To answer this question, I took a similar approach to looking at this workout as I did for Open WODs 2-5 this year (for more detail on the theory behind all this, see my post "WOD Design and Why It (Usually) Pays to be Well-Rounded"). Watching several elite athletes, I timed their splits on each movement. Once I had average times for how long each portion of the workout took, I could look at how much an improvement or decline on each portion of the workout would impact an athlete's final time.

What I did for each of the Open WODs was this:

- Use the average pace for each movement to calculate a baseline score.
- For each movement, reduce the average pace by 20%.
- For the other movements, increase their pace by an amount such that the composite pace is still 1.00. If we have 3 movements, that means increasing the pace of the other two movements by 10% each.
- Re-calculate the time for the workout. The percentage reduction in the overall score from our baseline is the "leverage" for that movement. Higher leverage generally indicates that a weakness on this movement will hurt an athlete a lot.
- Repeat this for each movement.

Based on the archived live footage of the top men's and women's heats from the South Central and Northern California, I calculated splits for as many athletes as possible. Camera angles prevented me from getting the entire field, but in total, I got 11 men and 10 women (I only included athletes for whom I could get all three of their splits). Applying the approach listed above yields these results:

These results would indicate that actually, the row is the most important movement, by a longshot. A 20% reduction in row speed really hurts the athlete, even with an improvement in the other two areas. Problem solved, right?

Well, not really. This analysis is useful, but the underlying assumption here is that an athlete might actually vary by 20% on the row just as easily as they might vary by 20% on the thrusters or pull-ups. In reality, these athletes will all post row times that are much closer to each other than that. Our average row pace for men was a 3:24 (remember, these are elite athletes only). A 20% reduction in pace would give us a 4:15 pace - none of these athletes are rowing at that pace unless they're rowing for at least 10K. On the other hand, the average athlete took 38 seconds to complete the pull-ups. A 20% reduction in speed means taking 48 seconds - that's very possible, even for an elite athlete.

What I did to try to account for this is to calculate the standard deviation in the split time for each movement. For those unfamiliar, standard deviation is a measure of how much variation there is among a set of values. The higher the value, the more variation there is. Below is a chart showing the average time for each station, the average time with pace increased by 2 standard deviations and the average time with pace decreased by 2 standard deviations*.

You can see that even though the row takes much longer, there is much less variation. The coefficient of variation (standard deviation divided by average) was 3% for men's and women's row, 8% for the women's thrusters, 9% for the men's thrusters, 14% for the men's pull-ups and 24% for the women's pull-ups.

With these values in hand, instead of calculating the leverage as I described earlier, I used the following method:

- Use the average pace for each movement to calculate a baseline score.
- For each movement, reduce the average pace by 2 standard deviations.
- For the other movements, increase their pace by a number of standard deviations such that we composite to a 0 standard deviations moved. If we have 3 movements, that means increasing the pace of the other two movements by 1 standard deviation each.
- Re-calculate the time for the workout. The percentage reduction in the overall score from our baseline is the "normalized leverage" for that movement.
- Repeat this for each movement.

Applying that to Jackie, we get the following:

What we see here are two very different stories:

**For the men, the workout is balanced. Thrusters are most important, but the row is critical as well.**The pull-ups aren't vitally important for these athletes because nearly all of them are going unbroken.**For the women, the workout is won or lost on the pull-ups.**The row doesn't separate the ladies that much, nor do the thrusters. However, athletes who were strong on the pull-ups could make up 20 seconds or more on that station alone.

To understand how some of the top athletes hit this workout, consider Jason Khalipa and Pat Barber:

- Khalipa set the current record (5:04) largely based on his blazing row time - his row pace of 314 meters/minute was 2.0 standard deviations above average, his thrusters were right at the average and his pull-ups were 0.8 standard deviations above average (remember, these "averages" are for the elite of the elite).
- Barber finished 15 seconds behind Khalipa (5:19), almost entirely due to the row. His row pace of 274 meters/minute was 2.1 standard deviations below average, and even after going 1.8 standard deviations above average on the thrusters and 1.6 standard deviations above average on the pull-ups, he still couldn't make up all of the ground he lost on the row.

In my view, this is an excellent way to understand the strategy for each workout, but there are limitations. The biggest problem is that data like this doesn't always exist without the benefit of video footage. The process of gathering it is also time-consuming and challenging (I'd love a bigger sample size, but it takes about 15 minutes to get the splits for a single heat). And obviously, this particular analysis really only applies to elite athletes - for someone shooting for a Jackie time closer to 8:00, the row is probably less of a factor since it's likely the pull-ups or thrusters that are sapping more of the time. The averages and the standard deviations need to be calculated using athletes of a similar caliber for them to make sense.

Still, I hope this has provided some insight into what's behind some of the times we're seeing these athletes put up at regionals. Enjoy week three everyone!

***You may notice that for the women's pull-ups in particular, the bars with plus and minus 2 standard deviations are not evenly spaced around the original average. That's because I calculated everything based on the pace (i.e. reps per minute) rather than the time (i.e. minutes per rep). When I converted it back to the time (because it's easier to visualize), the symmetry disappears. For example, 25 miles per hour converts to 0.040 hours per mile, 20 miles per hour converts to .050 hours per mile and 15 miles per hour converts to 0.067 hours per mile. The miles per hour are symmetrical, but not the hours per mile.**

Rowing power is proportional to the cube of rowing speed. The other two movements are roughly linear in terms of speed/power.

ReplyDeletea 3% increase in rowing speed requires a 9% increase in power output. Neat how the standard deviation between the row and the thrusters shows this ratio.

Interesting point. I'd like to see them use calories more often, too, because my understanding is that they more accurately capture power output. So you'd see a lot more variation if the workout required a set number of calories.

DeleteHello! I'd like to thank you for this blog. Your job is really incredible!

ReplyDeleteI think that Jeff found the problem with the first diagram. I've use his comment to find the final time for the 1000m row with 20% less Power (330Watt to 264Watt): 3min40 and that is realistic(3.66 min). This score seems really near +2DS on your graph!!!

With 20% less Power and 10% more one thrusters and pull-ups , final score is 5min28 for the event (+2.2%). So rowing seams to be as important(more important?) that the thrusters for this WOD.