May 17, 2012

How Much Does Winning Depend On Clutch Performance?

     LeBron James' two misses from the free throw line late in Miami's Game 2 loss to Indiana resurrected the discussion about how much James folds under pressure and, more importantly, how much that quality devalues his other accomplishments.  (Skip Bayless and Rob Parker believe he shouldn't have been named the MVP for that very reason.)

     A few weeks ago, when pretty much the same thing was happening (when isn't it?), I decided to test whether or not performance in the last 4 minutes of a game affects a team's chances of winning more than any other 4-minute block in the game.  It didn't make mathematical sense that one 4-minute section would somehow influence the score more than another, but I wanted to give this theory a fair deal.

     I looked at the Atlanta Hawks' non-overtime scores (they were about average in PPG), and they had an average of about 94.5 and a standard deviation of around 12.  The standard deviation was most likely too high since scores varied because of opposing defenses as well as randomness, so I estimated that the deviation against an average team would be about 7.  The specific numbers aren't a huge deal for the first part of this experiment since I wasn't looking at specific point values, just which team was better.

     I simulated 500 of these "games" and separated them into wins and losses.  Then for each third of a quarter I found out how often the winning team outperformed the losing team.  (A tie counted as half-and-half).  The result was this graph:

     For those who are confused, this is what the graph means:  In 60% of the team's wins, they outscored the other team in the last 4 minutes (the third third) of the first quarter.  In 40% of the team's losses, they outscored the other team in that same time span, and overall they outscored the opponent 50% of the time in that 4-minute block.

     The important thing to notice on this graph is that each line is at roughly the same spot no matter what time period you look at, and these lines will get flatter and flatter when more games are played. 

     What does this mean?  All points in the game are equally important.  The ability to perform in the clutch is only important if your players are both good enough and bad enough to get your team into such a situation.  In the simulation, the teams went into the 4th quarter separated by 5 or fewer points 46% of the time, and went into the final 4 minutes separated by 5 or fewer points 42% of the time.  And given the numbers used for the simulation, the margin would be 3 or less with 24 seconds left only 27.5% of the time.  Since half of those situations would involve the leading team having the ball and being able to make it a two-possession game, only about 15% of games between equal teams should end with a meaningful last-second shot.

     The reason LeBron James is the MVP is that in the other 85% of games, he plays so well that the team wins a lot of games without having to make a last-second shot. If winning is as important as everyone says, then clutchness cannot be.

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