Running Math

So it’s just 7 days until my next half marathon and I’m really not sure if I’m going to be able to achieve my goal of a sub-2 hour finsih. I’ve been far more diligent in my training since… well, pretty much since the first half marathon I ever ran. I completed all my hill runs. I’m doing my interval training. I did the long Sunday runs with my running club¹. I feel strong and I have improved my pace, but I just don’t know if I’ve improved it enough to reach my goal.

I’m hoping to see this (or better) when I cross that finish line next week:

Image Credit: Posted by Adam Fagen on Flickr.

The thing with races, you see, is that you always run way faster on race day than you do when you are doing a training run. You aren’t even really trying to do it – you are just full of adrenaline and the energy of the crowd takes you away and you start running and you don’t feel like you are running that fast but when you check your pace, you are. When I ran the Hollywood Half marathon I was convinced that the 2:15 pace bunny² was screwing up, because Alicia and I were way ahead of her and I was thinking “there’s no way we are running faster than a 2:15!” And then it turned out that we were – we finished in 2:09:57!

But the question is, just how much faster do you run on a race than during training? For example, the longest distance that I do in training is 20 km and my 20 km training run this time was 14 minutes quicker than my 20 km training run last June for Scotiabank. My finish time for Scotiabank last year was 2:15:05. Which begs the question: will a 14 minute improvement in my 20 km training run translate into a 15 minute improve on race day?

To try to figure this out, I turn to my old friend, Math. As luck would have it³, I have records of my 20 km training times for my last 7 half marathons (plus the finish times for my last 7 half marathons, of course). Now, I once swore to my MBA stats prof that I would always graph my data, so here’s a graph of said data:

The times are shown in seconds per km (rather than minutes:seconds per km) because despite all the awesome things that MS Excel can do, handling time values is not one of them. As you can see, my pace for my 20 km training time is not a good predictor of my pace on race day. On the plus side, my race pace is *always* faster than my training pace, but it has ranged from a mighty 1:15 per km faster (Scotiabank 2011) to a meagre 0:08 per km faster (Edge to Edge Tofino half marathon, of the horrible hills and knee injury infamy). I run an average of 0:46 per km faster on my races than my 20 km training runs, but given the aforementioned wide spread of the data, I wouldn’t take that average to be a good predictor Moreover, I hope it isn’t, because if I run my race next Sunday at 45 seconds faster than my 20 km training run, I’ll finish the half marathon in 2:13, which is despairingly slow.

Just to be sure that the graph wasn’t misleading me, I ran a linear regression analysis and found there is not, in fact, a statistically significant linear relationship between my 20 km training time and my pace time⁴. I even tried calling the Edge to Edge Tofino half marathon an outlier, so I could remove it from the data set, but there’s still no statistically significant relationship.

So, in conclusion, apparently my 20 km training pace is not a good predictor of how I’ll do next week. There’s just too many other facts at play I guess – whether I was giving ‘er on my training run or not, conditions on race day, whether the race route is insanely hilly à la Edge to Edge or a beautiful net downhill like Scotiabank⁵.

Something that Daniel taught me that he does with his races is having not just one goal, but a staged series of goals. If you only set a goal that you know you can achieve, then you aren’t going to have to push yourself to achieve it. But if you only set a goal that is really, really hard to achieve, you run the risk of not being able to appreciate what you do achieve because you didn’t reach that single, really tough goal that you set for yourself⁶. So I’m going to go into this race with three staged goals:

1. a sub-2 hour half marathon – This is my ultimate goal. As described above, I don’t know if I will achieve this, but I don’t think it’s totally out of the realm of possibility⁷.
2. a new personal best. My current PB Is 2:07:23, so I don’t acheive a sub-2 hr but I do better than 2:07:23, I willl be happy.
3. finish. Even if I don’t set a new PB, it will still be an accomplishment to finish a half marathon. And given that this is my 12th half, I think finishing an even dozen of these races will be an accomplishment to be proud of.

Footnotes:

1. Except for a few weeks where I have something else going on on Sunday morning, in which case I completed my long runs on my own at another time. [↩]
2. i.e., the person who runs at the pace that will result in finishing the race in 2 hrs 15 mins. Races have people like this for all sorts of different paces, so if you want to achieve a specific finish time, you can run with the corresponding pace bunny. [↩]
3. Where by “luck”, I mean, my nerdy habit of keeping records of everything. [↩]
4. I was hoping, before I started this, that I’d find a statistically significant relationship and then I could use the equation of the line to predict my finish time! Math, you have dashed my hopes! [↩]
5. Happily, next Sunday’s race route is also net downhill! [↩]
6. I’ve seen this happen before where someone sets a stretch goal and though they didn’t quite reach it, they really improved over their last race, yet they are sad at the end of the race and can’t enjoy the fact that they set a new personal best or took at a good amount of time off their previous race. [↩]
7. Unlike the last few times where I started training with a sub-2 hour goal, but wasn’t really diligent in my training and knew by race day that I would not be anywhere near that. [↩]