Simulated Derby Summary
Three Lanes; 104 Cars; Six Divsions

This summary data was generated from the output file of a simulated Derby.
The Derby had six Divisions (size from 10 to 23 cars, with total of 104 cars).
Four of the six divisions were allowed to send one finalist each to the Derby Finals.
The Number of Lanes was set to three (3).
The Elimination Threshold was set to six (6).

The Derby was run in simulated mode and the results file was analyzed.
The specific results reported here are:
bullet How many races were run
bullet Finish order and elapsed time statistics

How many Races in a Derby?
There are separate tables for the overall Derby Summary, Tigers, Wolf, Bear, Webelos I, Webelos II, Derby Finals, and Parents .
Derby Racing Summary  

This table shows the number of rounds, races in each round, and cars in each division for all divisions in the Derby.
In the actual Pack 34 Derbies, the average time to run a race, including planned breaks of 15 minutes between Divisions, was about 1.5 minutes. Usually, the average is closer to 2 minutes at the beginning and 1 minute at the end of the Derby. If you really have a tight schedule, I would recommend a pre-Derby training session for your volunteers.

Overall Derby Racing Summary  (Top of Section)  (Top of Page)
Division Rounds Races Cars
Tigers 7 31 19
Wolf 7 28 18
Bear 8 37 23
Webelos I 7 32 21
Webelos II 5 17 10
Derby Finals 4 9 4
Parents 6 23 13
Totals 44 177 108

 

Tigers and Wolf Racing Summary (Top of Section)  (Top of Page)
Tigers   Wolf
Round Races Cars   Round Races Cars
1 7 19   1 6 18
2 7 19   2 6 18
3 7 19   3 6 18
4 4 12   4 5 13
5 2 5   5 (Elim Runoff) 1 3
6 (Elim Runoff) 1 2   6 (Finals) 3 3
7(Finals) 3 3   7 (Finals -2nd) 1 2
Total 31     Total 28  

 

Bear and Webelos I Racing Summary (Top of Section) (Top of Page)
Bear   Webelos I
Round Races Cars   Round Races Cars
1 8 23   1 7 21
2 8 23   2 7 21
3 8 23   3 7 21
4 5 15   4 5 14
5 3 7   5 2 5
6 (Elim Runoff) 1 3   6 (Elim Runoff) 1 3
7(Finals) 3 3   7(Finals) 3 3
8 (Finals-2nd) 1 2        
Total 37     Total 32  

 
Webelos II and Derby Finals Racing Summary   (Top of Section)(Top of Page)
Webelos II   Derby Finals
Round Races Cars   Round Races Cars
1 4 10   1 2 4
2 4 10   2 2 4
3 4 10   3 2 4
4 2 6   4 (Finals) 3 3
5 (Finals) 3 3   Total 9  
Total 17          

 

Parents Racing Summary (Top of Section) (Top of Page)
Parents
Round Races Cars
1 5 13
2 5 13
3 5 13
4 3 9
5 2 4
6 (Finals) 3 3
Total 23  

 

Finish Order and Elapsed Time Statistics?

In this simulation, the track is absolutely fair. That is, the cars have a fixed order relative to each other in speed, with some variance (noise) from race to race independent of which lane they run in. The cars' speeds are randomly assigned some average value and variance at the beginning of the simulation for each division. Thus, they have a known relative ranking. If we ran a very large number of races, with random lane assignments, we would expect the average and median finish orders and elapsed times to be equal for all lanes. The average finish order would be two in this case (for a three lane track).

If, however, we run only a relatively few races, then the results become skewed depending on which cars race in which lanes. This happens in the real world as well. This makes it difficult to tell if your track really does have a "slow" lane, especially if it is not grossly off compared to the others.
Looking at the data for both individual divisons and the overall Derby, we see that for the sampling our Derby, which had relatively few races,  generated data which would appear to indicate a slight lane bias favoring Lane 1. This shows up as a slightly lower average finish order and elapsed time.

There are separate tables for the overall Derby Summary, Tigers, Wolf, Bear,Webelos I, Webelos II,Derby Finals, and Parents .

Derby Finish Order and Elapsed Time Statisitics (Top of Section)  (Top of Page)
Entire Derby            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5422 2.5482 2.5440
Average 1.920 2.040 2.028 2.5497 2.5523 2.5526
Min 1 1 1 2.5028 2.5034 2.5015
Max 3 3 3 2.6588 2.6426 2.6466

 
Tigers Finish Order and Elapsed Time Statisitics (Top of Section)  (Top of Page)
Tigers            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5390 2.5482 2.5495
Average 1.742 1.968 2.267 2.5477 2.5523 2.5587
Min 1 1 1 2.5028 2.5048 2.5050
Max 3 3 3 2.6588 2.6277 2.6323

 
Wolf Finish Order and Elapsed Time Statisitics (Top of Section)  (Top of Page)
Wolf            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5435 2.5536 2.5433
Average 1.857 2.107 2.036 2.5502 2.5530 2.5526
Min 1 1 1 2.5166 2.5158 2.5145
Max 3 3 3 2.6164 2.5877 2.6344

 
Bear Finish Order and Elapsed Time Statisitics (Top of Section) (Top of Page)
Bear            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5438 2.5394 2.5382
Average 2.056 2.054 1.865 2.5560 2.5532 2.5500
Min 1 1 1 2.5099 2.5105 2.5082
Max 3 3 3 2.6553 2.6337 2.6466

 
Webelos I Finish Order and Elapsed Time Statisitics (Top of Section)(Top of Page)
Webelos I            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5439 2.5517 2.5379
Average 1.813 2.125 2.063 2.5471 2.5554 2.5527
Min 1 1 1 2.5087 2.5139 2.5054
Max 3 3 3 2.6183 2.6426 2.6292

 
Webelos II Finish Order and Elapsed Time Statisitics (Top of Section)(Top of Page)
Webelos II            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5334 2.5398 2.5375
Average 2.059 1.941 2.000 2.5445 2.5423 2.5461
Min 1 1 1 2.5163 2.5106 2.5204
Max 3 3 3 2.5941 2.5787 2.6071

 
Derby Finals Finish Order and Elapsed Time Statisitics (Top of Section)  (Top of Page)
Derby Finals            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 3 2 2.5540 2.5783 2.5620
Average 1.889 2.222 1.889 2.5591 2.5741 2.5618
Min 1 1 1 2.5269 2.5212 2.5321
Max 3 3 3 2.5958 2.6279 2.6093

 
Parents Finish Order and Elapsed Time Statisitics (Top of Section)(Top of Page)
Parents            
  Finish Order ElapsedTimes
  Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Median 2 2 2 2.5343 2.5299 2.5397
Average 2.087 1.913 2.000 2.5431 2.5369 2.5406
Min 1 1 1 2.5068 2.5034 2.5069
Max 3 3 3 2.6042 2.5860 2.5833

 

Last Updated on January 15, 2005
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