Good Stats     Bad Stats

I watched the men’s downhill races yesterday. Matthias Mayer won the race. But as I watched the individual runs it was not at all clear that he would be expected to do so. The reason for this was in how the local (United States) network showed the split times as each racer moved down the course. My question then is there an alternative way to present the race that would give the viewing audience a better perspective on how their favorite racer is doing as he progresses through the course?

To be at bit clear on what happened let me focus on just three of the racers – Mattias Mayer, Bode Miller, and Christof Innerhofer. They finished in first, second and eighth place respectively. Mayer was the first of the three down the course. So when Miller and Innerhofer ran the course Mayer already had the best time.

Miller was the second of there to run the course. After the first split he held a lead of 0.27 seconds over Mayer. After the second spit he held a lead of 0.31 seconds over Mayer. These were the numbers that the media presented to their audience. Yet Miller lost the race by 0.52 seconds. The media made much of Miller’s “errors” after the second split time.

Innerhofer had a very similar experience to that of Miller. He led Mayer by 0.58 seconds. He still had a lead of 0.54 seconds at the second split. Yet he lost the race by 0.06 seconds.

The fallacy in the media presentation was in comparing the race times of Miller and Innerhofer to those of Mayer for each split. Reviewing the split times for the top ten finishers it becomes very clear that Mayer times were only about average for the first part of the course. He won because of how well he did on the second half of the course. At the first split Mayer was sixth of the ten top racers. At the second split he was also only sixth out of the top ten racers. At the third split he moved up to third place. It was only at the fourth split that he moved into the lead. Innerhofer was actually in first place at the first, second, and third splits.

As a consequence of this because of this both Miller and Innerhofer looked like they were doing much better than was actually true because their times for the first two splits were compared to Mayer more average times. Thus the surprise when the racers got the end of the course and had both lost to Mayer.

The analyst blamed Millers lose on his performance on the last part of the course. But that is where he made his errors. In truth Mayer made his errors, if you want to call them that, on the early part of the course. It is just that his errors were of less consequence. The analysts choose not to focus on that part of the race. Had they done so, they would have been saying that both Miller and Innerhofer outperformed Mayer on that part of the course.

This is really an issue of variance. Each racer performs differently on each section of the course. There is natural variation due to course conditions, difference in the course between racers depending on the tracks of the previous racers, changes in weather conditions as the race progresses, and where each racer makes his errors or does an outstanding job of racing. All of this variability is ignored when subsequent racers split times are compared only to those of the lead racer at that point in the race.

That only give an understanding of what happened in the race. The open question, and I do not offer a solution, is how to present the race result in real time so that the view has a better idea of how each racer is doing as he descends the course. That presentation also has to be clear to the viewing public who we should all assume does not understand these statistical nuances. I wonder if better understanding would occur if the splits were compared to the best times up to each split in the course rather than to the time of the best racer at that point.

The full results, including all the spit times for race can be found here.