Hindsight, Justification, and the Butterfly Effect

An interesting point of discussion was made by a friend of mine regarding a recent sporting event: regardless of what happened in the game, as long as the team came out as the winner, the positive outcome erases any sense of the word “mistake” on any play, by any participant, at any part of the game.  The justification for this argument is that by changing any part of the game, including those parts which were previously thought to be mistakes, might change the positive outcome of the game to a negative.  Does invoking the butterfly effect help justify this argument?

The butterfly effect, which is a term popularized by an incredibly bad movie by Ashton Kutcher, is an effect which is rooted in chaos theory: simply, it refers the possibility that the air coming from a butterfly’s flapping wings could, in theory, have this sort of effect:

• The gust of air coming from the butterfly’s wings encounters a small gust a wind from the sky.
• The gust of wind changes directions, knocking a leaf from a branch near a house.
• The leaf falls on the sidewalk, which scares a bug, which reacts by running across the driveway.
• A man going to check his mailbox sees the bug near his foot, and reacts by trying to step backwards out of its way.
• As the man steps backwards, he slips on a puddle and bumps his head.

So, as you can see, a simple wind from a butterfly’s wings have had a very large effect on the man’s life.  Had the butterfly not been there, or perhaps stopped to take a rest on a branch, the entire event wouldn’t have happened, and the man most likely would have went about checking his mail without adverse effects.

Applying this concept to an athletic event, there are, much like “real life” scenarios such as the one previously described, many variables which could affect the outcome of a game.  Certain participants getting playing time during special situations, the ball being hit in a particular way, or an official missing a call could have a large impact on the game play.  But, likewise, we cannot discount the small things that, much like the wind off the butterfly’s wings, could also potentially impact the game play in an adverse way: the ball missing a stitch, a chunk of ice stuck on a hockey player’s blade, or a small piece of treat missing from an athlete’s shoe.  These small aspects, employed in the right situation, could mean the difference between a positive and negative outcome for a participant.

The issue at hand, which was whether particular players being played in special situations was correct given the positive outcome of the game, seems to fit nicely with the butterfly effect.  While one might argue that a better player should have played in a particular situation, unless the outcome of that situation was distinctly negative, it’s difficult to argue against the lesser talented player’s participation.  As you cannot assume that a positive outcome would be accomplished by the more talented player, you simply can’t argue for the positive player’s expected participation.

Due to being unable to argue for a positive based on an assumption, it seems reasonable, then, that my friend’s argument is relatively sound: as the outcome of the entirety of the game — including everything I might have previously thought was a mistake — was one that was positive for the team I supported, then without making outstanding assumptions I cannot argue that a change would have made for a greater positive outcome.  Likewise, arguing for a “greater positive outcome” would be difficult in and of itself if the outcome was simply a win, and there little more, if anything, else to win.  In hindsight of a positive outcome, it seems justifiable to argue that the entirety of the game is a positive as a whole without any negatives.  My friend, by unknowingly invoking the butterfly effect, has seemingly made a great argument concerning principles in sport and game theory.