Now is the time of year when athletes and coaches are planning and implementing the early stages of training with an eye toward the coming year. In that planning the first step will be to lay out goals for the coming season.
We all have a goal of some sort. Many will be competitive goals like, qualifying for the XTERRA World Championship, winning one’s age group at a race, or maybe beating one’s training partner. For others goals will be fitness based, losing weight, improving one’s run, or so on, which, arguably could be grounded in performance as well. Either way, we all have a goal of some sort and will use it to develop our strategy for the coming year.
However, in developing that strategy toward achieving our goal are we truly considering what is in our best interest?
Often, it is very easy for coaches and athletes to get blinded by what they want rather than what they need to achieve their ambition. This is where Game Theory comes in. By using Game Theory you can identify where your greatest opportunity for improvement lies and move in that direction with your planning.
Game Theory is a multi-faceted and complex concept of higher mathematics, statistics, and philosophy. For our purposes I will be considering one aspect of game theory, minimax, and looking at it from a very simplified perspective.
In its most basic explanation minimax is the the idea of minimizing your maximum possible loss. Wikipedia states:
Minimax is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario. When dealing with gains, it is referred to as “maximin”—to maximize the minimum gain. Originally formulated for two-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty.
I should begin by saying I realize I am not interpreting Minimax strictly or accurately from a mathematical game theory perspective. Minimax is most often applied to a “zero sum” game, meaning a two sided endeavor where one side wins and the other loses. I however am adapting this to off-road triathlon and considering me as one player and the rest of the race’s participants as the other player. So, “second is the first loser” perspective.
From there I am considering how my training and preparation is designed based on what I know from mine and my opponents race performances.
My Example: If I Knew Then What I Know Now
I came to triathlon from a running and cycling background. I ran in college and raced bikes in the summer and professionally post college before getting into triathlon. However, I think I am hard wired to think of myself as a runner first and foremost.
Coming into triathlon, swimming was by far my weakest event. I had been a lifeguard but had never swam competitively. Starting my triathlon career in XTERRA in ’99, my swim wasn’t a huge issue as my mountain bike and run skills were strong enough I could still podium even after losing over 5 minutes on the swim.
Still, being that slow in the water was a significant detriment to my racing, and more importantly… embarrassing. After all, it was the motivation for “Kahuna” Dave Nicholas to dub me, Jimmy “The Rock”, as in, swims like a rock.
Going into 2018 my goal is to be competitive again. I’ve had several years away from racing and would like to get back to, or better than, the level I was at when I was racing well.
In beginning my planning this year I realized I’ve often made the mistake of wanting to follow the same basic plan I’ve done in previous years. This year I committed myself to not simply doing what I did in the past and expecting the same or better results. Rather I vowed to open my mind to options, possibly solutions, I had not explored with my previous training programs.
In opening my mind to the possibilities I began to realize that in the past I and my coaches had almost always began our approach to training from a flawed foundation that I am a very good runner, a strong cyclist and a weak swimmer. Therefore, improving my swim was the priority while maintaining my bike and run would hopefully offer some gains as well.
However, even in my best races I have found myself usually 5-10 minutes off the lead in major events, like XTERRA Regional or World Championships. Normally I would loose a few minutes on the swim, several minutes on the bike, and have one of the top run splits. The argument from my coaches being, had I come out of the water with the lead I would have ridden much better and closer to the lead because I would not have had to fight my way through tens or sometimes hundreds of other athletes who swam faster than me. In off-road triathlon where the passing on the mountain bike can be difficult at times I was losing minutes to the faster swimmers who had a clear trail.
I believe this was flawed logic.
Let us consider triathlon in its basic parts:
- The Swim is the slowest and usually shortest piece of the race by distance and duration, and its first so physical breakdown is a very limited factor. The time from first out of the water to last out of the water is usually 30-40 minutes over 1500m
- The Mountain Bike is the longest and fastest piece of the race. The difference from first to last split is usually a few hours.
- The Run is longer than the swim but usually around 1/3 the duration of the bike. The time difference from first to last split is usually close to 1 hour and fatigue can be an greater issue at the end of the race.
The above is differences for everyone in the race, but if we consider our main competitors those total time differences are less but the relative percentages remain. In general we stand to lose the least in the swim, and the most on the bike, with the run falling in the middle. So, for most people you will want to focus on the bike, unless you have a significant deficit (or sometimes fear) to over come on the swim or run.
Thus, I should focus on my bike performance and let my run and swim continue to negate each other.
If we look at this for myself, I lose 1-3 minutes at most in the water (my swim has improved since my early days). I’ll loose up to 10 minutes or so on the bike. While the run will be a gain against most of my competitors.
So, in the end, the loses I see on the swim are negated by the gains I see on the run, and the loss on the bike is what remains to determine my placing at the end of the race.
If we apply minimax to these statistics it really doesn’t matter what I do on the swim, because a 1-2 minute gain doesn’t change much overall and I will usually gain something on the run. However, none of that matters if I continue to lose time on the bike. Thus, I should focus on my bike performance and let my run and swim continue to negate each other.
In using myself as an example I should see an overall race improvement by prioritizing where I am losing the most, the bike. Thus minimizing my maximum potential loss, rather than prioritizing what is my weakest portion of the triathlon, the swim, for a minimal potential gain.
That said, everyone is a different athlete. An argument could be made for many people that they put so much effort into swimming that it effects everything down the line in the race, so, they should focus on improving their swim to benefit the whole triathlon. Or, perhaps and athlete puts so much focus and effort into the bike that whatever gains they see in that portion are sacrificed in the swim and run.
We are all individuals, but by using a bit of game theory and giving yourself an honest and realistic assessment of how you are approaching your goals, and where the greatest gains can be made you stand to make the best decisions in determining a strategy and training plan for your upcoming season.
** Mathmaticians in the audiance, please keep in mind this is game theory and minimax in is most basic assesment, I’m sure there are many flaws in my application of those concepts. **