I'm a big fan of the Olympics. My family was watching Men's Moguls last night and we were completely baffled by the scoring. I am writing this post to reveal how moguls are scored (almost). I still have a question that I haven't figured out. From Fisski as well as the commentators, the basics of the scoring are clear. Scoring is comprised of 3 components: turns, air, and speed. Turns and air are judged while speed is objective. In turns, 5 judges score the run with he lowest and highest scores thrown out. The final score gives 50% weight to turns, 25% to air, and 25% to speed. This all seems pretty clear, the difficulty comes when we try to decipher the scores provided by NBC as we are watching the coverage. The most striking example was when the last skier, Guilbaut Colas, completed his run and we saw the scores. It turned out that he was 6th while the American, Bryon Wilson, remained in 3rd. Looking at the scores (table below) provided by NBC this is completely perplexing.
 Rank Turn - J1 Turn - J2 Turn - J3 Air - J1 Air - J2 Speed Total Wilson 3 4.7 4.5 4.6 1.9 2.0 6.82 26.08 Colas 6 4.7 4.6 4.6 2.2 2.2 7.33 25.74
In this table, I have already thrown out the highest and lowest turn scores. From these numbers, it is pretty clear Colas is the better skier. He had 0.1 more for turns, 0.5 more for air, and 0.51 more for speed. Yet Colas is 6th and Wilson was 3rd!! What is going on here?!?!?! Previously we had seen perplexing results that generated a hypothesis. The skiers (both men and women) who did harder air tricks always received less points for air according to the NBC scores. Since this suggests that all skiers should do easier tricks, we thought something might be up. Finally, we found the vancouver2010 site with all the results from the Olympics. In the table shown above, only the scores for the first jump are shown. The missing information is the scores for the second jump as well as the degree of difficulty for the jumps. So the table above should be updated to the table shown below.
 Rank Turn - J1 Turn - J2 Turn - J3 Air1 - J1 Air1 - J2 DoD1 Air2 - J1 Air2 - J2 DoD2 Speed Total Wilson 3 4.7 4.5 4.6 1.9 2.0 1.41 2.2 2.2 1.24 6.82 26.08 Colas 6 4.7 4.6 4.6 2.2 2.2 1.24 1.6 1.7 1.09 7.33 25.74
Now it is at least clear how Wilson beat Colas. Wilson's second air had exactly the same degree of difficulty and scores as Colas's first air. But Wilson's first air had better scores and higher degree of difficulty than Colas's second air. This was enough to overcome the lower turn and speed scores. We are pretty close at this point, but still not quite there. It seems pretty clear that to get the total turn score, you simply add up the 3 judges turn scores. The speed score is what it is. Fiswiki says the air judges are scores are averaged but it doesn't say whether they are averaged for each jump or the total for both jumps are averaged. Either way the math doesn't work out. The closest I can get is to compute the judges scores for both jumps independently and then average these, but with that calculation Wilson should have had a 26.10 and Colas a 25.76. Perhaps the reported judges scores are just rounded? Anybody have any thoughts?