North-South Victor Calculation
For the 2011 Event
The winning side - North or South - will be determined by the number of finishers for each side who finish under 10 hours. Since there are far more North than South troops, we need a fudge factor to make it fair. Here is our calculation. We welcome anyone checking our math.
To make the math easier, we will give a Northern finisher a weight of 1. That means that a Southern finisher needs a weight well above 1. What should it be?
[We have rounded most of the numbers here. We will do this in a spreadsheet to eliminate problems with rounding (or, more properly, to blame rounding on the computer).]
Knowns:
- Total Entrants: 358
- North Entrants: 254
- South Entrants: 104
Our Calculation:
- x = Portion of entrants who are North: 70.9% [254 ÷ 358 x 100]
- y = Portion of entrants who are South: 29.1% [104 ÷ 358 x 100]
- z = Number of North troops for every South troop: 2.4 (x ÷ y) [to more decimal places: 2.4423076923076923076923076923077]
- (Those who are astute will notice that when you solve for z, the two 358s cancel out. Additionally, so do the 100s that are used to make percentages. So it's just 254 ÷ 104. We found the way above easier to work through, however.)
Check
If all runners finished under 10 hours, it should be a tie. Will it be?
- North Points: 254 x 1 = 254
- South Points: 104 x 2.4423076923076923076923076923077 = 253.99999999999999999999999999993
(The definition of an engineer is someone who multiplies 2 x 2 and gets 3.999999999999999.)
So at 4:30 p.m., we will count the number for finishers for each side. The points for the North will be the number of North finishers. The number of points for the South will be the number of South finishers multiplied by 2.4423076923076923076923076923077. (We will probably just use 2.4 unless it's close.) Anyone disagree?
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