Wednesday, December 5, 2012

To Live and Almost Die by the Three

After last night's game, I hope we do not play any more teams with "Southern" in their names.  Unfortunately, the Pac-12 guarantees at least two of those games.  So, last night was hard to watch.  The 1st half was brutal.  It reminded me of my days from graduate school when I would go into the Anthropology Department office the morning after a game, and the wonderful ladies who worked their would say, "Cardiac Cats".  As nice as it would be to lead wire to wire every game, and to end with a 20 point margin, it's just not going to happen.  Some games, the shots fall.  Others, they don't.

Does anyone else find it a bit of an enigma that the Cats have four legitimate post players in Tarczewski, Jerrett, Ashely, and Chol, and yet we take so many shots from behind the three point line?  Thus far, Arizona has shot 42.9% of its shots from behind the arc, a huge number.  In fact, that is the 15th highest three-point rate in the country.  On the positive side, we make a lot of them.  I suppose that having a lot of size in the paint leads to more outside opportunities, but still it makes me long for some good old fashioned post play.

The Cats are shooting 41.7% from deep compared to 58.5% inside the arc.  A quick calculation suggests that this long range offense is not entirely unjustified.  We score 1.25 points for every three pointer taken compared to 1.17 for every two.  The Cats currently rank No. 2 in effective field goal percentage (behind Creighton), which takes into account the added value of three point buckets.  So, perhaps shooting so many threes is not a bad thing.

One down side to having an offense so dependent on the three point shot is that you set yourself up for nights like last night when the shots simply won't fall.  Out of 20 attempted 3's, only six fell through the hoop.  Not only that, four of them came at interesting times in the game.  The Cats' first field goal of the night was a Solomon Hill three, just three minutes into the game.  Nick Johnson made one with four seconds on the clock to end the 1st half.  In the 2nd half, only two threes connected, our last two field goals of the game, both critical to stretching the lead. 

When you rely on a shot with a lower probability of success, you set yourself up for a boom and bust offense.  So, here's a trivia question for math nerds. Coming into the game, the Cats were shooting 43.8%.  They took 20 three point attempts.  For a team that shoots at that rate, in what percentage of games would you expect them to made six or fewer of those shots?  I'm going to spare you the details of the calculation, but the answer is 15.4%.  In other words, it should happen about once in every 6.5 games.  The point is that there was nothing unusual about our shooting last night.  It is expected to happen now and then.  After the game, Sean Miller said, "Sometimes for whatever reason you're stymied offensively."

Well, the reason, as Sean Miller knows, is the same as why if you flip a coin 20 times, once in a rare while, you will only get six heads.  Every shot is a coin toss (but not with a fair coin).  The likelihood of it falling is affected by many things, most importantly the shooting skill of the guy who let it go.  As for 27 turnovers, the chance of that happening again is minute.

Now, for the second trivia question.  The Cats are shooting two's at a rate of 58.5%.  In what percentage of games, would you expect them to make fewer than six of 20 two point attempts?  The answer is 1.3% of games.  Teams that shoot a lot of two's tend to have more consistent offensive outputs than ones that shoot a lot of threes.

For future reference, Arizona now has a three-point percentage of 41.7%.  In a game wherein 20 three's are taken, here are the probabilities of making any number of those shots:


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