To illustrate the concept of fungibility, Deirdre McCloskey (1985, p. 7, PDF) gives an example from basketball.

She claims that the last two points scored are no more important than any two points scored earlier:

The University of Iowa beats the University of Michigan for the Big Ten basketball championship by two points in double overtime, 70 to 68. Whose two points won the game? One's first thought is to look to the last points made. But points are fungible. Any two points can be viewed as the crucial points that make the difference between a score of 68 to 68 and 70 to 68. The shot that Weisskoff made in the first 5 minutes of play counts as much as the last. For the purpose of making the score what it is, there is effectively no last, no crucial, point.

Is this analysis correct? And if not, in what sense are the last two points more important than any two points scored earlier?

Two examples to illustrate the connection here to economics:

Example 1. Two politicians A and B are running for village mayor. The electoral process in this village is unusual — the two politicians have 12 hours to take turns going door-to-door soliciting votes. The end result is that politician A beats politician B by 35 votes to 34.

Question: Is the first vote scooped up by politician A just as important as the last vote?

Example 2. Two Girl Scouts C and D go door-to-door trying to sell boxes of Girl Scout cookies. The Girl Scout who sells the most wins Girl Scout of the Month. The final score is 35 to 34, with Girl Scout C winning by one box.

Question: Is the first box sold by Girl Scout C just as important as the last box sold?

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    $\begingroup$ This seems to be a question about baseball, not economics. $\endgroup$ – Michael Greinecker Aug 2 '17 at 9:29
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    $\begingroup$ I'm voting to close this question as off-topic because it is not related to economics. $\endgroup$ – luchonacho Aug 2 '17 at 10:02
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    $\begingroup$ @luchonacho Did you guys look up fungibility before voting? $\endgroup$ – Giskard Aug 2 '17 at 11:22
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    $\begingroup$ This seems like a good question to me. I would say that it is on-topic. It poses an interesting thought experiment that can be analyzed with the tools of economics and the answer to the question has some interesting implications for other topics within economics. I think @Alecos's answer could potentially support this conclusion: economics.stackexchange.com/a/17672/59 $\endgroup$ – jmbejara Aug 3 '17 at 4:42
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    $\begingroup$ Also, here's an example of a paper that is somewhat applicable: nber.org/papers/w17477 This question of fungibility might have implications for the analysis in the paper. $\endgroup$ – jmbejara Aug 3 '17 at 4:54

In economics and finance, fungibility means that we cannot distinguish between instruments. For example, we normally do not care whether we have one \$20 bill or two \$10 bills.

McCloskey's example is poor. In one sense, it is correct: when points are scored do not matter in the final tally. However, it is psychologically incorrect when applied to sports.

For example, in ice hockey, it is somewhat common to pull your goalie if you are behind at the very end of the game. You have a slightly greater chance of scoring since you have an extra attacker, but it is very easy for the other team to score if they get control of the puck. If you were leading 1-0, and then scored a second goal because the other team pulled their goalie, no sensible hockey fan would weigh the second goal as much as the first. The game was already effectively won by the earlier goal, and the second was just a statistic.

More generally, a team's effort during the game probably reflects the score. Piling up points early may be dangerous, as the team will then relax and sit on its lead. Therefore, later points are effectively more valuable. In order for McCloskey to be correct, we have to believe that the score of the game does not influence behaviour.

These problems do not crop up when using \$10 bills in your example.

  • $\begingroup$ Since your hockey example assumes subtle reasons for a goal, one might also assume subtle effects with the bills. Is the fake to real ratio of \$20 and \$10 bills respectively irrelevant to their value? $\endgroup$ – Giskard Aug 2 '17 at 12:30
  • $\begingroup$ Not sure I follow. It seems straightforward that fake (counterfeit) bills would not display similar fungibility characteristics as authentic bills, except in the context of playing a game like Monopoly. $\endgroup$ – Brian Romanchuk Aug 2 '17 at 18:38

First, quoting from wikipedia/Mariam-webster

Fungibility is the property of a good or a commodity whose individual units are capable of mutual substitution (i.e., interchangeability). That is, it is the property of essences or goods which are "capable of being substituted in place of one another".

Let's move now to McCloskey's example:

Ex post, It would appear that "points are fungible" as regards the question "which points won the game": Once the game is over, we have a passed, static situation of one team "having produced" 68 fungible units of the good, and the other team having produced 70 fungible units of the good.

But what happens when the game is ongoing? I.e., A dynamic situation? Here, not all points are the same, not all are as easy ("costly", "of the same value"), the sequence of scoring and the ups and downs of the score are important (most probably for behavioral reasons, and so squarely in the land of economics also, since many games are professional and material rewards are involved), there may be autocorrelation, or cross correlation, or forward causation or all of them... (Remember a "good" is also characterized by its place in time and space). So in this perspective, I would not say that we can argue that "points are fungible".

But then, if during the production process points are not fungible, and theoretically we could record and attribute differentiated value to each one of them, then in what sense, moving in the ex post view, after production has finished, we will suddenly say "points are fungible"?

I could only see that if we had no information on how the game evolved. Then we would be forced to say "absent any other information, we have to treat points as fungible".

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    $\begingroup$ This is perhaps an example of a non-behavioral reason for non-fungibility. As far as the dynamics go, there may be an option value that can account for the different valuation of points at different times of the game. Different scores earlier in the game may change my optimal strategy. For example, I may choose a higher-risk/higher reward strategy if I'm down a few points with significant time left. If I'm down a few points at the end, there is no time to adjust my strategy to have a very meaningful effect. Maybe I'm wrong, though. I'll have to think about it some more. $\endgroup$ – jmbejara Aug 3 '17 at 4:37

One possibility is to measure each basket's value using Win Probability Added (WPA). By this measure, given a tied game, the last basket will usually be much more important than the first. Baskets are therefore not (perfectly) fungible. Example:

At the start of the game, the score is 0-0. Let's say Iowa and Michigan are considered evenly matched and each initially have a win probability of 50%. Iowa scores the first basket and the score is 2-0. This raises Iowa's win probability to, say, 51%. So this first basket's WPA is 1%.

Now consider the end-game situation with 20 seconds left, the score at 68-68, and Iowa with the ball. Let's say Iowa's win probability is 60%. Iowa scores a buzzer-beating basket and changes the score to 70-68, just as time expires. So Iowa now has a 100% chance of winning. So this last basket's WPA is 40%.

And so by the measure of WPA, the last basket was 40 times as important as the first.

(We can change the example a little: Suppose Iowa's last basket leaves 2 seconds on the clock, the score at 70-68, and Michigan with the ball. Then Iowa would still have a very high win probability — say 95%. In this case, the last basket's WPA would still be a very high 35% and still remain much more important than the first basket.)

There is an analogy here to voting. In a simple single-seat, first-past-the-post election, all votes ostensibly count equally. But persuading an additional voter to vote for you the day before election day when the vote is very close, is more important than persuading an additional voter on the first day of campaigning, when the outcome is very uncertain.


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