Anybody remember
this conversation from almost two weeks ago?
The participation adjustment does punish people that show every week when others don't have the same dedication. That's kinda a slap in the face really.
Again 👍. Coming up with a system that is fair? That's another ball of wax.
In any case, this horse was beat, if not dead, at least badly enough that it died of it's wounds shortly after the discussion ended. Do we really want to dig up its grave and have it stinking up the joint again?
Anyways, go ahead and call me a monster truck because I'm about to go "Grave Digger" on this dead horse..
Ever since
our points adjustment system was implemented last November, I've pretty much been in love with it. It was never intended to penalize divisions with low numbers, but rather compensate for the increased or decreased difficulty in scoring points based on how many drivers were racing. However, if you go through the
recent resuls, you'll see that the winner of the division with the most drivers is awarded Prize A. That brings into question whether the ".03" multiplier that we've been using is too high of a multiplier. Perhaps we should use a ".02" multiplier instead? Or how about meet in the middle at ".025"? But whatever multiplier we use, it'll only be an estimation and can never be proven to be exactly correct. It's also based on an average grid size of 10 drivers, which is probably not an ideal factor to base a points adjustment system on since the average number of drivers can fluctuate week to week or month to month.
Therefore, I set out to to see if we could find another approach. One that doesn't give bonuses or deductions based on the number of drivers on the track, but rather predetermines the value of of each finishing position based on grid size. Also one that doesn't make any assumptions on what our average grid size is. Everyone knows that the maximum points that we can score in a race is 16 points. But if 1st place always gets 16 points no matter how many drivers are competing, why does the number of points last place gets change so radically depending on how many drivers raced? For example, if a driver finished last in a field of 15, he only gets 2 points. However, if a driver finishes last in a field of 7, he gets quadruple the amount with 8 points?? That's doesn't seem right..
So what if we took the maximum value of points that can be earned in each race (16) and then divided it into equal portions based on the number of drivers in the race. Once you find what that increment is, you award the usual 16 points to 1st place, then you award one increment less for each position down the finishing order. The resulting math looks like this:
y = number of drivers in the race
x = 16/y
z = number of positions behind the 1st place
16 - zx = points awarded
Here's the above formula decribed in detail:
Points awarded when 16 drivers in the race
y = 16
x = 16/y
x = 16/16
x = 1
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 15
3rd = 16 - 2x = 14
4th = 16 - 3x = 13
5th = 16 - 4x = 12
6th = 16 - 5x = 11
7th = 16 - 6x = 10
8th = 16 - 7x = 9
9th = 16 - 8x = 8
10th = 16 - 9x = 7
11th = 16 - 10x = 6
12th = 16 - 11x = 5
13th = 16 - 12x = 4
14th = 16 - 13x = 3
15th = 16 - 14x = 2
16th = 16 - 15x = 1 (last place always wins the value of x)
Points awarded when 15 drivers in the race
y = 15
x = 16/y
x = 16/15
x = 1.0666666
z = number of positions behind 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.933334
3rd = 16 - 2x = 13.866668
4th = 16 - 3x = 12.800002
5th = 16 - 4x = 11.733336
6th = 16 - 5x = 10.66667
7th = 16 - 6x = 9.600004
8th = 16 - 7x = 8.5333374
9th = 16 - 8x = 7.4666708
10th = 16 - 9x = 6.4000042
11th = 16 - 10x = 5.3333376
12th = 16 - 11x = 4.266671
13th = 16 - 12x = 3.2000044
14th = 16 - 13x = 2.1333378
15th = 16 - 14x = 1.0666666 (last place always wins the value of x)
Points awarded when 14 drivers in the race
y = 14
x = 16/y
x = 16/14
x = 1.1428571
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.857143
3rd = 16 - 2x = 13.714286
4th = 16 - 3x = 12.571429
5th = 16 - 4x = 11.428572
6th = 16 - 5x = 10.285715
7th = 16 - 6x = 9.142858
8th = 16 - 7x = 8.000001
9th = 16 - 8x = 6.857144
10th = 16 - 9x = 5.714287
11th = 16 - 10x = 4.571429
12th = 16 - 11x = 3.428572
13th = 16 - 12x = 2.285715
14th = 16 - 13x = 1.1428571 (last place always wins the value of x)
Points awarded when 13 drivers in the race
y = 13
x = 16/y
x = 16/13
x = 1.2307692
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.769231
3rd = 16 - 2x = 13.538462
4th = 16 - 3x = 12.307693
5th = 16 - 4x = 11.076924
6th = 16 - 5x = 9.846154
7th = 16 - 6x = 8.615385
8th = 16 - 7x = 7.384616
9th = 16 - 8x = 6.153847
10th = 16 - 9x = 4.923078
11th = 16 - 10x = 3.692308
12th = 16 - 11x = 2.461539
13th = 16 - 12x = 1.2307692 (last place always wins the value of x)
Points awarded when 12 drivers in the race
y = 12
x = 16/y
x = 16/12
x = 1.3333333
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.666667
3rd = 16 - 2x = 13.333334
4th = 16 - 3x = 12.000001
5th = 16 - 4x = 10.666667
6th = 16 - 5x = 9.333334
7th = 16 - 6x = 8.000001
8th = 16 - 7x = 6.666667
9th = 16 - 8x = 5.333334
10th = 16 - 9x = 4.000001
11th = 16 - 10x = 2.666667
12th = 16 - 11x = 1.3333333 (last place always wins the value of x)
Points awarded when 11 drivers in the race
y = 11
x = 16/y
x = 16/11
x = 1.4545454
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.545455
3rd = 16 - 2x = 13.09091
4th = 16 - 3x = 11.636364
5th = 16 - 4x = 10.181819
6th = 16 - 5x = 8.727273
7th = 16 - 6x = 7.272728
8th = 16 - 7x = 5.818183
9th = 16 - 8x = 4.363637
10th = 16 - 9x = 2.909092
11th = 16 - 10x = 1.4545454 (last place always wins the value of x)
Points awarded when 10 drivers in the race
y = 10
x = 16/y
x = 16/10
x = 1.6
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.4
3rd = 16 - 2x = 12.8
4th = 16 - 3x = 11.2
5th = 16 - 4x = 9.6
6th = 16 - 5x = 8
7th = 16 - 6x = 6.4
8th = 16 - 7x = 4.8
9th = 16 - 8x = 3.2
10th = 16 - 9x = 1.6 (last place always wins the value of x)
Points awarded when 9 drivers in the race
y = 9
x = 16/y
x = 16/9
x = 1.7777777
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14.222223
3rd = 16 - 2x = 12.444445
4th = 16 - 3x = 10.666667
5th = 16 - 4x = 8.88889
6th = 16 - 5x = 7.111112
7th = 16 - 6x = 5.333334
8th = 16 - 7x = 3.555557
9th = 16 - 8x = 1.7777777 (last place always wins the value of x)
Points awarded when 8 drivers in the race
y = 8
x = 16/y
x = 16/8
x = 2
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 14
3rd = 16 - 2x = 12
4th = 16 - 3x = 10
5th = 16 - 4x = 8
6th = 16 - 5x = 6
7th = 16 - 6x = 4
8th = 16 - 7x = 2 (last place always wins the value of x)
Points awarded when 7 drivers in the race
y = 7
x = 16/y
x = 16/7
x = 2.2857142
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 13.714286
3rd = 16 - 2x = 11.428572
4th = 16 - 3x = 9.142858
5th = 16 - 4x = 6.857144
6th = 16 - 5x = 4.571429
7th = 16 - 6x = 2.2857142 (last place always wins the value of x)
Points awarded when 6 drivers in the race
y = 6
x = 16/y
x = 16/6
x = 2.6666666
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 13.333334
3rd = 16 - 2x = 10.666667
4th = 16 - 3x = 8.000001
5th = 16 - 4x = 5.333334
6th = 16 - 5x = 2.6666666 (last place always wins the value of x)
Points awarded when 5 drivers in the race
y = 5
x = 16/y
x = 16/5
x = 3.2
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 12.8
3rd = 16 - 2x = 9.6
4th = 16 - 3x = 6.4
5th = 16 - 4x = 3.2 (last place always wins the value of x)
Points awarded when 4 drivers in the race
y = 4
x = 16/y
x = 16/4
x = 4
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 12
3rd = 16 - 2x = 8
4th = 16 - 3x = 4 (last place always wins the value of x)
Points awarded when 3 drivers in the race
y = 3
x = 16/y
x = 16/3
x = 5.3333333
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 10.666667
3rd = 16 - 2x = 5.3333333 (last place always wins the value of x)
Points awarded when 2 drivers in the race
y = 2
x = 16/y
x = 16/2
x = 8
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16
2nd = 16 - 1x = 8 (last place always wins the value of x)
Points awarded when 1 drivers in the race (as if we would ever had a 1-driver division
)
y = 1
x = 16/y
x = 16/1
x = 16
z = number of positions behind the 1st place
16 - zx = points awarded
1st = 16 - 0x = 16 (last place always wins the value of x)
Using the charts provided above, here's a breakdown of how last week's division winners would have scored:
martin20az
Round 1 / Race 1: Finished 2nd out of 9 drivers, which equals 14.222223 points
Round 1 / Race 2: Finished 1st out of 9 drivers, which equals 16 points
Round 2 / Race 1: Finished 7th out of 9 drivers, which equals 5.333334 points
Round 2 / Race 2: Finished 2nd out of 9 drivers, which equals 14.222223 points
Round 3 / Race 1: Finished 3rd out of 9 drivers, which equals 12.444445 points
Round 3 / Race 2: Finished 1st out of 9 drivers, which equals 16 points
Subtotal 78.22 points + 1 Pole =
GRAND TOTAL 79.22 points
jlbowler
Round 1 / Race 1: Finished 8th out of 9 drivers, which equals 3.555557 points
Round 1 / Race 2: Finished 1st out of 9 drivers, which equals 16 points
Round 2 / Race 1: Finished 2nd out of 9 drivers, which equals 14.222223 points
Round 2 / Race 2: Finished 1st out of 9 drivers, which equals 16 points
Round 3 / Race 1: Finished 2nd out of 9 drivers, which equals 14.222223
Round 3 / Race 2: Finished 6th out of 9 drivers, which equals 7.111112 points
Subtotal 71.11 points + 1 Pole =
GRAND TOTAL 72.11 points
The2ArmedMen
Round 1 / Race 1: Finished 1st out of 15 drivers, which equals 16 points
Round 1 / Race 2: Finished 9th out of 15 drivers, which equals 7.4666708 points
Round 2 / Race 1: Finished 1st out of 13 drivers, which equals 16 points
Round 2 / Race 2: Finished 4th out of 13 drivers, which equals 12.307693 points
Round 3 / Race 1: Finished 1st out of 14 drivers, which equals 16 points
Round 3 / Race 2: Finished 4th out of 14 drivers, which equals 12.571429 points
Subtotal 80.35 +1 (Pole) +1 (Pole) +1 (Pole) +1 (Triple Crown) =
GRAND TOTAL 84.35 points
Bandit0627
Round 1 / Race 1: Finished 1st out of 7 drivers, which equals 16 points
Round 1 / Race 2: Finished 3rd out of 7 drivers, which equals 11.428572 points
Round 2 / Race 1: Finished 1st out of 6 drivers, which equals 16 points
Round 2 / Race 2: Finished 3rd out of 6 drivers, which equals 10.666667 points
Round 3 / Race 1: Finished 1st out of 6 drivers, which equals 16
Round 3 / Race 2: Finished 3rd out of 6 drivers, which equals 10.666667 points
Subtotal 80.76 points + 1 (Pole) +1 (Pole) =
GRAND TOTAL 82.76 points
EAO-HarleyMan
Round 1 / Race 1: Finished 2nd out of 7 drivers, which equals 13.714286 points
Round 1 / Race 2: Finished 1st out of 8 drivers, which equals 16 points
Round 2 / Race 1: Finished 2nd out of 8 drivers, which equals 14 points
Round 2 / Race 2: Finished 2nd out of 9 drivers, which equals 14.222223 points
Round 3 / Race 1: Finished 1st out of 9 drivers, which equals 16 points
Round 3 / Race 2: Finished 1st out of 9 drivers, which equals 16 points
Subtotal 89.94 points +1 (Pole) +1 (Pole) =
GRAND TOTAL 91.94 points
And this is how this proposed adjustment system would compare to
last Sunday's results:
Division 1
- martin20az -------- 87 points (
84.39 79.22 for Prize B prize purposes only)
Division 2
- jlbowler ---------- 82 points (
79.51 72.11 for prize purposes only)
Division 3
- The2ArmedMen ------ 86 points (
95.42 84.35 for Prize A Prize B)
Division 4
- Bandit0627 -------- 94 points (
83.68 82.76 for prize purposes only Prize C)
Division 5
- EAO-HarleyMan ----- 89 points (
84.26 91.94 for Prize C Prize A)
One tweak to this proposed system that I would be in favor of is to apply
Bowler's system to the Pole Position and Triple Crown
bonus points. In other words, if there are ten drivers competing for Pole Position, the winner of it gets exactly 1 point, but if say, there are only 7 drivers competing for pole, the winner would only get .91 points. On the flip side, if there are 15 drivers competing for pole, the winner would get 1.15 points etc.
Please let me know your thoughts on this new system to determine our prize winners. If you guys don't like it, I've developed a system based on what I call a "success ratio" or a "performance percentage". In short, it basically take the number of drivers that you finished in front of during the night and divides it by the number of drivers you finished behind during the night. Best ratio wins! However, I like the idea of determining our prize winners using points and not ratios. Plus, the ratios get scewed up by the pole bonuses.