Preface

Christian Service Brigade calls it's model car race a Shape N Race Derby. The Boy Scouts of America calls it's model car race a Pinewood Derby. Other organizations and companies have their own names for similar events (e.g., PineCar Derby, Kub Kar Rally). In all cases, the basic idea is the same: Participants build model cars from a standard kit and then race them down an inclined track.

It is my intention that this document benefit everyone, regardless of any specific organizational affiliations. Throughout this document, I will use the term derby to refer generically to CSB's Shape N Race Derby, BSA's Pinewood Derby, and any other model car races of a similar nature.

Table of Contents

• Preface
• Table of Contents
• Race Methods
• Elimination Methods, General
• Elimination Ladder Methods
• Ladderless Elimination Methods
• Lane Rotation Method
• Round-Robin Methods

Race Methods

The obvious goal of a derby race is to determine which cars are the fastest, so that awards can be presented to the winners. However, there are other important goals which must be considered, including enabling the leaders to run an orderly event and retaining the attention of the entrants and their parents. It is also important that a race method accomodate imperfections in the track, cars that need emergency repairs, etc.

Elimination Methods, General

Single elimination is a standard divide-and-conquer technique. Everyone who wins in the first round moves on to the second round. Everyone who wins in the second round moves on to the third round. Repeat this process until only one car is left, and this car is the winner.

Unfortunately, single elimination only identifies the winner accurately. Since a single loss will eliminate any car, the second fastest car could have been any of the cars that lost to the winner over the course of the event. To remedy this, the multiple elimination methods were developed. To accurately identify 1st through nth place, you will need to use an n-tuple elimination method.

Another way to adapt the single elimination method is to determine first place, and then repeat the entire competition with the remaining cars to determine second place, and so on. This works for a few entrants (half a dozen or so), but for large groups, it is thoroughly impractical.

A weakness shared by all elimination methods is that they do not accomodate unfair tracks well. Losing because you drew the slow lane moves you one step closer to elimination, and there is no way to recover.

There is another problem with using elimination methods in pinewood derbies and similar competitions where all the matches are held during a single event. Elimination methods work by eliminating contestants from the competition. Contestants who are eliminated early often lose interest in the rest of the procedings. One can accomodate this to some degree by postponing the elimination as long as possible, but it does present a crowd-control problem to the event organizers.

Elimination Ladder Methods

Single elimination ladders are easy to find (or make). Double elimination ladders are more complex, but still managable. Triple and higher-order elimination ladders are much more complex and are harder to find (or make).

Ladderless Elimination Methods

Many elimination systems avoid the use of ladders by simply recording the number of losses each entrant has had, and generating matches randomly among entrants who have had the same number of losses. The specific techniques for keeping track of the number of losses each car has had vary, but conceptually they are the same. Each time a car loses, it moves down one level of a hierarchy that has those cars with no losses at the top. After it's nth loss, a car is eliminated. When there is only one car left in each level of the hierarchy, the car with no losses is the winner, the car with one loss is second, etc.

To maintain suspense, it is a good idea to wait as long as possible before actually determining the winners. Eliminate cars until each level of the hierarchy contains no more cars than your track has lanes, and then quickly finalize the results with a few quick races.

In all of these methods, you will almost certainly have to schedule races for a group that is not an even multiple of the number of lanes on your track. Adjust the last few races to keep all the races as even as possible. For example, if you have a three-lane track, and you have one extra car, then the last two races should race two cars each, rather than one race with three cars leaving one car with no opponent. As another example, if you have a four-lane track, and you have one extra car, then the last three races should race three cars each, rather than four, four, and one, or four, three, and two.

One method uses tables to keep track of where each car is in the hierarchy. Cars start on the "No Losses" table, and as they lose, they move to the "One Loss" table, to the "Two Losses" table, etc. It helps if you have a "Current Heat" table from which to stage each round of races. Cars that win are returned to the table they came from, and cars that lose go to the next lower table in the hierarchy.

Another method uses display boards with rows of hooks, and numbered cards that correspond to the numbers assigned to the cars. Each board has as many columns of hooks as the track has lanes, and as many rows of hooks as are necessary to hold all the numbered cards. Everyone starts on the "No Losses" board, and moves to the "One Loss" board, to the "Two Losses" board, etc. It helps to have a second set of numbered cards attached to wristbands that are worn by the cars' owners.

Another method uses a series of rosters. Winners are copied to a fresh "n Losses" roster, and losers are copied to the "n+1 Losses" roster, or possibly a fresh "n+1 Losses" roster. This provides a permanent record of how the race progressed, although I'm not sure why anyone would care.

Lane Rotation Method

This is the technique used in the past by my CSB Stockade unit. Our track has four lanes, therefore the following discussion will assume a track with four lanes. However, the method is easily adapted to tracks with different numbers of lanes.

The primary goal of the lane rotation method is to accomodate imperfections in the track (i.e., fast and/or slow lanes) by racing each car once in each lane of the track. After every car has raced once in each lane, the overall performance of each car is evaluated.

With a four-lane track and twenty cars, races are scheduled like this:

                     Lane 1   Lane 2   Lane 3   Lane 4
        Race 1          1        2        3        4
        Race 2          2        3        4        5
        ...
        Race 19        19       20        1        2
        Race 20        20        1        2        3

Points are assigned to each car based on how it placed in each of its races (1st = 3 points, 2nd = 2 points, 3rd = 1 point), and those cars with the most points move into the finals, where the whole process is repeated.

Running the race is very simple. Return the car in lane 1 to the display rack, place the new car in lane 4, and move everyone else over one lane. Scoring is simple too, if you use a overhead transparencies for the roster, and a scoring template that looks like this:

                  Number/Name:    Lane 1  Lane 2  Lane 3  Lane 4
        Lane 1    ______________          ######  ######  ######
        Lane 2    ______________  ######          ######  ######
        Lane 3    ______________  ######  ######          ######
        Lane 4    ______________  ######  ######  ######
        On Deck   ______________  ######  ######  ######  ###### 

For each race, write each car's score in the open box, then move the entire roster up one place. Repeat. When you're done, each car's scores are lined up to the right of its entry, ready for you to add up its final score.

Note that the "On Deck" entry isn't actually involved in the current race; rather, it serves as a reminder that the next race will include this car in lane 4. Also note that you will need to copy the entries for the first three cars to the bottom of the roster, and you'll need to consolidate their scores since some will be recorded at the top of the roster and some will be recorded at the bottom of the roster.

Another advantage is that every car races four times, once in each lane. This tends to balance any problems you might have with fast or slow lanes on your track. It also guarantees that each car will race at least four times. You'd have to run a quadruple elimination race to guarantee as many of races for each car. With more lanes on your track, you can guarantee each car even more races.

Unfortunately, each car races against the same opponents repeatedly, which is unfair to the cars next to the fastest car in the race. To reduce the unfairness, you should set the cutoff for moving to the finals (or semi-finals) such that about half of the cars move on. For large groups, this can require semi-finals and even quarter-finals before the winner can be determined. It would also be good to rearrange the cars into a random order when you move them into the finals (and semi-finals, and quarter-finals).

Also, even though each car races 4 times, all 4 of those races are one right after the other (except for cars 1, 2, and 3, which race at the very beginning and then again at the very end). Thus, boys have a lot of excitement all at once, and then they sit around.

Round-Robin Methods

The idea of this system is to schedule the races so that cars race in different lanes and against different opponents as much as possible. Points are assigned to each car based on how it placed in each of its races, and when the races are finished, the cars with the most points win. A runoff race or two can be used to break ties, or both entrants can receive the same award.

The obvious advantages of round-robin races are accomodation of fast and/or slow lanes on a track, and not matching the fastest (or for that matter, the slowest) cars against the same opponents repeatedly. Interest is maintained because each car's races are generally distributed throughout the event, and each race matches new opponents against each other. And without the need for extended semi-final and final rounds, you can guarantee each car more races, and still finish the event in the same amount of time.

Round-robin races can be scheduled or unscheduled. In a scheduled round-robin race, the schedule of who races against whom is known in advance. This schedule is generally created by a computer program. The schedule can be generated randomly, or the program can deliberately create a schedule to avoid racing cars in the same lane or against the same opponents repeatedly. One system that deliberately creates such a schedule is called the Stearns-Borom Method, and is available as freeware. See the Web site: and http://www.wtrfrd.com/pack339/339stern.htm

Unscheduled round-robin races look chaotic by comparison. Each boy is given n race tokens, numbered 1 through n. Boys line up, arranging themselves however they want. The boys at the head of the line turn in their 1st race token and race their cars. Once everyone has used their 1st race token, others can use their 2nd race token. Multiple tracks and refreshments will help keep entrants and spectators occupied. You can either have race officials keep track of race results, or you can place stickers on the cars themselves (blue=1st, red=2nd, etc.).

If you want to write your own program to deliberately schedule round-robin races, the following prioritized rules work well for assigning cars to each lane for each race.

Rule 0:

Never schedule a car in more than one lane of the same race. (Yes, this seems obvious. But if you don't design the rule into your program,...)

Rule 1:

Schedule cars for the same number of races each.

Rule 2:

Given the above, schedule cars against different opponents as much as possible.

Rule 3:

Given the above, schedule cars in different lanes as much as possible.

Rule 4:

Given the above, avoid scheduling cars in two consecutive races. (This helps the event run smoothly, because you avoid having to rush a car from the finish line to the starting gate.)

Rule 5:

Given the above, give preference to cars that have been scheduled for fewer races so far. (This helps spread a car's races throughout the derby event.)

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Copyright © 1995, 1996 by Darin McGrew. Permission is granted for individual and non-profit use and reproduction, provided that this document remains intact with this copyright message clearly visible. Commercial use and reproduction rights are retained by the author.

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