mathematical vs real limits

average race paces chart
average paces from various races starting in 2012 until mid 2013, including MAF tests for 7 months


I’m no mathematician, I’ve always been bad at math. But that’s not keeping me from playing around with numbers and charts.

Math is not everything, people defy probabilities on a daily basis. We are more than the sum of a few equations. But having said that, there are some real world limits that we bump up against that can be quantified and perhaps useful when finding patterns and setting goals.

So with the chart above I’ve laid out my various road race times from the last couple of years to see what it can tell. (trail runs are too unevenly paced to make any sense of) From a progress point of view it looks promising, the MAF score is coming down nicely. Road races are few and far between for me, so the results there are pretty flat at the moment. Hopefully my next marathon in November will produce a nice step down.

Is there a way to extrapolate from this chart how I may perform in the future? I know that past performances cannot be reliable in projecting into the future, but that doesn’t stop most people from guessing. The stock market is full of people who do this on a daily basis. I think in this case there’s not enough data points to make a guesstimate of where my fitness level will be in say 2 years. I do have some very loose goals for the near term, medium term and long term, but these goals are always shifting and being adjusted. Especially the longer term goals. Hopefully this chart when filled in with more races will give me a clearer picture of where I can expect some hard limits.

race pace curve graphs
some leveling off of the race paces has to happen at some point

A gradual falloff in performance is expected. It’s impossible to improve beyond a certain point of course. But will the line follow a relatively even curve or will it be a messy jagged affair? Also, with changes in training volume and technique, evaluating the reasons for progress become difficult. Am I getting better due to the type of training or the increase in volume? I plan on gradually introducing new training techniques over time, so this should make it a little easier to point out causation. Perhaps this gradual fitness buildup I’m doing will give me a relatively even curve, such as the sketch shows above.

other thoughts

Is it counter productive to find an artificial limit? This could be used as an excuse not to exceed the limit. What’s the point in trying to get better if the data show a physical limit that is “impossible” to breach?

What kind of curve will the data distribution reveal? Is this an exponential curve? What will the asymptote be? This might have something to do with extreme value theory I think. I suppose I have to brush up on some real math, sigh.

I’ll revisit the race chart once or twice a year from now on when I have some more data points. Hopefully I can read something from the tea leaves as time progresses.

I also plan on upping my road race schedule next year just a little. I prefer trail running overall, but still enjoy running at a faster pace on roads. There’s something to be said for mixing up the type of running one does. If all I did were long ultra races I think I’d just be good at running slow.