one race.
4 lanes, each boy racing 4 times, 6 out of 12 boys wins at least one race.
5 lanes, each boy racing 5 times, 5 out of 12 boys wins at least one race.
6 lanes, each boy racing 6 times, 3 out of 12 boys wins at least one race.

These numbers are not always going to work out to the same number for actual races, but I think they demonstrate the concept. (Also, We would likely have more than 12 races for a rank, but ) The general conclusion is:

In the same number of races, more lanes means more races per boys, but the number of boys who win at least one race decreases.

We want more people to have the thrill of winning a race, not just a few. At a pack level race, this is probably important. And more racing isn't = to more fun for the kids who aren't bring home a top 3 finish. I am sure some parents might not believe this, but that is the case.

By using 6 lane track versus a 3 lane track, most of us would initially think that that means the boys race more, and thus the number of boys winning a race would have to increase, but because of a closed field, the opposite is true.
-Rob
Fun for one, Fun for all.
Rob D
User avatar
Stan Pope
Pine Head Legend
Pine Head Legend
Posts: 6856
Joined: Sat Jul 05, 2003 7:01 pm
Location: Morton, Illinois
Contact:

Re: Why Less is More.

Post by Stan Pope »

Interesting observations.

The analysis is flawed in that a different speed distribution among participants does not necessarily yield the same counts.

None-the-less, on the same basis of comparison and using 13-car Young & Pope charts (from PPN Generator), there is a bit of a shift.

Lanes Winners-1 round Winners-2 rounds
2 . . . . . . . 7 . . . . . . . . . . . . . . 8
3 . . . . . . . 9 . . . . . . . . . . . . . . 9
4 . . . . . . . 7 . . . . . . . . . . . . . . 7

The interesting difference is that the number of racers winning at least one race peaks for 3-at-a-time racing rather than 2-at-a-time.

BTW, I never run a 12 car chart. If I have 12 cars, I run a 13 car chart with a bye... it is more accurate!
Stan
"If it's not for the boys, it's for the birds!"
User avatar
MathGuy
Master Pine Head
Master Pine Head
Posts: 178
Joined: Tue Dec 16, 2003 11:33 am
Location: NW burb of Chicago

Re: Why Less is More.

Post by MathGuy »

Stan,

Thanks for the confirmation. I was fairly sure that those numbers would change if we mixed up the distribution of cars. Add some staging error and track bias, the numbers would change again.

We use a 6 lane track, and and race by rank. I know that I have seen that you don't like any more than a 4 lane track. That we typically have between 10-25 boys in each rank, using all 6 lanes might produce two few of winners, and two many disappointed boys. (For a large council event of winners racing against winners, the criteria of increasing the number of winners might not be as important.)

I do think for scheduling methods, a criteria should be the following (not ranked):
1. Accuracy of top 3
2. Perceived Fairness
3. High Min Number of Races per boy
4. High Number of Boys winning a race.
5. Pace of Races
Fun for one, Fun for all.
Rob D
User avatar
Stan Pope
Pine Head Legend
Pine Head Legend
Posts: 6856
Joined: Sat Jul 05, 2003 7:01 pm
Location: Morton, Illinois
Contact:

Re: Why Less is More.

Post by Stan Pope »

MathGuy wrote:I do think for scheduling methods, a criteria should be the following (not ranked):
1. Accuracy of top 3 *
2. Perceived Fairness
3. High Min Number of Races per boy **
4. High Number of Boys winning a race.
5. Pace of Races
Nice list. Here are some changes that I'd suggest:

* Accuracy in trophy / recognition awards. (If you are giving trophies for first thru sixth, then the method should award each of them with reasonable accuracy.)

At most, the method should make only very general speed rankings toward the bottom of the speed list! Uncertainty at the bottom of the pile is good. It is good for the method to say, "Johnny had the fastest racer!" The method should not say, "Jimmy had the slowest racer!" (unless being the slowest is the goal of the races.)

** The method should not make it awkward for a racer to withdraw if he decides that he is racing a pig.

These last two paragraphs are a particular strength of Multiple Elimination-No Chart. They are also supported by two-stage PPN/PN or Stearns/PN racing in which the preliminary stage seeks to select a group of racers for the finals which has high confidence of including the N fastest. (N = number of trophy places.)
Stan
"If it's not for the boys, it's for the birds!"
Post Reply