Thursday, May 14, 2015

Can I use 5k time to predict Beer Mile time?

Next week I will be timing a variation on a Beer Mile: a Beer relay. In this event, the rules are pretty simple. Each team has two members, who proceed as follows:

1. Teammate #1 drinks a beer and runs a half-mile
2. Teammate #2 drinks a beer and runs a half mile
3. Repeat 1 and 2 above.
As a timer, this presents an interesting difficulty: How many people can do this event at once without chaos ensuing?

My initial hunch is that we can time 50 teams at once. But if 50 runners are passing through the finish line area in roughly the same amount of time, this could be problematic. Then we'd have the craziness of those runners finishing and their teammates trying to chug beers, and it might not be possible to keep track of everyone to identify the winners (we're tracking the top male, female, and mixed teams).

What I'm hoping is that beer-chugging ability and running ability will naturally sort everyone out, and the runners will be nicely spread out by the time they reach the finish, even after just a half mile. This is certainly what happens in the 5Ks we time. In fact, I have lots of data about real-world 5K times from all the races I have timed to back this up. But just because runners spread out over 5K doesn't mean they'll spread out as much over a half mile.

So I decided to take a little survey in a couple different running groups I participate in. I asked three questions:
1. What is your 5K PR?
2. How fast can you run a half-mile (805 meters)?
3. How fast can you chug a 12-ounce (355 ml) beer?
What I wanted to know is how well peoples' 5k times correlate to their half-mile and beer-chugging times. Thirty-one people responded, and after removing three folks who are either freakishly slow in the half-mile or accidentally entered their half-marathon time instead of half-mile time, I created this chart of the results:

 Click for a larger version
The chart correlates half-mile time (blue) and beer-chug time (red) to 5K PRs. As you can see, half-mile time correlates pretty well with 5K PR. The R-squared value for that data suggests that 5K time explains about 48 percent of the variance in half-mile times. By contrast, 5K time explains only 8 percent of the variance in beer-chugging times. The beer-chug times are all over the map!

So how would that correspond to an actual race? Well, if everyone who answered the survey completed the first lap of the race in the times indicated in the survey, the finish would look like this:

There might be a little bunching among the first 5 or 6 finishers (four runners are each predicted to arrive after a total of 180 seconds), but after that things spread out quite nicely. And let's not forget, these survey respondents, members of running clubs, are faster than your typical 5K runner; the slowest among my respondents reported a sub-30-minute 5K, whereas in the last 5K I timed, 73 percent of the participants were slower than 30 minutes! Also, I think it's reasonable to expect that running times will be unequally affected by the consumption of beer, with some runners able to shrug off those effects more easily than others.

But to answer the initial question in this post, how does 5K time correlate to Beer-Mile time? We can't know for sure since we don't know how the beer consumption will affect running pace, but assuming its effects are negligible, this chart correlates 5K PR to total time for chugging a beer and running a half-mile:

The R-squared value suggests that this correlation may be significant; 5K time explains 50 percent of the variance in first-lap Beer Relay time. But of course, we won't know for sure until we run the actual race!