Marcus P. Borom, Ph.D.

Pack Master

Pack 37 - Niskayuna, NY

In conjunction with

Richard E. Stearns, Ph.D.

January 1975


One of the highlights of any cubbing year is the Pinewood Derby.Excitement runs high and the competition is keen.A perennial problem is how to maximize participation on the night of the race and ensure ultimate fairness in the final outcome.Pack 37 of Niskayuna, NY conducted a Pinewood Derby this year (1975) unlike any I have ever attended and with such success that we feel compelled to share the technique with others.


In my eight years of cubbing with my four sons, I have been involved in many father-son pinewood races.Every race was conducted on a tennis-ladder type elimination with a second ladder set up for the losers of the first heat.In such a system, one-half of the contestants are eliminated by the second heat.Interest in the race drops and discipline becomes a problem.When a four-lane track is fully used, the early loss of contestants is even higher.There had to be a better way.


Pack 37 was fortunate to have Dr. Richard Stearns as a participating member.Dr. Stearns is a mathematician and a world authority on game theory.As pack master, I presented him with the challenge of designing a race schedule for a four-lane track that will maximize participation, assure that all cars will race on each lane and race against as many other cars as possible.


His solution, he claims, was simple.I still believe that what he did was impossible, but the results are fantastic.Consider a field of 20 to 32 cars.With the Stearns/Borom method, which weíll consider in more detail later, each car races against 21 other cars and never against the same car twice; each car races seven times; and the winner is not determined until the last race.


Comparing in Table I (not shown here) the Stearns/Borom method against the usual two-lane tennis ladder shows the following.In the tennis ladder where each heat is settled on a best-two -out-of-three basis, the two finalists see a lot of action but, unfortunately, only 5 opponents and half the cars make only 4 to 6 runs down the track and meet only two opponents.The Stearns/Borom method is a winner from the standpoint of both continuous participation and maximum exposure.


The schedules for Pinewood racer fields of 24, 28, 32 and 36 cars respectively are given in Table II, Table III, Table IV, and Table IVa
[Note: Click the "Table" link above to view the race table]

Each schedule is divided into 7 rounds with each round consisting of from 6 to 8 races.The cars participating in each race are designated by number and are assigned to a specific track for each race.The schedules in the form of Tables II through IV are required to determine at a glance, the participants in any given race as the competition proceeds.


The schedules are presented in a second form in Table V, Table VI, and Table VII, and Table VIIa .
[Note: Click the "Table" link above to view the race and rounds tables.]

Tables V through VII allow the contestants to locate their race number for each round, and also serve as running tally sheets for determining the winners.


With Tables II through VIIa in hand, you are ready to consider the details of conducting the race.The three different schedules were necessary since we were uncertain of the number of participants, which could have varied from 21 to 32.Each schedule is adjusted so that the three highest number cars never race one another and races, therefore, will never involve less than three contestants.


My contribution here was to reduce the theory to comprehendible practice.


The materials needed to run a Stearns/Borom Pinewood Derby are:

a. ††††††† a transparency of the contestant sign-up list

b.†††††† transparencies of Tables II through VII

c.†††††† pens for marking on transparencies

d.†††††† two overhead projectors

e.†††††† two projection screens

f.††††††† one four lane track

g.†††††† a scale, for checking maximum car weight

h.†††††† a registration table

i.††††††† numbered stickers for each car

j.††††††† numbered tags for each cub to wear corresponding to his assigned car number

k.†††††† electric drill and lead weights for last minute weight adjustments

l.††††††† spare parts for pit stops

m.††††† display table for all cars with display slots indicated by number on a long, brown-paper roll on the table top

n.†††††† a portable PA system for the race announcer (and pack master) to use

o.†††††† clip boards


On race night, each car is weighed and adjusted to within the maximum weight limit.After the car is accepted by weight, and by whatever other standards were agreed to in advance (ensure that rules have been dispersed early), both the cub and the car are assigned their identification number (he numbers are assigned in order of acceptance).A sticker bearing the identification number is attached to the car.The cubís name is entered legibly and in numerical order on a transparency of the contestants sign-up list.The sigh-up list is cut from a transparency of Table VII.The cub then places his car on the display table in the matching numbered slot.The numbered slots also aid in judging for design awards.


The race starter is supplied with a copy of either Table II, III or IV depending on the final number of participants.A transparency of the appropriate Table II, III or IV is also displayed on one overhead projector or copies are provided to the audience.


The complete cub contestant sign-up transparency is attached to a transparency of the body of the appropriate Table V, VI or VII, respectively, as determined by the number of contestants.The combined viewgraph (contestant list and winnerís list) is displayed on the second overhead projector.A person is assigned to mark the winners of each race on the overhead projector by circling the winnerís race number associated with that round and to enter a mark for each win in the column at the far right of the table.Everyone is then able to follow the progress of the race by contestant.


During the course of each Pinewood Derby race, four cubs are at the finish line waiting to retrieve their cars while four cubs are directed to be on deck with their cars ready to go in the next race and four more are anticipating being called on deck.Twelve cubs out of a field of 28 cars are involved at any one time during the race - that is an over 40% rolling, active participation.Discipline is no problem.A little planning in placing the track (center stage is best) with occasional vigil in keeping the spectators a reasonable distance from the track makes for enjoyable viewing by all.


The first, second and third place winners are determined by the total number of races won.In the case of a tie, a one on one race can be conducted.An example of race results are shown in Table VIII.An example of race results are shown in Table VIII.There was a three-way tie for third place which was resolved by an additional sudden death race.


On paper, the race procedure sounds a little complicated, but in practice it works quite smoothly and I highly recommend it to other packs.

A note in closing. If you are unable to print the tables, try "selecting all" and then copying and pasting into an Excel workbook. If that does not work for you,


and I will send you the table files in an Excel format. Good luck with your Derby.
Additional modification and extension of our initial procedure has been provided by numerous other Cub Scouting enthusiasts. I will add links to their efforts and contributions as they are made known to me.
If you use our technique and it produces a rewarding experience, I would enjoy hearing from you.
If you have any questions or suggestions, please contact either me or Dr. Stearns.