Sports fans shouldn't value the fourth quarter more than the second—but they do.
Who said LeBron James isn't clutch? In the fourth quarter of last night's loss to the Boston Celtics, he went 4-of-7 from the field for 11 points, carrying the Heat while the rest of the team went 1-of-15 for seven points.
Whoops, I lied. That wasn't the fourth quarter. It was the second quarter. In fact, James actually put up just four shots for the final 8:10 of the game, leading most of sports media to once again question his so-called "clutchness." But the fact that I lied isn't important. What's important is: Did the fact that I lied in the first paragraph matter? Is there any reason to think that the fourth quarter is really more important than the second?
The good sports fan's answer to this question is that of course it matters. Clutchness is next to greatness. Players don't go down in history for random second-quarter lay-ups, but rather for game-clinching fourth-quarter buckets. It's not how you start, but how you finish, and so on.
The mathematical answer is more boring, but also more accurate. Clutchness is a myth. It's not just a myth for the fact that the sample size of "clutch shots" is almost always too small to make a meaningful judgment, nor just for the fact that many players tend to perform very close to their overall average in "high-pressure" situations (i.e.: being clutch really just means not choking). It's a myth because we fetishize an athlete's performance at the end of a game even though we know--or should at least allow ourselves to recognize--that games aren't won and lost exclusively in the closing seconds.
Let's stick with basketball for our purposes. Consider this thought experiment. Imagine a guard who makes every shot he attempts, forever. What is his most valuable point? You'll agree the answer is: none of them, and all of them. They are all equally valuable. There is a boring sameness to his performance.
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But when confronted with randomness and less-than-100-percent field-goal percentages in the real world, we are more likely to judge certain shots as being more important--and, implicitly, more valuable--than others. James notched 30 points on 25 shots with 13 rebounds in 45 minutes. Does the distribution of those points make them more or less valuable? No. Is fourth-quarter performance more statistically important than second-quarter performance? No. The only difference between two points scored at 8:30 in the second quarter and two points scored at 0:01 in the fourth quarter is the significance we attribute to it.