No Chart, Multiple Elimination Racing

Summary

This is a non-chart method for Pinewood Derby racing.

• Racers whose cumulative "non-win" heat finishes exceed a threshhold are eliminated from the competition.
• Until they are eliminated, every racer runs in every round.
• Until the finals, all racers race against others with like scores, i.e. the same number of "non-wins."
• The field is gradually pared down to a group of finalists consisting of one racer in each score group.
• For the finals the two lowest scoring racers compete until one accumulates enough "non-wins" to be eliminated. Competition continues up the list of finalists.

The terms "win" and "non-win" may be defined in a variety of ways. On a two lane track, each heat has one "win" participant and one "non-win" participant. On a three lane track, one "win" and two "non-wins" is recommended.

If three or more lanes are used, avoid more than one bye per heat, if possible.

If you want to see the number of heats and how racing would progress, use this Javascript page to enter your parameters and display the characteristics.

I did not originate the basic method. I have observed the method in practice and added some revisions that improve some aspects of the competition.

Example - Quintuple Elimination on a Three-Lane Track

There will be up to 5 pools of racers (score groups). For convenience, lets call them "0", "1", "2", "3" and "4", because the name corresponds to the number of "non-wins" by each of the cars in that pool. In practice the pools could just as well be called 1, 2, 3, 4, and 5, or A, B, C, D and E, or Yellow, Red, Green, Black, and Blue, or Ferraris, Jaguars, Mercedes, Corvettes, and Cobras, but it might be more difficult to keep track of which is which.

Round 1

All the racers start in score group 0. If you don't use the recommended "C" method for lane draw, mix the racers somehow. (For instance, line them up and fold the line on itself a few times.) Lead the line, in order toward the starting line. They race three at a time, after drawing for lanes. The heat winners go to form a new group 0 and the non-winners go to group 1.

Lane draw procedures are detailed in No Chart N-Elimination Racing - Drawing Procedures. The "C" method is recommended.

Round 2

Repeat the above with group 1 (to form a new group 1 and group 2) and with group 0 (to form a new group 0 and add to group 1.) Now we have three groups.

Round 3

Repeat the above with group 2, group 1 and group 0. Now we have four groups. (Still no one has been eliminated.)

Round 4

Repeat the above with group 3, group 2, group 1 and group 0. Now we have five groups. (Still no one has been eliminated.)

Rounds 5, 6, 7, ...

Repeat with group 4 (winners form a new group 4 and non-winners form a cadre of cheerleaders), then group 3, group 2, group 1 and group 0.

Caveats

Continue, always working from the lowest scoring group up, until each group has one racer in it. Then the finals begin.

Racers in single-member groups still should make a run when it is their group's turn, just to equalize the "graphite shake-out."

Finals

Preferred Method

The two "lowest ranking" remaining racers are paired for a "race-off." The higher ranking needs to win one heat, the lower ranking needs to win two.

First, in our example, the racer in group 3 races against the racer in group 4 until either the group 3 racer wins once or the group 4 racer wins twice. The eliminated racer earns 5th place! The winner continues. Before each heat, they draw for lane assignment.

Then the racer from group 2 races against the surviver until one of them is eliminated to earn 4th place. Again, the higher ranked racer needs to win once and the lower ranked racer needs to win twice.

Then the racer from group 1 races against the surviver until one of them is eliminated to earn 3rd place. Again, the higher ranked racer needs to win once and the lower ranked racer needs to win twice.

Finally, the racer from group 0 races against the surviver until one of them is eliminated to earn 2nd place, and the winner gets 1st place! Again, the higher ranked racer needs to win once and the lower ranked racer needs to win twice.

Note that this is not a true quad-elimination final... the eliminated racers may have accumulated fewer than 5 non-wins. None-the-less, I prefer this method.

Alternative (True N-Elim) Method

In the finals, the racer in group 3 races against the racer in group 4 until one of them is eliminated and earns 5th place! (keep counting non-wins; keep stamping their record cards.)

Then the racer from group 2 races against the surviver until one of them is eliminated to earn 4th place. (keep counting non-wins; keep stamping their record cards.)

Then the racer from group 1 races against the surviver until one of them is eliminated to earn 3rd place. (keep counting non-wins; keep stamping their record cards.)

Finally, the racer from group 0 races against the surviver until one of them is eliminated to earn 2nd place, and the winner gets 1st place! (keep counting non-wins; keep stamping their record cards.)

I think that this alternative is less accurate because the source of losses is limited to one opponent. Consider the group 2 finalist: If the group 2 finalist survives to race the group 1 finalist, the number of non-wins needed to eliminate the group 2 finalist depends on the finals record of the group 2 finalist and the group 3 finalist.

Managing Groups

My worst fear is loosing track of who is in which group. What if everyone needed to go to the wash room at the same time?

Some form of "marking" is needed. Here are some alternatives.

1. At the end of each heat, apply a sticker to the car designating which group it should go to. Offset the stickers slightly so that you can verify heats entered.
2. Like above, but apply the stickers to the Scouts instead of to the cars.
3. Each participant has a numbered ID/record card pinned to his shirt! At the end of each heat, apply a rubber stamp with their new group-id onto the participants' record card. Every heat finisher gets a stamp, so, at the end of each round everyone who is still racing should have the same number of stamps on his record card. The stamps could be anything, but group numbers 1, 2, 3, etc. seems obvious. I think that I prefer this method.

Observations

For recording heat results, stickers are nice. However, they are expensive if one is awarded to each heat participant! I used colored stickers for one race with about 80 participants. Stickers were awarded only when they changed groups. This raised the possibility for a "cheat" as follows: "After the first round, one of the participants retires to the wash room for several rounds, returning to competition with no indication on his record card that he didn't race in those heats. With 80 participants (and occasional wash room needs), it is really hard to tell who raced and who didn't." I don't know what I would have done if I thought that one of the scouts had "hidden out". I think that rubber stamps, applied to the record cards of each participant after each heat, will eliminate this fear.

Running a Group consists of randomly arranging the boys in the group and racing them in heats 2 or more at a time, depending on the number of lanes available. Exception: as the end of the group approaches, check the number of boys. If a heat would include 2 or more "byes", then divide the last groups so that there is 1 bye each.

If the "Simple", "A" or "B" method for Lane Draw is used, there is a slight advantage to being one of the last few racers in a group. Because of this, the "C" method is recommended, since racers who do not draw a lane number go to the back of the line. The "C" method has an additional advantage in that the last fellow in line gets to the front to draw or draw again much more quickly.

For the finals, use the two most equally matched lanes on the track. Start with the two groups with the worst records. For each heat, draw for lane assignment.

If groups were not mixed after racing, then, on a 3 or 4 lane track, racers will tend to race the same persons again. This violates part of the underlying theory of the method. If race officials arranged the racers arbitrarily, then the fairness of the proceedings might be called into question... even if no bias is present. If the racers were allowed to arrange themselves, there may be disagreements as to who should race when. However, if there is no provision for randomly mixing the group, this would be the next best procedure. Whatever method is used, adding a "next heat" or "end of line" tokens to the drawing for lanes and including an extra racers in the draw reduces the possibility for manipulation.

I did some scratch-pad estimates for some probabilities ... I think that they are correct. In a 3-lane race when two boys stand next to each other when their group lines up to race, using the "Simple Method" for draw pairing, the probability is 0.67 (two thirds of the time) that those two boys will race against each other during the round. Using methods "B" or "C" the probability reduces to about 0.29 or 0.30 (less than 1/3 of the time). If I use the recommended Method C, I'd let to boys line up any way they wanted to because the lane draw procedure will mix them up well enough to reduce the probability of them racing each other multiple times.

"Loser": In practice, I prefer to avoid the term "loser." That is the reason for the awkward "wins" / "non-wins" terminology above. When announcing the heat results, "first place" and "second place" seem much better to me. Similarly, I would rather refer to "group 3" than "the group with 3 losses." Besides, every boy who spent time with Dad or Mom or Grandfather to build a car arrived at the start of racing as a winner.

Organization

Here are some track staff jobs that will be needed:

Group Leaders

One person for each score group. The racers should stay close to their respective group leaders. Each should carry some sign of the group that they lead. Under guidance of the "Mixer", the "Group Leader" also stays at the front of his group in the line of racers until that group starts racing. Then he returns to receive his new group.

Mixer

One person who takes each group in turn, scrambles it, lines it up, and gives it back to the "Group Leader" to lead toward the starting line.

Marker

One person who positions at the end of the last group in line to race. He assures that no one joins the line erroneously. (Sometimes enthusiastic Cubs will finish their heat and try to get in line again rather than joining their new groups to watch and wait their turn.)

Draw

One person who manages the "draw for lanes." He should have (at least) three sets of tokens to draw from. He tries to stay just ahead of the starter, so that as soon as a heat is started, the next participants can begin staging. Needs to understand the "draw procedure" thoroughly.

Pit Supervisor

One person (or two) who watches the car storage area and assures the safety of the cars and racers as they get their cars and return them after their heats.

Starter

One person who operates the track's starting mechanism and who assures that the cars are staged in the correct lane without interfering with the other cars. This means that he must hold the starting lever to avoid movement and watch each of the racers as the cars are staged. Since the starter is usually at the side of the track, staging should begin on the lane nearest to the starter. The starter should keep all participants at the starting line until all are staged. Then send them to the finish line. When the racers are in position at the finish line, he releases the cars with a swift, smooth motion. If one participant touches another's car, the participant should be warned or "guided", and the car's owner should be called back to check his car. In no case should the "Starter" adjust the cars.

Finish line judges

Three people (or two people and one set of electronics) who determine, by majority rule, the heat winners. The judge identifies (announces) the heat winner and directs the heat participants to the proper recorders.

Recorders

Two people (one for "win", one for "non-wins") who stamp the participants record cards and direct them to the correct groups.

Announcer

One person who keeps the audience apprised of "what is going on."

Ombudsman

Responsible to the participants to field their questions and appeals.

Chief Steward

Responsible for all race operations. Makes sure that it is "done fairly." (He also wanders around a lot.)

Conducting Pinewood Derbies
Major update: 8/27/99
Latest update: 4/02/2010 - Designate Draw method "C" as "recommended", estimate repeat matchup probabilities.

Copyright © 1997, 1999, 2000, 2008, 2010 by Stan Pope. All rights reserved.