Many of you probably could have guessed, had you know that a Basketball Breakdown was pending, that this would be the topic of choice for this week. For those that couldn’t, you probably didn’t see the incredible 43 point display that Illinois guard Brandon Paul put on the Buckeyes on Tuesday night. You don’t necessarily want to watch the highlights – it’s pretty gory.

Let me start out from the get-go by saying that scoring 40+ points in a game is an incredible feat. Much applause to Mr. Paul for pulling it off, particularly against the #5 team in the country (at the time). There’s a reason the Buckeyes are ranked so high, and solid defense is one of them. Scoring that many points against a sound defensive team makes it just all the more impressive.

But how can it happen? How can such a sound defensive team allow a player to score so many points? I submit that this had less to do with poor play from the Buckeyes (though that definitely contributed) than it did with some excellent planning and fantastic play on Illinois’ side of the ball. I definitely don’t want to see anyone take anything away from Brandon by saying that it was entirely Ohio State’s fault. He (and his team) had a lot to do with it.

Let’s start by asking how you can tell if a player a hot (or cold) night.  Obviously when you’re watching a game you can see it in the player’s and team’s reactions to him hitting (or missing) a lot of shots.  Statistically, it’s a little more difficult.  You have to look at the player’s averages – preferably over a season, but career can work too – and look at how statistically ridiculous a particular night of shooting is.

Let’s consider William Buford first.  Buford has been accused of having some pretty cold nights and not producing particularly well.  Looking at his averages, Buford is scoring a little more than 15 points per outing this year.  If you consider that he plays on a team with two other lights-out scorers (Jared Sullinger and DeShaun Thomas), and you consider that a good team typically has one guy who averages more than 15 per night, then it’s suggestive that he’s not as cold as people think.

But what about on any given night?  Against Illinois, many people thought that Buford did not play to his usual potential.  I contend that he scored precisely his average – 15 points.  But there has to be some reason why people feel that he didn’t perform well.

The answer is to look at a measure of his shooting efficiency.  How many points did he score against the number of shots he took, and how does that compare to the rest of the season?  For the season (including the Illinois game), Buford has a 1.144 shooting efficiency.  That means that on average Buford scores 1.144 points for every shot he takes.  That’s pretty reasonable efficiency numbers for a basketball player.  An average player, someone who maybe hits 40% from 2 and 30% from three will average 0.85 points per shot.  So clearly Buford is playing above average basketball this season.

Against Illinois, Buford’s efficiency was 0.833.  In other words, he had a below average game for him, but played about as well as an average basketball player.  That’s not bad.  If a poor night for you is an average night for your typical D-1 basketball player, you’re doing pretty well for yourself.  In fact, considering the typical variance in Buford’s game from night to night, he will tend to have an efficiency somewhere between 0.744 and 1.544 in just under 70% of his games.  Anything way outside of that might be considered statistically significant – for example, his 0.29 efficiency against Texas Pan-American (2 points on 7 shots).

Interestingly, people also thought Buford did not play particularly well against Indiana.  Turns out that’s not so true.  Buford has a 1.142 efficiency rating against the Hoosiers – an average night for him.

How about Brandon Paul’s numbers?  Obviously he went completely crazy against the Buckeyes by scoring his 43 points.  He’s only the second player to do that since 1997 in the Big Ten, and the previous was Jared Sullinger last year.  That really puts that performance (and Jared’s from last season) in perspective.

On the season, excluding the Ohio State game, Brandon Paul is averaging 13 points per game and an efficiency of 1.07 points per shot (plus/minus 0.4).  Those are pretty good numbers, and Paul is certainly an above average basketball player.

Against Ohio State, Paul had an efficiency of 2.867.

I want you to let that sink in for a minute.  Brandon Paul not only exceeded his average efficiency, he exceeded it by 1.8 points per shot.  For the scientist’s out there, that’s 4.5 standard deviations outside his average.  For the non-scientists, that means that if Brandon Paul were to play 100,000 basketball games against D-1 competition, this should happen exactly once.

The theoretical maximum for efficiency by this measure would be 4.  That’s assuming a player shot nothing but three pointers, hit every single one he took and got fouled on each one, and still hit all the free-throws.  That might be possible with one shot, maybe even two, but not 15.

Is this a fault of Ohio State’s defense?  Absolutely not, and here’s how you can tell.  Let’s consider the average efficiency of the best scorers in each of Ohio State’s game’s this season: (rows are: Team Name; Points; Shot Attempts; Efficiency)

13 17 17 10 21 18 22 13 21 20 21 10 20 13 17 13 9
8 16 11 5 18 14 18 9 9 12 10 7 14 12 9 14 10
1.63 1.06 1.55 2.00 1.17 1.29 1.22 1.44 2.33 1.67 2.10 1.43 1.43 1.08 1.89 0.93 0.90
Avg 1.477 0.418

These are the stats of whichever player was managing to put the most points on the board, and therefore drawing the most defensive attention. Only three games saw players break 2 points per shot; two were forwards who didn’t even attempt a single three pointer. Both of them made it to the line on about 50% of their shots – yet more evidence that big men getting fouls down low can be a big advantage. The last, UNF’s surprising inclusion, was a guard off the bench who shot 3-5 from the floor, and earned four free-throws during the game. Not a world-beating effort, just a low total shot-count.

You should notice that Brandon Pauls efficiency rating is a huge outlier here too, about 3.5 standard deviations outside of Ohio State’s best opponents.  That implies that the Buckeyes would have to play 5000 games in order to encounter just one player pulling off such a feat.

But that’s much more likely than Brandon Paul having such a game.  Why is it more likely to happen against Ohio State’s defense than it is for Brandon Paul to do it?  Well, first off, while Brandon Paul is a very good Basketball player, he’s not the kind of guy who’s going to explode with his scoring very frequently.  Ohio State has faced a number of great players who find different ways of scoring points in big games.  Therefore, Ohio State’s numbers are skewed because we’re looking at the best of each opponent on the night OSU played them. That’s unfavorable to the Buckeye’s defense, as the one scoring the most points is not likely the opposing team’s best player. The best player probably got shut down, forcing the opponent to look to other options for scoring – sound familiar?

Also, there’s something to be said for the reactions of the teams as a whole to a streaky shooter.  Recall Jon Diebler’s 10-straight 3 pointer game against Penn State last year.  The Buckeyes continually fed Diebler, and more importantly, continually found ways to try to get Penn State’s defense off Diebler so he could have an open look.  When a player is hot, teams and coaches will work to get them the ball more in a game.  This is what made Ohio State so dangerous last year: Diebler, Lighty, Buford, Thomas, Sullinger, and even occasionally Craft, could go crazy in any particular game, and there were enough good players around to make it possible to get the hot shooter open, while forcing defenses to guard the rest just in case.

In Brandon Paul’s case, he started out fairly slowly in the game.  He was a big piece of what Illinois wanted to do – he was one of their top three scorers after all – but he wasn’t the only piece.  Once the Illini realized that Paul was on fire they did everything in their power to make sure he got open.  You may recall a previous BBB where I broke down the double-screen look.  I caught Illinois employing that play, running Paul under the basket and providing two consecutive screens, more than once to free up Brandon Paul on the wing for an open look.  That’s not necessarily a fault of Ohio State’s defense, simply Illinois taking advantage of the hot hand.

So why don’t teams with good shooters, like Ohio State with Diebler last year, just run plays like that all the time?  Clearly that play works against a defense!  Well, obviously eventually the defense will figure out how to counter the play if you do it too often.  Second, while an open three point shot is a great shot, it’s not always the best shot – particularly if your shooter is having an average night.  Plays like this are perfect to call if the opposing defense is focusing on the paint, or simply aren’t expecting a three point look.  It’s the same reason you don’t run Dave three times to the same side of the field on consecutive plays.  The defense eventually figures things out.  Also, if your shooter misses the shot, you may have just given the other team the ball, as it tends to leave them in better position for the rebound than your own players.

Don’t forget also, towards the very end of the game Brandon Paul took that dagger three pointer with Aaron Craft’s hand firmly in his face.  Heck, Craft was basically in physical contact with Paul’s body the whole time.  Paul was so locked in that he simply couldn’t miss no matter what.  Shooters will tend to feed of the energy of the crowd and the energy of their team, and lift themselves to even better heights.  This shooting night was the perfect storm against Ohio State, and there was nothing to be done but desperately try to keep up.

Some will point to Craft and Sullinger’s comments about lack of effort after the Illinois game as a likely culprit for Brandon Paul’s game.  While Aaron and Jared may have a point, and while it may even have contributed to Brandon Paul getting hot – in the sense that not playing quality defense early allowed him to hit shots and build confidence – its not the whole story.  Paul still had to hit those shots, he still had to go 8/10 from beyond the arc. That’s no small feat and certainly should not be viewed as such.

We witnessed an amazing feat of basketball performance, one that will be remembered for a very long time – much like Diebler’s three-point shooting effort at Penn State. We should applaud Paul’s effort, shake our heads at our bad luck at being forced to face it, and realize that it required a superhuman 43 point effort from the Illini’s third best scorer to beat us by only five at their place. That’s just the way it goes sometimes in College Basketball.