15th Burlington (Bubble Sort) Racing Method
by Stan Pope, Morton, IL
a Volunteer Scouter for W. D. Boyce Council, BSA, Peoria, IL
Throughout my pinewood racing lifetime, I have placed a high value on racing methods that (1) award trophies accurately, (2) provide a lot of racing for each entrant, and (3) involve the participants heavily. This "Bubble Sort" method achieves all of these goals!
Most racing methods for large groups produce a low ratio of racing time to waiting time... a little time racing and a lot of time waiting. This method improves the ratio greatly.
Because the method involves multiple tracks, it is best suited to competition involving multiple groups, e.g. Cub Scout District or Council racing, where each group is encouraged to bring its track to the competition.
There may be other ways to find the fastest cars in a group more quickly, but they do so at the cost of "lots of racing for each entrant."
- The Bubble Sort racing method utilizes multiple three-lane tracks. The number of tracks to use is recommended to be selected so that there will be between 7 and 15 racers per track. So ...
- Racers run frequently, typically every third to fifth heat, depending on the number of tracks and racers.
- When each heat has been run, the heat winner moves to the next track toward the first track, and the third place racer in the heat moves to the next track toward the last track.
- Racers compete for a scheduled time period, planned to provide at least 2 runs per available track. There must be enough heats so that even with the worst initial track assignment and queue sequence, there will be enough heats for the fastest cars to reach the first track, even if a few of their heats don't finish "according to form."
- Racers compete against a wide variety of other racers. But as racing progresses, more and more racers will tend to race against others of similar speed. The result is that more racers get to claim heat victories.
- The method selects finalists with high probability that those deserving of a trophy reach the finals.
I did not originate the concept for the method. I first saw it described at 15th Burlington Scoring System. I have made some changes to speed up the process, (2) improve the accuracy, and (3) clarify the selection of finalists, and (4) offer some guidelines regarding effectiveness.
The method is an implementation of the concept of the Bubble Sort, which is an efficient method that is often used in computers to sort records into ascending or descending order according to some criterion. The implementation is not exact, but is very close. The "inexactness" is resolved by the second and third phases, "Finalist Selection" and "Finals."
Tracks are lined up with their finish lines nearest the audience. There should be about 6 feet between tracks. In that space there is a line of racers waiting to race and a path for racers to move from the starting line to the finish line. If space is available, tracks can be farther apart or tracks can be angled to give a better view of the finish line.
Select one end of the row of tracks to be called "GOLD" and the opposite end to be called "SILVER". The end tracks will be called the GOLD Track and the SILVER Track, respectively. Racers who finish first in their heats will move toward the GOLD Track; racers who finish third in their heats will move toward the SILVER Track.
A Pit Table and chairs or benches should be set up just past the GOLD Track. These will be used for impounding finalist cars and for finalists to sit while waiting for the field of finalists to be filled. Notice should be posted to the effect that anyone other than finalists who occupy that area will be "evicted" when finalist selection begins.
Preliminary Racing - Everybody Races!
The basic idea used is that racers are initially randomly assigned to tracks. Racers assigned to a track line up along the track on the side toward the SILVER Track. Racers nearest the starting line "draw blind" for lane assignment in the next heat.
When each heat finishes, the racers are disposed as follows:
Racers join their next track's line of waiting racers at the end nearest the finish line.
- 1st place: racer moves to the next track toward the GOLD Track, unless the he is already on the GOLD Track.
- 2nd place: racer stays on this track.
- 3rd place: racer moves to the next track toward the SILVER Track, unless he is already on the SILVER Track.
The cumulative effect of this disposition is that faster racers migrate toward the GOLD Track; slower racers migrate toward the SILVER Track. They tend to migrate until they reach a track populated with racers of comparable speed. Then they tend to stay on or close to that track.
Preliminary Racing Heat Ties:
- Two-way tie for 1st: Tied racers draw to decide which moves to the next lower number track and which stays. The last place, of course, moves to the next higher number track without being involved in the draw.
- Two-way tie for 2nd: Tied racers draw to decide which stays and which moves to the next higher number track.
- Three-way tie for 1st: Tied racers draw to decide who goes where.
A container of tokens should be available to each finish line judge
- Two-way tie for 1st: Tied racers move toward the GOLD Track. The 3rd place racer moves toward the SILVER Track.
- Two-way tie for 2nd: Tied racers stay on their current track.
- Three-way tie for 1st: All three racers move toward the GOLD Track.
If the equipment were insensitive enough to produce a lot of tie heats, this alternative could radically upset the balance of racers on each track. Experience of the method originators shows that this is not a problem.
Preliminary racing continues for a planned period of time. When the period expires, racing changes to "Selection of Finalists."
Finalists Selection - Everybody Races!
At the end of the "Preliminary Racing" period, "Finalists Selection" begins and the rules change slightly:
- GOLD Track heat winners become "Finalists", and stop racing until the finals. The number of finalists selected should be the greater of 7, the number of racers on the GOLD Track at the start of Finalist Selection, and about three times the number of trophies to be awarded. The method for finals may affect the exact number of finalists to be selected.
- Other heat winners move to the next track toward the GOLD Track as before. The 2nd and 3rd place racers stay on the same track.
- Finalist Selection Heat Ties:
- Two- or three-way tie for 1st on the GOLD Track: All racers tied for 1st on the GOLD Track become "Finalists".
- Two- or three-way tie for 1st on other tracks: All racers tied for 1st advance one track toward the GOLD Track.
- When the number of racers on the SILVER Track reaches 1, that racer races The Cubmaster's Car for the right to move up to the next track. (Since that last racer may not have won a heat all day, this procedure assures that every Cub entered and still racing wins at least one heat. "The Cubmaster's Car" is an especially prepared car to race against this remaining racer. That car needs to be slow enough to nearly guarantee the Cub a heat win and a move up to the next track. Taking time for this heat with the Cubmaster also causes the racer to be separated in the next track's queue from the racer that he last raced. (Note: it is possible that an average race car that starts near the gold track will after some 3rd place finishes, reach a track on which he is the average competitor and finish in 2nd place on that track for the rest of the competition, thereby never winning a heat. This is a low probability event, but can be covered by inviting those racers to the SILVER Track to race "The Cubmaster's Car" while the Finals are conducted on other tracks.)
- Rules about absence from the track do not apply. Racers need to race in order to become finalists!
Finals - Only Finalists Race
Preferred: In an event in which several classes will race separately (such as in Wotamalo where Tiger races Tiger, Wolf races Wolf, etc.), use a separate, comparable track for Finals. This track should be one on which none of the entrants will have tested or competed. In this way, the track is fair to all and Finals for one group can overlap with Preliminary and Finialists Selection for the next group! A possible source of such a fair track is a pack in another district. This plan also avoids the time pressure to finish finals quickly, which allows either Race by Time or Race by Points to function effectively. It also makes more time available for Preliminary and Finalist Selection racing!
Alternative: Since the tracks are supplied by various groups, selection of one track to run the finals would be considered to give members of the group that supplied that track a "home field advantage." It is useful to conduct the finals using more than one track and to select the tracks to be used using some random process. So, first eliminate any tracks which showed "incidents" during racing and any tracks which don't have the requisite equipment to support the finals method. Then draw lots to determine which tracks will be used.
- Race by Time
Racers will run once on each lane of each finals track. Racers are to be ranked by the sum of all of their heat times. Lower heat time is better.
Groups of finalists of approximately equal size, one group per finals track, are formed. The groups race a PN chart on each track.
Some race managers like to drop a racer's worst time. This is not appropriate for finalists because dropping the slowest run gives an advantage to less consistent racers and all of these racers have shown proficiency to avoid "bad runs".
- Race by Points
I have found no reasonable multi-track "Race by Points" method that is accurate. I think that the number of heats involved would be very high in order to accomplish the requisite equality by lanes, tracks, and opponents. Single track solutions include 3 and 4 lane, 13 racer Perfect-N and Complimentary Perfect-N charts.
If there are not enough tracks available with timing capability, then this 13-racer single track solution may be best.
- Graphite Lubricant Only:
Since the schedule of racing extends toward the upper limits of graphite lifetime, since liquid lubricants lifetime is significantly greater, and since highest performance oils involve both expensive lubricants and prohibitively expensive preparation materials, restricting lubricants to dry graphite seems to be the fairest and most easily enforced rule. The graphite restriction places a premium on good wheel and axle polishing and on good graphite application. Enforcement is easily done by requiring application of dry graphite to the wheel bores during inspection. (Dry graphite applied to oiled wheels is known to hurt performance badly.) Since results of early races are immaterial to final results, no graphite break-in is needed.
- Avoid Multiples of Three:
When track queue sizes are a multiple of three, the total mix of opponents tends to be more limited than it should be, especially if the tracks run heats in near lock-step. Differences in time per heat, occasional incorrect routing of racers, and use of 4 token draws will mitigate the effect. Alternating the initial queue sizes around a multiple of three can also be applied. For instance, if 72 racers are to be served on 8 tracks (average 9 racers per track), assign 8 racers to the track 1, 10 racers to track 2, 8 racers to track 3, etc.
- Let Each Track Run at its Own Rate:
Do not try to keep the tracks running in "lock step." This just slows the whole process. And avoiding lock step helps the racer mix.
- Check Heats per Minute Rate and Adjust Prelim Duration:
Part way through preliminary racing, measure the "heats per minute" that tracks run and, if necessary, extend the end time for preliminary racing. If the end time is changed, make appropriate announcement to racers and audience, well before the end time.
- Race Car Adjustments:
It is reasonable for drivers to adjust alignment of their cars during the time between their heats if they can do it without delaying racing.
- Finish Line Judging:
Finish line judging can include the racers. When the heat completes, have the racers point to the 1st place car. The majority, including the judge decide the issue. Then have them point to the 2nd place car. This can be especially helpful if the electronics malfunction.
- Number of Finalists:
In selection of finalists, the most important consideration is including all of those deserving of a trophy. The selection process is set to err on the side of including the undeserving rather than excluding the deserving. This is why more than the minimum number of racers are selected.
- Directing Traffic After Heat:
If a racer erroneously "self promotes", i.e. changes tracks as though he finished 1st in his heat when he really finished 2nd or 3rd, and you don't know that it happened later, just let it go. He will get flushed back down soon. Remind the finish line judges to "direct traffic", especially on the tracks near the GOLD Track, to keep these errors low. Such errors do create a persistent imbalance in the numbers of racers/track, but unless the errors are rampant, they will have only a small effect on the number of heats that each racer gets to run, and will have no effect on accuracy.
- Consistent Representative Track Types:
Tracks recruited for the racing should be of the profile described in the Cub Scout Leaders HOW TO Book since this is the style on which most racers qualified. There are other track profiles manufactured, but their smaller radius of curvature puts cars with elongated noses or tails at risk of dragging, and would place an insurmountable block against such cars progressing past that track. If track availability requires that such tracks must be used, then those track should be located towards the SILVER Track and racers which drag in the curve should be treated as though they won, regardless of actual results.
- Estimating Tool:
Download this OpenOffice spreadsheet to help plan the event. (Don't try to "Open" the link directly, but use the "Save as ... " function instead. The reason is that Open Office will try to open the file with read and write and the usual location for "Open" is protected from write.) The spreadsheet calculates the Preliminary and Finalists Selection Durations for various parameters. (Fully functional OpenOffice software is available to individuals at no cost here.)
- Late Arrivals:
Competitors who arrive at the site after their age group has started "Preliminary Racing" but before their age group has finished "Finalist Selection" should get priority in inspection (if other groups are being inspected) and be assigned to start racing on the SILVER Track after successfully completing inspection. The late arrival might have a slight advantage due to being at a different point in its graphite performance curve, but will have a disadvantage due to having fewer available heats to reach the GOLD Track. I think that it is a net disadvantage to arrive late!
- Recommended Draw Procedure:
Preferred: During "Preliminary Racing" and "Finalist Selection", a member of track staff holds a container for the next four racers to draw from. For the first racer in line, the container holds three tokens labeled "Lane 1", "Lane 2", and "Lane 3". After the first racer has drawn, a token labeled "Draw" is added to the container. Racers who draw a "Lane" token race in the next heat in the lane drawn. The racer who draws the "Draw" token returns to the front of the line and will be the first to draw for the next heat.
Note: If staffing is a problem, a volunteer (including Boy Scouts!) from the audience could easily learn to conduct the draw.
Alternative: During "Preliminary Racing" and "Finalist Selection", the first racer in line holds a container in which there are 4 tokens labeled "Lane 1", "Lane 2", "Lane 3", and "Draw". The next 3 racers in line draw from the container, and the scout holding the draw container receives the token not drawn by others. Those who draw Lane numbers race in the next heat using the drawn lane number. The racer who draws "Draw" conducts the draw for the subsequent heat. (Note that involving more than three tokens in the draw slowly randomizes each track's line of racers waiting to run and may result in a slight difference in the total number of heats run by each racer. Changing the waiting line sequence greatly increases the mix of competitors, and that benefit outweighs the slight inequity in runs.)
Note: If during his draw a racer lifts more than one token to a level that either can be seen, that draw invalid. The tokens so drawn must be returned to the container, the container mixed, and the racer must draw again. We have used poker chips marked with a felt-tip pen in the past. Larger marked uniform objects such as ping-pong balls would be easier for participants to draw exactly one token.
- Racers Who Leave the Track:
Note: This section is being analyzed to minimize "gaming the system". Substantial changes are likely!
Leaving the track during racing is discouraged. If needs must, then until the last 10 minutes of Preliminary Racing, racers may leave the track once for up to 5 minutes without penalty. To do so, they must check out with their track finish line judge, leaving their car and driver's license there. The judge will secure the car and note the exit time. (If the absence is for car repair, then the judge will not keep the car but will have the Scout accompanied to the pit area.) Upon the racer's return to the track, he must report to the finish line judge of the track that he left who will, at his next possible opportunity, check the absence time, determine which track the racer must resume racing on, return the racer's car and driver's license, and direct the racer to the back of the correct waiting line. The exception to this is that if he is to resume racing on the GOLD Track, he will be directed to the front of the waiting line. Leaving during the last 10 minutes, extended absences and repeat absences cost track position (moving up to three tracks toward the SILVER Track), scaled to the duration of absence at one track position per 5 minutes or portion thereof.
Rules about leaving the track briefly apply to racers from the GOLD Track and the next two tracks, only.
The reasoning for this rule is to avoid a racer attempting to gain an advantage by not racing. On the GOLD Track, the purpose is to avoid placing third in a heat, either by racing and placing 1st or 2nd or by not racing. Secondly, by not racing, the racer delays the degradation of his lubrication and obtaining thereby some small advantage. The closer to the GOLD Track that a racer is, the more significant the potential advantage. Further toward the SILVER Track, the racers need to race and win, so any advantage from deferring racing is slight or nil. Placing a racer who is returning to the GOLD Track at the front of the waiting line also discourages attempting to gain advantage by not racing.
- Worst Case Initial Arrangement:
The worst possible initial arrangement of racers would have the fastest cars starting on the SILVER Track, arranged by speed. That is, the fastest three race each other first, then the next fastest three, etc. If heats finish according to form, then it will take one more heat per racer than there are tracks to get all of them to the GOLD Track. For instance, if there were 10 tracks, then it would take 11 heats to get them all to the GOLD Track. Here is a text picture of the sequence.
After the fastest have reached the GOLD Track, then the slowest of each group of three will alternate between the GOLD Track and the adjacent track.
- When the Fastest Car in a Heat Doesn't Win:
A race that does not finish according to form will cost the fast racer a second heat to recover if he were unlucky enough to finish 3rd instead of 1st. Assume that in 10% of the heats the fastest car in the heat finishes 3rd. That is rather pessimistic, I think.) This would add two, maybe four, more heats to the minimum needed to assure that the fastest cars have enough heats to win even with the worst initial arrangment.
- "I Won A Race" Ribbon:
Since this method is most applicable to large numbers of racers from a number of tracks, a small percentage of the entrants will win a trophy. I like to send each entrant home with some positive remembrance. A 6" long blue ribbon printed with "I won a race at the (your event name) Pinewood Derby" has been popular. As noted above, almost all of the cars that finish the event in working order will have qualified. The format of racing makes it feasible that even cars that don't make it to the finish line (which is rare in a district derby where each entrant has won an invitation) or which suffer some damage have time to rectify the problem in the pits and return to competition.
Here are some track staff jobs that will be needed:
Responsible for all race operations. Makes sure that it is "done fairly." (He also wanders around a lot.)
One person who keeps the racers and audience apprised of "what is going on."
Draw, one per track
One person who conducts the "draw for lane".
Starter, one per track
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 may have to 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 judge, one per track
One person along with a set of electronics who determines the heat placement. The judge identifies (announces) the heat winner and directs the heat participants to the proper places.
There are two pit areas to watch:
Finalists Pit: One person 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. This function should only be needed during Finalist Selection and Finals phases.
Inspection Pit: One person who watches the pool of inspected cars. After cars complete inspection and until racing starts, the cars are impounded and may not be touched by anyone. Once racing starts, the cars will remain in the hands of the owner unless he leaves the racing area.
This race method was introduced to me through the 15th Burlington Scouting Group web site. 15th Burlington is a part of Scouts Canada. Kub Kar racing is the Scouts Canada equivalent of our Pinewood Derby.
The 15th Burlington Scoring System has been altered as a result of their experience, but (as of this writing) the web page has not caught up. One important difference is that the Gold Track is populated initially just as all the other tracks.
Update: 6/7/2011 - Retitle in honor of originating group.
Update: 6/8/2011 - Qualify rules about absence from the track. Warn about tracks with small radius of curvature sections. Correct possible defect in handling tied racers during Finalist Selection.
Update: 6/14/2011 - Handle late arrivals.
Update: 6/15/2011 - Reorg details, Add "Estimating Tool", "Late Arrivals", "Worst Case Initial Arrangement" and "When the Fastest Car in a Heat Doesn't Win" to "Observations" section. Move "Recommended Draw Procedure" and "Racers Who Leave the Track" to "Observations" section.
Update: 6/16/2011 - Add notes about the "I Won A Race" Ribbon.
Update: 7/21/2011 - Add "separate track for finals", Revise "improper draw" handling.
Update: 7/25/2011 - Add "Credit" section with link to 15th Burlington web site.
Copyright © 2011 by Stan Pope. All rights reserved.