a. Final ranking vs. WOD 1 ranking
b. Final ranking vs. WOD 2 ranking
c. Final ranking vs. WOD 3 rankings
The following is a brief statistical analysis of the Midwest sectional. The fundamental purpose of this analysis is to determine the relative importance that each workout had on the final ranking of each athlete. In an ideal competition each workout should equally predict/determine the final rankings (unless for some strange reason the organizers feel one workout should contribute less weight than others, but let us assume that is not the case).
The degree of predictability, expressed as a percent predictability, can be determined using a least-squares regression analysis. But don't sweat the details, the basic idea itself is very simple. For each workout make a graph of each athlete's final ranking in the competition vs. their ranking on the individual workout (see figures a-c above). If a workout is strongly predictive (close to 100%) all the points on the graph will made a tight band about a line i.e. 1st place overall gets first place on WOD 1 and 10th place overall gets 10th on WOD 1 etc.
From the above figures we see that WOD 1 (The Air Force WOD) forms a tight band of points, strongly predicting the final outcome (69% predictability). Whereas WOD 3 appears to have randomly scattered points, with a very low predictability of 28%. While WOD 2 has a predictability of 47%. This analysis method can be also used for a combination of WODs. WOD 1 & 2 have predictability of 89%, WODs 1&3 giving 82%, while WODs 2&3 yielding 56%.
From these data it is clear that WOD 1 was overwhelmingly the determining factor of the final rankings. WOD 1 had a higher predictability, 69%, than both WODs 2&3 combined, 56%. In other words, the competition (from a final rankings point of view) was essentially over after WOD 1. Therefore specializing in the modalities of WOD 1 was a huge advantage in this competition.
When designing a competition it is obviously difficult to exactly determine the relative weight of each workout prior to the competition. That being said, making WOD 1 shorter (perhaps removing an exercise entirely, such as the front squats) may have made this a much more balanced competition. Alternatively, WOD 3 could have been increased in length.