The economics of comparative advantage and Usain Bolt (VIDEO)

Welcome to Part four of Liam Lenten’s Some Sports Economics.

Welcome to Some Sports Economics, a six-part video series explaining economic concepts through sport, by La Trobe University senior lecturer, Liam Lenten.

In the fourth part of this series, Liam explains the economic concepts of absolute and comparative advantage - and how Jamaica’s decision not to run the world’s fastest man (Usain Bolt) in the final leg of the Beijing Olympics 4x100m relay final helped them win the race.

You can watch Liam explain the video.

Part four of Liam Lenten’s Some Sports Economics.

Or read through the transcript below.

As fans, we often get frustrated when our team loses – it’s natural to blame someone…often the coach?

We ask questions, such as: ‘why the hell does the coach play player X there’? The following is an elegant case study for an Olympic year. We need think back no further than the last Olympics in Beijing, 2008, for an illustration.

The example? In relays, the traditional sequence of runners in a team is picked from slowest to fastest. Selectors of the Jamaican Men’s 4×100 metre relay team confronted this very conundrum. Jamaica faced some hot opposition (fortunately for them, Great Britain was disqualified in their semi, while USA dropped the baton in theirs) leaving Caribbean rivals Trinidad and Tobago qualifying first for the final by five one-hundredths of a second, but Jamaica were still hot favourites for gold, because they had ace up their sleeve, with Usain Bolt (missing in the semi) to come back into the line-up for the final, but where… in what position?

He was selected in the third leg, begging the question why, since he was clearly faster than Asafa Powell (who was picked as Anchor – the final leg)? The boring answer is that analysts will talk about how Bolt was a 200 metre specialist earlier in his career, giving him more experience at running the bends.

The more interesting (that is, economic) answer, applicable to all sorts of similar problems in many industries, is based on the distinction between absolute and comparative advantage. In its purest form, it’s used as a means of explaining why countries engage in trade of goods and services, leaving everybody better off.

Let us imagine that the grid below outlines times selectors expect both to run their splits. From this, it is clear that Bolt has the absolute advantage over Powell in either position, but since there is only one Usain (not four), you can only run him in one position – so which? In short, comparative advantage tells us in which position Bolt should run.

Note also from the grid that both run the straight quicker than either runs the bend, which my experience in athletics some time back tells me is completely logical.

Anyway, how to work this out? That old economic chestnut – opportunity cost (defined simply as: best opportunity forgone).

Opportunity Cost:

OC (Bolt at Third-leg) = 9.74 - 9.65 = 0.09

OC (Powell at Third-leg) = 9.85 - 9.73 = 0.12

Now, if we run Bolt in third, we obtain a time from him of 9.74, but in doing so, we forgo running him as Anchor, hence subtract 9.65 from this, leaving us with nine one-hundredths of a second. Using the same logic, the opportunity cost of running Powell in third is twelve hundredths of a second.

The objective is to: minimise opportunity cost (ultimately, it is a cost) – so, select the runner with the lower opportunity cost in that position. Conclusion: Run Bolt in the third-leg.

Usain Bolt returns for the relay final, but in what position?

But that’s not quite the end of the story; we need to know that the true also works in reverse.

Opportunity Cost:

OC (Bolt at Anchor-leg) = 9.65 - 9.74 = -0.09

OC (Powell at Anchor-leg) = 9.73 - 9.85 = -0.12

Contrapositively to before, running Bolt at Anchor produces 9.65 but imposes forgoing 9.74, leaving an opportunity cost of negative 0.09 seconds, and via equivalent reasoning, .12 seconds is the opportunity cost of Powell as Anchor.

Conclusion: Run Powell in the anchor-leg. This story has a happy ending! Jamaica won the final, astonishingly by almost a full second, smashing the 15-year old World Record in the process – a Tour de Force of rational economic decision-making in sprint team selections.

Watch previous videos from Some Sports Economics:

When scoring an own-goal is the only way to win (VIDEO)

Full versus half-full stadiums in maximising profits (VIDEO)

The economics behind inelastic ticket pricing (VIDEO)