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Scoring System

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15th Burlington Main Site

The Burlington Kub Kar Event tried a new type of scoring in 2002. To our knowledge, Burlington was the first place anywhere to use this system.  The system has since been adopted and modified by a few other Cub Scout groups, including a council in Peoria, IL.  Details of their modification to the system, and the success they have had with it, can be found on Stan Pope's Pinewood Pages.

Rationale
In previous years, most Cubs raced eight times. Then the 30-35 fastest Cubs raced another 8 times. The purpose of this new scoring system is to give every Cub more races, with less waiting time between races.

Principle
This system is based on a type of computer program called a "bubble sort". In essence, the Cubs will score themselves by moving from track to track as they race. At the end of two hours of racing, the Cubs should have sorted themselves out from fastest to slowest by always moving one track to the left if they come in first, one track to the right if they come in third and staying at the same track if they come in second.

The Details
1. Eleven tracks are set up. The Cubs are randomly distributed at ten of the tracks, where they line up. (The eleventh, the Gold Track, at the left end of the gym, is unoccupied at the start.)
2. The first three Cubs at each track race.
The first Cub in line is put in Track 1
The second Cub in line races on Track 2
The third Cub in line races on Track 3
3. After the race is run, the Cubs who raced join a line-up for their next race depending on how they placed:
The first-place Cub joins the line at the track immediately to the left.
The second-place Cub rejoins the line at the same track.
The third-place Cub joins the line at the track immediately to the right. 4. The next three in line at each track set up their cars and race.
5. The tracks at either end of the gym are a bit different: at the track at the right end of the gym (slow track), the 2nd and 3rd place cars stay at the track, while the first place car moves left as usual. At the other end of the gym, at the Gold Track, the 1st and 2nd place winners stay there, while the 3rd-place car moves to the right as usual.

Scoring System Flow Diagram How it works
The faster cars work their way to the left. The slower cars move to the right. Eventually, the fastest cars end up at the Gold Track, the slowest cars at the opposite end of the gym, and the others somewhere in between.

The Gold Track
The "Gold Track" starts off empty. When the first three winners from the track beside it have moved up to it, they begin to race as usual. The first few cars to visit the Gold track will not be the fastest cars, but will merely have the advantage of starting close to it. However, after the first 30-60 minutes, the fastest cars will have worked their way across the gym to the Gold Track, displacing the slower cars that got there first. After the first hour, officials at the Gold Track will begin scoring the cars at the Gold Track to determine which one is the fastest; by the end of the second hour of racing, they will determine the three fastest cars.

What will setup look like?
Because the Cubs will be scoring themselves, there will be no need for scoring tables in between the tracks. The Cubs will line up beside each track so they can watch the racing while they are waiting in line. The setup will look something like this:

Track Setup

How many races?
There was some discussion at our organizational meeting about how many races could be run at each track each minute. Since all the starter has to do is put the cars in the gate, and wait for the finish line officials to clear the track, some thought up to 4 races per minute; others thought 2 races would be run per minute. The total number of races run will also depend on the number of Cubs racing. Obviously fewer Cubs mean shorter lines which will mean more races. More Cubs will mean longer lines and fewer races. Below is a table illustrating the possible number of races a Cub could experience with this system over two hours, based on either 2, 3 or 4 races per minute, and with either 240 or 350 Cubs attending. This assumes 10 tracks (not counting the Gold Track, which will only have 3 or 4 Cubs at it at any one time):

Average number of races in two hours per Cub
Number of races per minute 240 Cubs attending 350 Cubs attending
2 races per minute (30 sec each) 30 races 19 races
3 races per minute (20 sec each) 45 races 28 races
4 races per minute (15 sec each) 60 races 38 races

Hopefully this will mean that even in our worst case scenario (only 2 races per minute and 350 Cubs attending), that each Cub-even the slowest car-will get more races than a finalist would have in previous years.

Some tracks have faster lanes than others. Won't this penalize a fast car that hits a slow lane?
Yes, a fast car might have a bad race because of a slow lane and head in the wrong direction, but it would be against the odds for a fast car to keep hitting the same slow lane to prevent it from moving towards the Gold track. Those of you who like math and probabilities can read the theory a bit further below.

Will this new system work?
As mentioned before, this apparently has never been tried anywhere else, so it's a certainty that unexpected problems will arise. But we are Scouters! We will find a solution. And if this system proves less than reliable, we can always go back to the old scoring system next year.

When bad things happen to good cars: A case study including the math
Let's assume
that the infamous lane 1 at Watkins Glen is so out of alignment that every car that races in it, no matter how fast, will always come in 3rd
that the fastest car in the meet starts at Watkins Glen, and that the owner, Billy Bob Bodine, is standing 16th in line
that each track manages exactly 3 races per minute
  1. The racing starts. Billy Bob waits 1 minute and 40 seconds for his first race (3 groups of 3 Cubs per minute means 5 groups/15 Cubs will race ahead of him. 5 groups x 20 seconds = 1 minute 40 seconds).
  2. Because Billy Bob is 16th in line, he is first in line after the first 15 Cubs have raced, so his car goes into lane 1. Given the bad alignment of lane 1, Billy Bob comes in third and is sent to the track immediately to the right.
  3. However, because he has the fastest car and the lanes are more equal at this track, Billy Bob comes in 1st and heads back to his left, to Watkins Glen.
  4. Because he is walking at the same rate as the other Cubs, he will reach the end of the line at Watkins Glen at the same time as the Cub who just came in 2nd place at Watkins Glen, and the Cub arriving from the track to the left because of his 3rd place finish. So let's assume that the order they arrive in line is random. Billy Bob has a 33% chance of hitting lane 1 again-the same probability as rolling a 1 or a 2 on an ordinary 6-sided die.
  5. If he does hit lane 1, it's back to the right and then back to Watkins Glen again. The chance of hitting lane 1 twice in a row would be 1/3 x 1/3 = 1 chance in 9. The chances of hitting it three times in a row would be 1/3 x 1/3 x 1/3 = 1 chance in 27.
  6. If we assume that Billy Bob raced 19 times, and he hit lane 1 at Watkins Glen every time, we should also assume that Billy Bob will be running out and buying a lottery ticket, since the chances of hitting lane 1 every time would be almost 1 in 60,000! (Every other race of 19 races equals 10 races at Watkins Glen. His chances of hitting lane 1 are 310 = 59,049)
  7. Assuming that Billy Bob got hung up a couple of times on lane 1 but finally managed to race in another lane; he would pass the Watkins Glen road block and head over, one track at a time, to the Gold Track where he rightfully belonged.
  8. Assuming 350 Cubs, 3 races per minute, if Watkins Glen was the second track from the right, and Billy Bob hit track 1 three times, it would take him 15 races to get to the Gold Track (7 races bouncing back and forth between Watkins Glen and the right-hand track, then 8 races to get to the Gold Track), which would take him 15 races x 4 min = 60 minutes. (35 Cubs per track/3 = 12 groups; 3 races per minute mean 4 minutes to race 12 groups of 3; 15 races x 4 minutes = 60 minutes.)
  9. That's why Gold Track official won't start scoring for the fastest car until the second hour of racing-so Billy Bob can hit a few snags on the way up the ladder.
If you have any questions, concerns or comments about this new scoring system, please contact Bill Kowalchyk.

 

Scoring system and diagrams, courtesy Alan Brown (2002 Burlington District Kub Kar Fun Day Coordinator), reproduced here with permission.

 

E-Mail ScouterBill@scouter.ca

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Page last revised Monday February 20, 2012.