After posting a lengthy essay on the benefits of switching to the Standard Deviation scoring system, I felt like I had to apply the scoring system to this year's Games and see what I could learn. Obviously it would be interesting to re-calculate the final standings with the new system, but I think there are a few other things that we can do with this new system. Because we are now scoring based on performance rather than simply rank, this new system allows us to compare events and individual performances across separate events. I'll try to keep this one relatively short, just hitting on the highlights of what I found.
Remember all events are converted to a power output (think reps or stations per minute, instead of time to completion). This was a painful process b/c of the way HQ scored athletes who did not finish a workout in the allotted time. I also generally assumed every "station" was worth equal weight (so on the Medball HSPU, the 8 medball cleans were equal to the 7 HSPU). This was the simplest solution. On the obstacle course, because I was basically forced into using the rankings and not the actual performances, I assumed a normal distribution and converted the ranks to an equivalent number of standard deviations from average. If HQ were to adopt this scoring system, they'd have to make the decision on how to weight the stations.
Anyway, enough with the math and onto the results:
Which event had the widest spread?
We can judge this based on the coefficient of variation for each event, which is the standard deviation divided by the average.
For the men, the widest spread came in the Medball-HSPU workout. The average score was 0.60 stations/minute (9:56) and the standard deviation was 0.18 stations per minute, giving us a coefficient of variation of 29%.
For the women, the widest spread also came in the Medball-HSPU workout. The average score was 0.56 stations/minute (which translates to finishing in 10:48, which is over the cap) and the standard deviation was 0.32 stations/minute, giving us a coefficient of variation of 58%. This shouldn't be surprising, considering the winning time was just over 5 minutes, but more than half the field didn't even finish.
Which event had the tightest spread?
For the men, the tightest spread came in the sprint. The average score was 6.60 meters/second (45.48 seconds) and the standard deviation was just 0.32 meters/second. The coefficient of variation was 5%. The second-tightest was Pendleton 2 at 8%.
For the women, the tightest spread also came in the sprint. The average score was 5.83 meters/second (51.49 seconds) and the standard deviation was just 0.31 meters/second. The coefficient of variation was 5%. The second-tightest was the clean ladder at 8%.
What was the most dominating individual performance over the field?
We'll measure this based on the number of standard deviations from the mean by the winner.
For the men, this came in the Rope-Sled event, where Matt Chan had a result of 1.32 stations/minute (7:33.6), which was 2.80 standard deviations above the average score of 0.87 stations/minute (11:48).
For the women, the most dominating performance came in the clean ladder, where Elisabeth Akinwale had a score of 235.6, which was 2.42 standard deviations above the average of 195.76.
What were the widest and tightest margins between first and second in an event?
Similarly, we're looking for the standard deviations between the first and second place finish.
For the men, the widest gap came in the Rope-Sled event. Chan was 0.89 standard deviations ahead of second-place Jason Khalipa, who had 1.18 stations/minute (8:27.0). The closest event came in the sprint, where Nate Schrader finished in 7.14 meters/second (42.0 seconds), just 0.11 standard deviations ahead of second-place David Levey at 7.11 meters/second (42.2 seconds).
For the women, the widest gap came in Elizabeth. Deborah Cordner Carson had a score of 25.09 reps/minute (3:35.2), which was 1.04 standard deviations ahead of second-place finisher was Kristan Clever at 21.79 reps/minute (4:07.8). The tightest race came in the clean ladder, where Lindsay Valenzuela basically tied Akinwale (she had the same lift but completed one fewer deadlift).
*In the events before any cuts, the biggest gap on the women's side came in the ball toss, where Cheryl Brost's score of 61 points was 0.53 standard deviations ahead of second-place Elizabeth Akinwale (57 points).
Seriously, what do the revised standings look like?
OK, I'm going to caveat this by saying that it's not totally fair to say the standings would have looked like this if we had scored the event differently. Obviously the athletes may have approached workouts differently had they been higher or lower in the standings, and they may have pushed harder for those extra few points in each event when more than just a simple ranking was involved. I think this is probably the least important thing we can learn from the new scoring system, since the event is done and there's nothing we can do to change it.
But that being said, for amusement purposes only, here is your revised top 12 for men and women (no one from outside the top 12 could move into the top 12 because of the cuts):
*UPDATED 1/19/2013 - An error in the Obstacle Course scoring has been fixed and these have been revised. Only major shift was Foucher going from 4th to 2nd on the women's side. Otherwise pretty similar to prior results.
1. Rich Froning (15.49)
2. Matt Chan (11.97)
3. Scott Panchik (8.75)
4. Jason Khalipa (7.99)
5. Kyle Kasperbauer (6.96)
6. Dan Bailey (6.57)
7. Austin Malleolo (5.27)
8. Marcus Hendren (4.82)
9. Nate Schrader (4.23)
10. Graham Holmberg (4.07)
11. Ben Smith (2.77)
12. Chad Mackay (1.78)
1. Annie Thorisdottir (13.70)
2. Julie Foucher (9.19)
3. Talayna Fortunato (8.77)
4. Kristan Clever (8.55)
5. Camille Leblanc-Bazinet (6.14)
5. Lindsey Valenzuela (5.65)
6. Elisabeth Akinwale (5.60)
8. Valerie Voboril (5.28)
9. Jenny Davis (4.74)
10. Rebecca Voigt (2.84)
11. Stacie Tovar (1.43)
12. Christy Phillips (0.75)
*These scores assume that the ball toss, broad jump and sprint were given half the value of the other events.