Friday, January 14, 2011

Improving Marginal Gains

One challenge of physical training is facing up to diminishing (or marginal) gains. Even if we train perfectly, there are limits to how much faster we can get. Sometimes, we put in huge amounts of work for a tiny reward; the rewards-to-work ratio diminishes. Sometimes, even, we put in huge amounts of work and get slower--in this case, not only do we have diminishing marginal returns, we have negative marginal returns.

Sort of like beer drinking. The first one's great, giving you perfect happiness (see below). The second's almost as good, but then diminishing marginal returns kicks in, and by the fifth or sixth, things are going south real fast. At some point, you're facing negative marginal returns.

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Our markets are set up in recognition of this, so that the value of, say, the second tub of ice cream, or, say, that extra 64 ounces in that 300 ounce Mammoth Gulp Sludge Bucket, costs less than a mere 300 ounce Big Gulp. This is the principle of Costco--the more you buy, the less you pay for it.

It's also, as Louis CK observes, the principle at Cinnabon:

This kind of declining returns is not, mind you, a result of aging or decripitude. That's a wholly other thing, equally sucky. No, this is simply a result of having limited appetites and capabilities.

Here's another example, which helps illuminate the principle of marginal returns in physical training:

Suppose we take Usain Bolt, put him around in 1900 when the first 100 meter dash events were held, and then make him perpetually young. What kind of times would he have run then, and what kind of times would he run now?

I suspect his 100 meter times would be a little faster than those recorded in the era, but not much, since training methods and better equipment are in large part responsible for imrpovements in time. Bolt would get better, quickly at first, but then not as quickly, and then, quite rarely. He would best his previous times less and less, and less and less. His rate of improvement would slope downward toward 0, looking exactly like the rate of improvement of humanity a whole since 1900:

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The idea is that Bolt's rate of improvement, even if he did not age and he trained perfectly year after year, would slow to an imperceptible level of improvement. Eventually, he would break his record every century, then every millenia, then every billion years, and so on.

And that's supposing that he kept at it, the Earth was not consumed by the Sun, and so on.

Here's another example taken from cycling: the world hour record. As cycling became popular, fitness and equipment improved, and the record fell in gobs, but over time its improvement has slowed. Humanity is pushing its limits.
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Our rate of improvement as a species in the hour record has the same downward slope as the 100 meter days record. We're still improving, but we're doing it at a decreasing rate. We're witnessing declining marginal returns.

The same principle of declining marginal returns that holds humanity's upward trajectory in check also limits individual fitness development.

Let's say you started training in 2005, and you tracked your FTP over six years. It would probably look something like this:
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The very sad part about personal development is that even if we train optimally, we will see declining, then negative marginal returns--even if we're doing everything right! Lance Armstrong, for example, probably trained about as perfectly as possible for the 2010 Tour, but not only had he not improved, his fitness had clearly declined from 2009.

Then again, maybe Lance just learned to accept his limitations and be happy. "It is, wrote Erasmus, "the chiefest point of happiness that a man is willing to be what he is."

Thankfully, we can never conclusively say when we hit declining marginal returns because we can never conclusively say when we train optimally. We know way too little to say, "It's downhill from here." Most of us have a long way to go before we hit our limitations.

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