# Conducting Pinewood Derby Races

## Purpose

Aside from assuring that everyone has a "rocking good time" (i.e. fun), plan pack racing so that the fairness of the method is obvious, even to the most casual observer. Results should be dependent only on

• The Cub
• The Car
• Chance
and not on anyone's arbitrary decision, such as chart number assignments.

Better yet... use an accurate, fair method, where results are dependent only on

• The Cub
• The Car
and not on chance or anyone's arbitrary decision.

What if method "A" is 80% accurate and method "B" is 90% accurate? Is method "B" only 12% better than "A"? NO!

Consider the errors: The error in "A" is 20%; the error in
"B" is only 10%. "A" is twice as bad as "B".

In my district 20 Cubs represent my pack at district races. If an 80% accurate method were used to select them, there are probably 4 Cubs who deserve to go to district, but who don't get to go... they lost out to inferior cars. If a 90% accurate method were used to select them, there are probably 2 Cubs who deserve to go to district who don't get to go.

## Two measures of Accuracy:

• Qualifying: How well does the method select the N fastest cars?
• Trophy: How well does the method award lst thru Nth place trophies?

Here is a process that I have used to evaluate race method accuracy.

## Approaching perfection...

The "Perfect-N" charts have half the error of a comparably sized double elimination chart by either measure. The comparison is based on computer simulation of a millenium of pack racing! And the advantage gets better as the track departs from perfection or as the number of place trophies increases! This performance derives from its strong theoretical basis.

The Perfect-13 charts are laid out for a 3 or 4-lane track and up to 13 cars, so it works well for most pack "age group" racing.

Don't be tempted to try to change the chart unless you first understand its theoretical basis. If you change it, you run a very strong chance of inflating the error rate significantly. Then, even if you understand the theoretical basis, you should revalidate the error performance by, for instance, running additional simulations.

If you're "from Missouri and gotta be shown," use this as an extra fun racing opportunity for the boys. Run 3 or 4 or 5 full series for the same boys, reshuffling the numbers each time. Observe the consistency in the results!

## Theory

Perfect-N series derives from adhering to the following rules:

• Each car races the same number of times in each lane, and
• Each car races the same number of times against each other car.

Since each car races exactly the same number of times in each lane and exactly the same number of times as each other car, almost all of the lane disparity effects balance out. Since each car races every other car in the competition the same number of times, no one has the advantage of racing a poor car extra times, or the disadvantage of racing a hot car extra times.

Poorer tracks (tracks in which the lanes are more unequal) will require more tie-breaks than tracks in which the lanes are almost perfectly equal. As track quality deteriorates, car scores tend to collect toward the "average," and depend upon tie-breakers to resolve that tendency.

Here is more about the Mathematics of Perfect-N.

## Achieving Perfection?

In spite of the balance in Perfect-N charts, there is still some possible residual error resulting from lane inequities and low probablility combinations of lane assignments. The next logical step is to attempt to eliminate that residual error by assuring that every "match-up" is balanced by a later swapped-lane match-up. Cory Young identified the idea of this extension in this letter.

The result of this collaboration is detailed in the paper Complementary Perfect-N Racing Charts which shows how every "Perfect-N Chart" can be extended to form a "Complementary Perfect-N Chart".

There is some "homework" yet to be done. "Complementary Perfect-N Charts" have not been subjected to extensive evaluation. However, the strength of the underlying theory seems sufficient to expect the charts to excel.

Charts which satisfy the more demanding Complementary Perfect-N criteria will be marked "CPN" in the directory of racing charts.

Try this frames / JavaScript Chart-maker: Perfect-N Chart Generator.

## Contraindications:

For group sizes above 13 (on a 3 or 4 lane track), the charts get pretty unwieldy. Breaking the competitors into groups to select finalists defeats part of the goal of keeping everyone involved. My conclusion is that this method (Perfect-N) is best applied to smaller groups or to "finals", where a large group has been "pared down" to the best 7 or 13 cars and now you want to do a good job of accurately awarding the trophies.

For example, if you have 4 trophies to award to the 4 fastest cars in a group of 14 or more cars, use a final standings method like Stearns to select 7 finalists. Chances are good that the 4 fastest cars will be in that group, but they won't necessarily finish 1-2-3-4, because of the spotty nature of Stearns match-ups. Then have those 7 finalists compete in a P7 or CP7 finals.

If the initial group of contestants is very large, then select 13 finalists to increase the probability that the needed fastest cars will be among the finalists. Then use P13 or CP13 for the finals.

## Application Example - Perfect 13 Chart

Assign racing (chart) numbers 1 through 13 to boys "by lot". Have the Cubs "draw" for the numbers that they will wear during the race. As each Scout draws his number he goes to the Scorekeeper to record it. If you have fewer than 13 Scouts, assign the undrawn numbers as "byes". The presence of "byes" in this chart do not significantly affect its performance.

Note: If there are multiple "byes", however, they will race each other. For example on a 3-Lane Perfect-7 or -13 chart, in one heat there will be one car and two byes. This will give the appearance of an advantage to that car. It isn't really an advantage, but it will appear to be, so I try to avoid it if I can. (The condition would be "fair" because the racer numbers were assigned by lot, but it would appear to be inaccurate.)

Call the racing numbers by heat. Starter, assure that each Scout's car is in his assigned lane. The starter should have a copy of the chart so that he can check the boys as they place their cars on the track.

Record each Scout's "heat finish place" on the left part of the chart (in the square next to his racing number. Record each Scout's "points" in square under his racing racing number. (Assign points "golf style" (1 for first, 2 for second, etc. and "low total" wins; or 4 for first, 3 for second, etc. and "high total" wins. Your choice, but be consistent!)

When all heats have been run, total the heat scores, break any ties, and name the winners!

## Application Example - Very Small Groups

Small packs may have difficulty providing enough competition for some age groups. Here is a technique that works pretty well to provide lots of racing without too many repeat matchups.

Suppose there are four Tigers, six Wolves, and two (or three) siblings' or parents' cars that need to race. Taken together, there are 12 or 13 racers, a good number for a P13 or CP13 chart! P13 and CP13 are accurate enough that the groups can be combined without impacting the results, so long as everyone is trying to win.

By lot, determine which group gets which set of adjacent numbers. Having one member from each group draw is fair. For instance, if there are 3 groups joined together for racing, have one member from each group draw from the numbers 1 through 3 to determine which group gets the low numbers, which gets the middle numbers, etc.

Suppose that the Wolves draw 1 (the low numbers), the Tigers draw 2 (the middle numbers) and the siblings draw 3 (the high numbers.) Select numbers 1 through 6 and have the Wolves draw from them. Have the Tigers draw from the numbers 7 through 10, and have the siblings draw from the numbers 11 through 12 (or 13). As each draws his number, he goes to the Scorekeeper to record it.

Scores for heat places are computed as though there were no distinctions between the competitors. Only when comparing final scores is any distinction made. Scores of Wolves are compared against each other to determine first, second, etc. place. Similarly, the score of the Tigers are compared against each other to determine first, second, etc. This is why each group has contiguous numbers. It makes comparing the scores much easier for scorekeepers as well as interested observers!

When all heats have been run, total the heat scores, break any ties, and name the winners! Note that only ties within the groups, and only those which bear on important issues such as trophies or representation, need be broken.

## Tie Breaking

If you must resolve a point tie between two cars, select the two most closely matched lanes on the track. Race the tied cars on alternating lanes, until one racer wins two successive heats.

If the race continues beyond two heats, then probably the cars are more evenly matched than the lanes, and the winner will be determined by the first driver who makes a mistake in staging his car. (This is a time where it is very important that the boys, not the adults, are racing the cars!) If trophies are at stake, set some arbitrary limit to the number of heats, e.g. 4 or 6 or 8, after which the result will be be declared a true tie, and an additional trophy of the correct kind will be acquired and presented.

To resolve ties among more than two cars, use the tie-break charts in the links below.

Remember that a 3-lane chart, including tie-break charts, can be run on a track with 3 or more lanes.

## Timed Racing ... Touted Perfection?

Heat timing hardware is becoming more commonly available on pinewood derby tracks. Properly used, timing can provide excellent accuracy in identifying the fastest cars. Improperly used, it creates misunderstanding at best and severe error at worst. There are some pitfalls and misconceptions regarding timed racing that should be avoided. Here are issues that must be dealt with when considering timed racing for a competition:

1. Communication
2. Obviously correct Operation?
3. Heat Schedule
5. Track Consistency
6. Starting Gate Operation and Consistency
7. Run-to-run Variance of Individual Cars
8. Equipment Malfunction
9. Sufficient Precision

Some of these issues require extensive discussion, so they are presented in a dedicate web page on Timed Pinewood Racing.

## Other Resources:

This site is planned to be complementary to (i.e. mesh well with) the well-written Pinewood Derby Planning document housed at the US Scouting Service Project. Good job, guys!

## Stearns Method:

Stearns Method software may be obtained from the US Scouting Service Project on the "Pinewood Derby Reference Materials" page.

## A Challenge:

See the challenge in "Stearns Method" Critique. Algorithms / programs submitted will be listed with references and appropriate credits. (The algorithm or program must be defined with sufficient clarity to permit simulation or analysis.) Please use the "mailto" icon at the bottom of the page.

Last changed 11/20/2008