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The Case for a Good Track

A good racing method can overcome the uneven lanes on a poor track -- some of the time!

A Complementary Perfect-N racing chart is one that satisfies the following conditions:

Every car races the same number of times in each lane.
Every car races every other car the same number of times.
Every race between two cars has a corresponding rematch where the cars switch lanes.

This is about as strict a set of criteria that can be used to run a set of Pinewood Derby races. Anything more would result in too many races to run in a reasonable time.
Intuitively, such a format would never put the fastest car in second place. Sure, maybe if the lanes were bad enough, the fastest car might lose a race to a slower car. But that race would have a associated lane-reversal rematch which would be won, of course, by the fastest car. Thus, the best the slower car could achieve is a tie. Right???
Wrong! Consider a hypothetical District finals, with conditions as follows:
There are four cars: A, B, C, and D.

Car A is 2 inches faster than Car B
Car B is 4 inches faster than Car C
Car C is 6 inches faster than Car D

There are three lanes: 1, 2, and 3

Lane 1 is 5 inches faster than Lane 2
Lane 2 is 3 inches faster than Lane 3

The following Complementary Perfect-N chart is used:
          Lane 1   Lane 2   Lane 3

Heat 1       A        B        C
Heat 2       B        A        D
Heat 3       D        C        B
Heat 4       C        D        A
Based on the relative lane and car speeds, and assuming no random elements, here are the race results:
           1st     2nd    3rd

Heat 1:     A       B      C
Heat 2:     B       A      D
Heat 3:     B       C      D
Heat 4:     C       A      D
Even though Car A is objectively the fastest, it finishes second behind Car B. How could this have happened using a Complementary Perfect-N Chart?
A careful examination shows that Car B's victory was due to fortuitous lane assignments. Car B won both races against Car C, because they raced in fairly even lanes. However, Car A lost one its races to Car C, because they raced in the most uneven pair of lanes.
Of the available racing methods, Complementary Perfect-N is one of the most accurate at correctly identifying the fastest cars. Yet, in this case, it was not enough to overcome the obvious lane inequties. For less accurate race methods, such as double-elimination and Stearns, the ill effects of lane inequities will be even more severe.
Regardless of the race method you use, be advised that identifying the fastest cars will be error-prone if the lanes of your track are "more uneven" than the cars that are racing. And at higher levels of racing (e.g. District or Council races, and probably a lot of Packs out there) the best cars will usually be very evenly matched.
In other words, if accuracy in determining winners is one of your priorities, you might want to check out the following links:

Darin McGrew has a nice page of Four-Lane Track Plans. He also has a section on tracks on his Derby Resources page.
Ron Morrison has several pages describing the various components of Pack 240's very impressive formica-covered track.
At his San Diego 500 site, Larry Bosworth has a large (and still-growing) section on tracks which includes information about the new aluminum track plating.
Don DeYoung has a number of track oriented links on his Pinewood Derby Tracks page.
For that final race between the top two cars, which two lanes of your multi-lane track should you use? This essay by Stan Pope helps you answer that question.

Last updated on December 13, 2006, 12:00 PM
Copyright 1999-2006 © by Cory Young. All rights reserved.