Script Title: How We Know that the 15th Burlington Racing System Works" Version: 0.1 Hello, Racers and Racer Mentors! I am Stan Pope. I have been analyzing and evaluating Pinewood Derby Racing methods for about 25 years. In a previous video I introduced you to the 15th Burlington Race Method. The method is exciting to me because it drastically reduces the amount of time that entrants in a large racing event such as our Wotamalo District Derby spend waiting to race. I think that more racing and a lot less waiting will be exciting to your Racer as well. If you have not already done so, please review that video before proceeding. One of the important considerations in selecting a racing method is whether it works, i.e. whether it accurately identifies the fastest racers so that the most deserving racers get the trophies. The purpose of this video is to describe the steps that I took to prove to myself that the method does, indeed, satisfy that important criterion. When I first heard the method described by its authors, Scouters from Canada's 15th Burlington district, I subjected the method to detailed mathematical analysis and process analysis. I identified some shortcomings and adjusted the method accordingly. In subsequent discussions with the authors, I found that they had found some of those same issues when they attempted to use the method and had made the same corrections! After those adjustments, I found the theory of the method to be sound. If you locate the 15th Burlington web site and read their description of the method, you may find that the authors have not yet documented what they learned and that the original issues persist there. In my analysis, I observed that the number of cars on each track tends to stay nearly constant. That is important, since the number of racers on each track is the biggest factor in how many heats those racers run. There are some exceptions, however. Tracks which run faster than the adjacent tracks will have slightly fewer cars in their pool of racers. That is because each heat that is run sends (most of the time) two cars away to adjacent tracks. Heats from adjacent tracks each send one car to this track. If the imbalance persists, the faster track might "run out of work." This will naturally slow down that faster track and prevent a full scale "run away." A better solution, of course, is for the other tracks to improve their rate, since this benefits all of the racers! When a heat includes a tie the balance can be disturbed. [For instance a two-way tie for first sends two racers to the next track toward the GOLD Track and one racer to the next track toward the SILVER Track, so three racers are removed. Meanwhile the track receives two racers from adjacent tracks, so this track loses one racer net and the next track up adds one racer. A two-way tie for second place causes two racers to be retained on this track and none sent to the next track down toward the SILVER Track. Ties cause a slow drift of racers toward the GOLD Track.] If there were a large number of ties, this would become a problem. However, our experience with racing at recent district races in which racers also tend to race against others of comparable performance indicates that ties are rare enough that we will not have problems from it. I further observed that if tracks were run in exact "lock step" and were to have a multiple of three racers each, racers would race throughout the Preliminary Racing against a subset of the total list of entrants. For instance, the first three in line at the beginning of racing would race only against others who started among the first three in line, shifting among the tracks as racing progresses. Those who started among the other triads on each track would experience a similar limitation. If this were to occur, the effectiveness in sending the fastest cars to the GOLD Track would be reduced, and more finalists would have to be selected to overcome the worst cases. To avoid this situation, I have recommended the following steps: 1. Each track is encouraged to run at its own pace, generally as quickly as the heats can be conducted safely. 2. The order of Racers in the line for each track is randomized slightly by having the next four racers in line draw for the three racing lanes, and one is held over to the next heat. 3. Optionally, if the chairman thought #1 and 2 to be insufficient, the number of racers starting on each track may be adjusted. For instance, instead of having 9 racers on each of 8 tracks, assign these sizes: 8, 10, 8, 10, 8, 10, 8, and 10 racers. Since racers tend to move between tracks, no disadvantage to the racers should result. Lastly, if enough heats are run for each racer, typically half again as there are tracks in use, what happens in the first few heats has little bearing on the final outcome. This fact has benefits for us. First, freshly applied graphite which ordinarily causes the next 2 or 3 runs to be slower than usual doesn't hurt the accuracy of the process. Second, the random assignment of starting track does not confer a random advantage or disadvantage on the racers. A racer who starts on or near the GOLD Track but doesn't deserve to be there quickly moves toward the SILVER Track. Conversely, a racer who starts on or near the SILVER Track but deserves much better, quickly wins his way toward the GOLD Track. Following those "pencil and paper" analyses, I ran some manual simulations using dice and a deck of playing cards to observe whether the fastest cars became finalists. I found that it works well if the rules are followed. More interestingly, I found that it works well if the rules are followed at least almost all the time! I observed that the system is much more "fault tolerant" (for errors committed either by racers or by track officials or equipment) than either Quintuple Elimination, Double Elimination or Timed Racing. In formulating the simulation, I dealt playing cards to each of 5 tracks. Three tracks had 10 Racers and two tracks had 11 racers for total of 52. Racer speed was determined by the sequence and suit of the cards, e.g. Jack of Hearts or Diamonds > 10 of Spaces or Clubs > 10 of Hearts or Diamonds > 9 of Spaces or Clubs. Cards of the same color and sequence will tie. I randomized the "lane draw" with one die, throwing it until it showed 1 through 4 to identify the racer to be held over to the next heat. I used two dice to select fastest car flames out (throw of 1 and 1) or slowest car wins (throw of 6 and 6). One in 36 chance for each of those cases seemed at least as bad as real life would be. To simplify the process when doing the simulation alone, I ran the tracks in lock step. If separate persons, each with his own dice and "track" of cards, were able to run their tracks, the results would be closer to real life. Even with the limitations, the simulations showed that the process is strong. Show link to simulation procedure. Show clip of running the simulation. Next time I run the simulation, I will alter that procedure so that the first racer in line (the one held over from before) does not get held over this time. To do this, I will throw the single die once and hold over the second racer in line if a 1 or 2 show on the die, the third in line if a 3 or 4 show, etc. I will also change the speed method so that ties occur less frequently and more randomly by ranking cards (racers) by the Bridge sequence and using the results of the 2-dice throw to signal ties: Two-way tie for 1st on a 2 and 2 throw and two-way tie for 2nd on a 3 and 3 throw. These will reflect reality more closely. Finally, I "put on my hacker hat" and looked for ways that I could "game the system", i.e. win with an inferior car while still obeying all the rules (or at least appearing to do so). I found and closed three exposures. Did I find all the loopholes? I think so, but time will tell. Although I don't expect any Scouts to try to "game the system", I believe that each racer and mentor will have more confidence in the accuracy of the results if the process guards against such abuses. In summary, the method works well and will provide our Racers with an accurate and more rewarding event. If you still have questions, please contact me via email at 15thBurlington@stanpope.net. =================== Resource information ======================== loopholes: oil vs graphite absence to avoid GOLD Track elfr promotion Initial track assignment: Decide on the number of tracks to use by dividing the number of pre-registers by 7 and discarding the remainder. Then, if necessary, reduce the number to the number of tracks available. Give numbered track slips to each racer as he finishes inspection. Slips arranged 1-2-3-4---n-1-2-3 ... Initial Speech: (short and sweet) As you finished inspection, you were each assigned a track on which to race your first heat. Here is the plan for racing during the next hour of Preliminary Racing: Which tracks you race on next is determined by your finish place in your last heat: When you finish 1st in your heat, you will move one track toward the GOLD Track. When you finish 2nd in your heat, you will stay on the same track. When you finish 3rd in your heat, you will move one track toward the SILVER Track. In each case you join at the end of the short line of waiting racers. You will be racing often, so stay alert. The design is for each racer to run at least every 5 minutes! The more promptly you follow instructions, the more racing you will get. If your car develops a problem, you may take it to the pits to repair. There is a small penalty. You may not add lubricant or weight (beyond 5 ounces), but you may make other adjustments! If you do this, check out with your Track Staff before leaving. Return to that same Staff member for instruction. At the end of the hour, stay where you are. Everybody will continue racing, but the rules change slightly. We will remind you of those changes at that time. Everybody, Good Luck! And Good Racing! 2nd Hour Speech: Congratulations! You survived the Preliminary Round of Wotamalo Racing! But stay where you are. Here is the plan for racing now for Finalist Selection: Start where you finished the hour of Preliminary Racing. Which tracks you race on next is determined by your finish place in your last heat: When you finish 1st in your heat, you will move one track toward the GOLD Track. When you finish 2nd or 3rd in your heat, you will stay on the same track. Nobody moves toward the SILVER Track. In each case you join at the end of the short line of waiting racers. If you raced on the GOLD Track and finished 1st there, you are a Finalist! Park your car and wait for the rest of the Finalists to be selected. You will be racing often, so stay alert. The design is for each racer to run at least every 5 minutes! The more quickly you follow instructions, the more racing you will get. If your car develops a problem, you may take it to the pits to repair. There is a small penalty. You may not add lubricant or weight (beyond 5 ounces), but you may make other adjustments! If you do this, check out with your Track Staff before leaving. Return to that same Staff member for instruction. Everybody, Good Luck! And Good Racing! Finals Speech: Congratulations! You have qualified to be a Finalist! You racers will compete against each other for lowest total of your heat times. You will race once on each lane. Every heat counts. You will be called to race by name (or number). Pay attention and stay alert. Good Luck! And Good Racing!