The Price of Anarchy is a theory that has been circulating the nerdy basketball circles that yours truly dabbles in. In short it’s a way to explain how a basketball offense can become more efficient when its best (and most used) players take fewer shots.

This theory might sound familiar if you have ever heard of Bill Simmons’ Ewing Theory. Simmons’ theory attempts to explain how a team can lose its best player and somehow improve. Simmons lays out the theory in his typical satirical and entertaining ways and cites remarkable occurrences of teams improving when superstars get hurt, it also focuses a lot more on psychological issues. Brian Skinner’s recent paper and presentation at the Sloan Sports Analytics Conference begins to explain how something like this could be mathematically possible.

You can read the full article for the technical jargon and mathematical explanations or Skinner’s blog post on the topic. I recommend reading at least one or the other because Skinner explains the concept in great detail (really, read it). The main idea is that basketball is a network problem. Every route to the basket (simplified as every player or shooting option) is a different way to a similar goal: scoring a basket. Some players are more efficient than others but all options are capable of scoring. The catch is that the more an option is used, the less efficient it becomes.

The standard problem used to explain the price of anarchy is rush hour traffic. In the rush hour problem, it becomes clear that the whole community can experience faster commute times if some people choose to take slower routes. The social welfare maximizing outcome prevents other roads from becoming backed up and the average commute for the entire community decreases despite some people experiencing longer commutes.  The most extreme example of this is when big cities experience more efficient traffic flow after closing the most traveled roads. (This whole example is explained much better in the original paper and also at Gravity and Levity.)

So on the basketball court the idea is that an offense is most efficient when there is an equal chance that every player on the floor will shoot the ball. Here’s Skinner:

On the basketball court, possessions are like cars. Each one starts at point A (the in-bounds) and attempts to travel to point B (the basket). Different plays are like different roads: each one has a different efficiency that will generally decrease the more it is used. In principle, all of the methodologies and “paradoxes” associated with traffic patterns should be applicable to basketball as well.

This obviously keeps the defense more honest (they can’t just focus on a specific outcome) but it logically holds up without even considering the defense. Skinner’s article explains “skill curves” that attempt to project that the optimum number of shots a star player should take. It’s nearly impossible to accurately graph every player’s skill curve but there is no doubt truth behind this concept.

We see examples of this phenomenon all the time in sports. Some of them could be chalked up as sample size errors but they happen. Just over the last few months in college basketball we saw Michigan State play surprisingly efficient basketball for a stretch without Kalin Lucas. We also saw Notre Dame turn their season around when their best player, Luke Harongody, got hurt. Harongody just happened to take 37% of Notre Dame’s shots when he was on the floor, the highest percentage in the country.

You probably realize where this is going in relation to next year’s Michigan team.  Michigan lost two players who accounted for around 60.2% of the team’s shots. A quick glance over KenPom numbers yielded only 3 high major teams that had a pair of players combine for shot% over 60%: Stanford (Fields, Green), Georgia (Thompkins, Leslie), and Notre Dame (Harangody, Abromaitis).

Sims and Harris also took more shots than any other duo in the Big Ten and Michigan is also the only team to lose both of their top two shot takers in the Big Ten. Here’s a breakdown of how many shots each Big Ten team’s “top two duos” took:

Not surprisingly, the most common thought that fans have about Michigan’s season next year is doom. When Michigan won, Sims and Harris typically had monster games. When Michigan lost, they disappointed. In this era of superstars, they are all we remember. Not to mention the other players on the team either regressed from their freshman year or had inconsistent freshman seasons.

Sims and Harris took an average of 28 shots per game last season. Obviously, one or even two people won’t step up to take all of these shots. Instead they will be more optimally distributed among the team.

All returning players that are expected to be key cogs in next year’s offense took less than 16% of Michigan’s shots when they were on the floor, well below even an equal distribution of 20%. The fact that they didn’t get take their shots in the last two years is a bit troubling but there’s no doubt that the dynamic of next year’s team will be different.

Ideally next year’s team will look something like John Beilein’s West Virginia teams. His 2005 team had six players take over 19% of the team’s shots when they were on the floor. Similarly his 2007 team had 4 freshmen and sophomores in a group of 6 players that took  over 18% of the team’s shots when they were on the floor. Beilein’s offenses over his last three years at West Virginia ranked 18th, 12th, and 13th in Pomeroy’s rankings and were in many ways the epitome of balanced offense.

There are also some flaws with this analysis… None of Novak, Douglass, Morris, or Lucas-Perry was able to hit shots at a particularly efficient rate last season. They all had an eFG% between 43 and 48 percent, making the likelihood that they will become more effective with more shots unlikely. The greatest hope here is that last year was some kind of sophomore slump but we won’t find that out until next year.

Expecting an elite offense next year would be ludicrous however the Price of Anarchy gives us at least some reason for hope. It’s unlikely that Michigan will have a player that takes over 25% of their shots next year. The question is what happens to the multitude of players who will add a couple more shots per game.

This is an over simplistic model because there are also other factors effecting a game beyond shooting. Sims and Harris accounted for around half of Michigan’s rebounding and rebounding might be Michigan’s biggest concern next year. It also doesn’t consider other abilities like Harris’ 27.7% assist rate.

There are a lot of shots available next year and someone is going to have to take them. Under John Beilein, Michigan  has maximized their possessions by limiting turnovers which means that the shot attempts will be there. Novak, Douglass, Lucas-Perry, Morris, Vogrich, McLimans, Morgan, Hardaway, Smotrycz, Horford, and any other freshmen that enter the picture will get their looks. The scary part is that we haven’t seen half of next year’s play college basketball and not all balanced teams are good teams, you still have to make shots.

Point guard is the hardest position to play as a true freshman. Similar to the quarterback position on the football field, the point guard has an overwhelming amount of responsibility. First, he has to have a great understanding of the offense. He is also typically tasked with defending one of the opposition’s best players. And even more importantly, he has to keep the team grounded through thick and thin because he has the ball in his hands every possession.

Because of the stress surrounding the point guard position, it’s very hard to find true freshmen making a major impact as point guards. The John Walls, Derrick Roses, and Mike Conleys of the world are the exception rather than the norm.

The strenuous nature of the point guard position is also why I think that Darius Morris has the ability to make a major jump in production from year one to year two.

Inconsistency is the trademark of a freshman point guard. Flashes of brilliance are intertwined with boneheaded turnovers. It’s no surprise that teams led by freshmen point guards also tend to be woefully inconsistent.

Let’s take a look at this year’s freshman point guards who were rated in the top 100 and see how they have fared this year. I pulled a group of the top 15 point guards (using RSCI, Rivals, and Scout rankings) and then looked up their basic stats: min/game, min%, points/game, offensive rating, usage, assist%, turnover %.

The results were pretty clear, there are only a couple point guards who have been successful this year. There are only three freshmen point guards who are scoring in double figures and two of them play on the same team. There are only four freshmen with a higher assist percentage than turnover percentage. Finally, over half of the top 100 freshmen point guards in the group are shooting under a 50% effective field goal percentage on the year.

The group that I would call successful includes John Wall (UK), Eric Bledsoe (UK), Tommy Mason-Griffin (Oklahoma), and Michael Dixon (Mizzou). In the end, the “average” top 15 freshman point guard has more turnovers than assists, doesn’t shoot the ball very well and isn’t all that efficient. The average stat line is 21 min, 6.5 ppg, 47.1 eFG, 97.9 Ortg, 20.6 A%, 24.4 TO%. And that’s including freshman phenom John Wall, removing him knocks everything down a point or so.

There are also a few guys who play complementary roles on loaded teams. Brandon Triche (not listed in the table) starts at the point for Syracuse but he plays alongside 5th year senior Andy Rautins. Maalik Wayns has been efficient for Villanova but he’s playing alongside guys like Scottie Reynolds and Corey Fisher.

Looking at the group of freshmen, Darius Morris is just about right in the middle, a touch below average, compared to the other prized point guard recruits. Morris’ numbers are: 24.5 minutes, 4.6 points, 22.2 A%, 25.7 TO%, 91.6 ORtg.

So while Darius Morris’ season might still be a little disappointing from the eyes of Michigan fans that expected an instant impact player. I think it might be a little too early to rush to a conclusion.

Morris has shown flashes of potential. He’s big, athletic, and willing to defend. He seems to have good lateral quickness and has shown improvement over the course of the season. It’s also pretty clear he has some glaring weaknesses. His shot is fundamentally flawed and needs tweaking, especially from three point range and he still tries to make a few too many fancy plays.

But in the end, he appears to be a pretty average top 100 freshman point guard. The future is bright for Darius Morris, despite taking a few lumps this year. An offseason to focus on improving his jump shot and continue getting acclimated with the offense is just what the doctor ordered.

It’s a consensus that Michigan struggled to rebound the ball last year. They played a 6-foot-8 center and a 6-foot-5 power forward so the results are not all that surprising.

On the season Michigan’s defensive rebounding percentage ranked 222nd in Division 1 while their offensive numbers were even worse at 282nd. They shored up their defensive rebounding in conference play, ranking 3rd, but were still 9th on the offensive glass. Despite the improved numbers in conference play, Michigan still had several painful rebounding games.

Luckily, John Beilein seems to have figured out a way to win without rebounding.

Using Ken Pomeroy’s correlation statistics, which compare the effect on offensive and defensive efficiency of each of the four factors (eFG%, OR%, TO%, FTR). Here are Pomeroy’s correlation numbers for Michigan last year:

                          Correlations
                        to OE       to DE
                 Pace:  +0.18       -0.41

                 eFG%:  +0.87*      -0.23
                  OR%:  +0.07       -0.06
                  TO%:  -0.44*      -0.06
                  FTR:  +0.23       +0.00

             Opp eFG%:  -0.34       +0.72*
              Opp OR%:  +0.08       +0.17
              Opp TO%:  -0.17       -0.45*
              Opp FTR:  -0.47*      +0.52*

             Bold  values are significant with a 95% confidence
             Bold* values are significant with a 99% confidence

The effect of some statistics is blatantly obvious. Naturally, shooting percentages are going to have dramatic effects on offensive and defensive efficiency. Some of the other numbers allow us to make some interesting conclusions about a specific team. For a further explanation of the correlation numbers, check out Ken Pomeroy’s thoughts on the matter.

The issue at hand is Michigan’s rebounding numbers. There appear to be no significant correlations between Michigan’s offensive rebounding and their offensive efficiency. Similarly, on the defensive side of the ball, there is minimal correlation between defensive rebounding and defensive efficiency.

Judging by Michigan’s results, these numbers make sense. Michigan won plenty of games when they were dominated on the glass. They won seven of the nine games in which they allowed their opponents to rebound over 40% of their misses. On the other hand, they were 6-3 in their nine best rebounding games. In the remaining 16 games, Michigan was 7-9.

On a game by game basis, there are plenty of examples where Michigan was dominated on the glass and somehow came away with a victory. Here are visual representations of the four factors in Michigan’s five worst defensive rebounding performances of last season.

Against Minnesota, Michigan was able to pull out a narrow upset thanks to valuing the basketball and forcing a ton of turnovers.

Against Clemson, Michigan survived because Clemson couldn’t make a shot. Clemson put up a futile 36.2% eFG% compared to Michigan’s almost respectable 49%.

UCLA was another case of winning thanks to the turnover battle. Michigan hung around in an ugly low scoring game thanks to winning the turnover battle.

There are also cases where it just doesn’t work. Rounding out the bottom 5 rebounding performances were the Maryland and Connecticut games.

Being able to hold onto the ball actually kept Michigan in both of these games as well but they fell just short.

John Beilein clearly has a strategy in place. Looking at statistical profiles of old Beilein teams, the emphasis is clear: shoot threes, don’t turn it over, and keep opponents off the line.

The four factors were developed by people smarter than me to represent the most important factors to winning a basketball game. Dean Oliver’s original weights on each factor were 40% shooting, 25% turnovers, 20% rebounding, 15% free throws. In this case it appears that, for Beilein teams, rebounding is the least important of the four meaning it should probably be weighted a little less.

There are obviously many ways to skin a cat, or in this case win a basketball game. There are numerous examples in this very conference of differing styles Wisconsin slows the game down to a crawl, Michigan State crashes the glass, and Purdue plays in your hip-pocket all night on defense. You can make arguments over which style of play is best but at the end of the day winning is winning, whether you play a 50 possession game, shoot 40 threes, or rebound half your misses.

A common opinion among Michigan fans is that the team will be able to play big this year, shoring up last year’s poor rebounding numbers, with the additions of Ben Cronin and Jordan Morgan. The best way for Michigan to improve isn’t to improve what they were worst at. It’s to improve what’s most important to winning. The option to go big doesn’t hurt but at this point it’s not going to make Michigan the best team.

Three point shooting is an area that will have a much more tangible effect. I analyzed the three point shooting of last year’s team and there is certainly room for improvement. And we all know that when the threes fell, Michigan won. They were 15-5 (75%) when they shot over 31% from three point range but only 6-9 (40%) when they shot 31% or below.

As much as it may sound like heresy to basketball traditionalists, it’s possible to win without crashing the glass.

There is no question that Michigan is going to be a perimeter oriented team again this year. I think it makes more sense to be excited about becoming a better one rather than shifting style of play. Ben Cronin will be useful in situations against oversized teams like UConn last year but he’s not going to change what Michigan does night in and night out.

It’s easy to remember the exciting parts of last season. Whether it is the early season win over UCLA or rushing the court after the Duke game. Maybe finally winning a big road game at Minnesota or the NCAA tournament win over Clemson. Last season was a breath of unexpected fresh air that caught most Michigan fans off guard.

Now, expectations are real: this is an NCAA tournament team. Michigan has typically fallen in the 10-20 range in most pre-season polls and success is expected.

All signs point to a successful season this year but let’s play devil’s advocate for a bit now and take a look at five of Michigan’s not so glorious moments. It’s important to remember that although they made their first NCAA tournament appearance in a decade, Michigan was a couple bounces (versus Savannah State or Indiana for example) away from the NIT.

No team looks great every time they take the floor, but these five games stand out as the worst performances by Michigan last year and reminders that there is still a ways to go.

December 31st – Wisconsin 73 – Michigan 61 (Recap)

Michigan started their conference slate with a dud. Wisconsin came out on fire with an eFG% of 65.2% and maintained a comfortable lead from start to finish. This was Michigan’s worst defensive performance of the year as they allowed the Badgers to score 1.24 points per possession.

This was a rude awakening for Michigan — taking games off in conference play doesn’t work. Michigan had played four relatively easy games after the huge Duke win and it was clear that they lost their focus over the holidays.

This was Michigan’s worst home performance of the year and Wisconsin remains one of the two teams that Michigan has yet to beat under John Beilein.

January 17th – Ohio State 65 – Michigan 58 (Recap)

Gut wrenching home losses appear to be the theme of this list. The Ohio State game felt like one that Michigan was supposed to win. It was Ohio State and the 1989 team was in the house, there was a great crowd, and Michigan had the opportunity to go to 4-2 in conference.

Michigan fell behind early but managed to claw their way back into the game before falling just short. In the end Ohio State ran away with the game thanks to BJ Mullens alley-oop dunks and Evan Turner’s 14 free throw attempts. It was another game where the opponent simply picked apart Michigan’s defense, scoring over 1.1 points per possession.

January 20th –Michigan 58 – Penn State 73  (Recap)

Garbage time began with 12:55 left in the 2nd half (HD Box)

That’s pretty much everything you need to know about this one. Penn State absolutely man handled Michigan from the tip. Jamelle Cornley pounded them inside for 17 points on 9 shots before Penn State got started from long range — hitting 9 of their 17 three point shots.

Manny Harris scored 4 points on 9 shots and took a seat early after his lackluster play. Michigan was 5-30 from three point range, refusing to go inside despite making 65% of their twos. This performance probably hurts a little more when you realize that Michigan beat the same team two weeks later by 20 points at Crisler Arena.

February 10th – Michigan State 54 – Michigan 42 (Recap)

42 points. That’s all Michigan could muster against their in-state rival on their own floor. Michigan State is the other Big Ten team that Beilein has yet to knock off. The capacity crowd at Crisler was held at bay from start to finish as Michigan State controlled the game. Every Michigan run was answered by the Spartans who managed to make enough big plays to coast to victory.

In a dreadfully slow 53 possession game Delvon Roe and Kalin Lucas made just enough shots to keep Michigan an arms length away. It was another painful shooting day for Michigan, who hit only 4 of 24 three point attempts.

Michigan didn’t do anything well on offense, scoring only .79 points per possession and turning the ball over on 22.5% of their possessions. Michigan State managed to hold onto the ball, control the glass, and get to the free throw line enough to win the ugly game.

February 22nd –  Michigan 60 – Iowa 70 –(OT) (Recap)

There was actually a mysterious benching in Iowa City before Tate Forcier was even a household name. Beilein’s benching of Manny Harris in overtime led to a 10 point Iowa run. A quick run through of the comments after that game shows that people were convinced that Beilein was throwing away the season and could care less about making the tournament.

The bottom line is that Iowa had no business taking Michigan to overtime. Iowa was a team in disarray and they had just given Indiana their only Big Ten win. Harris only managed 9 points on 13 shots and Sims put up a meager 13 points on 13 shots. Three weeks later Harris and Sims combined for 45 points on 70% shooting in a 28 point romp of the same Iowa team.

So What?

This year’s team should be very good. John Beilein is one of the best teachers in the country and his teams almost always improve from year to year, especially when they return this many players. However, this team is far from perfect and bad things can happen to good teams. There are endless reasons to be excited about the upcoming season but it’s important not to blow expectations out of proportion.

The Big Ten is stronger than it has been for years and the difference between 3rd place and 6th place very well could be one or two games. There are teams of all different styles that will provide a different challenge night in and night out. Conference play is going to be an 18 game war.

This post should serve as a reminder that last year was far from perfect and this team has a long ways to go. Last year’s team lost 7 out of 9 games at one point before rebounding and putting some wins together.

The high points were certainly fun and there are numerous reasons for excitement but we are still talking about a team that finished .500 in conference play and tied for 7th in the conference.

Like it or not, John Beilein’s basketball teams are perimeter oriented teams. Beilein has a model and, besides a few tweaks here and there, he is comfortable sticking to it because it works. The ideology behind a POT is that you shoot a lot of threes while sacrificing offensive rebounding for not turning the ball over; the catch is that you have to make your threes.

While Michigan’s statistical profile last year was a lot closer to the West Virginia Beilein model than the year before, it still wasn’t quite there. The main issue was Michigan’s team three point shooting percentage of 33.4% (32.1% in conference).

Luke Winn points out that Michigan doesn’t return any one who made over 34.5% of their three point shots while Beilein’s best team at West Virginia returned 6 players that topped that mark.

Basically Michigan managed to win a lot of games last year despite being a perimeter oriented team who can’t make threes – the cardinal sin. To repeat that success, or improve upon last year, they are going to have to make more of their threes if when they shoot so many.

To put this in perspective, I put together a scatter plot of 3PA/FGA (how many threes a team takes) versus 3pt field goal percentage.

(The Big Ten teams are all listed with conference-only numbers, while Beilein’s WVU teams are from their entire season.)

The axes are aligned at conference averages (35% 3PFG%, 37% 3PA/FGA) which leaves us with four quadrants.

• Bottom left: teams who shoot few three pointers and make them at a below average rate.
• Top left: teams who shoot a lot of three pointers and make them at a below average rate.
• Top right: teams who shoot a lot of three pointers and make them at an above average rate.
• Bottom right: teams who shoot few three pointers but make them at an above average rate.

The graph is pretty intuitive but here are some thoughts about other teams in the conference:

• Offensively challenged teams like Minnesota and Illinois fall in the lower left quadrant but at least they aren’t wasting their attempts.
• Ohio State shot the three point shot very well but could have probably shot it a little more.
• Northwestern is the only team in the top right quadrant, they shot the three a lot but managed to make it consistently.
• Wisconsin and Purdue are pretty central, meaning they have some good three point shooters but they are also very balanced.
• Michigan State doesn’t shoot a terrible percentage but they rarely shoot the three.

You can see Michigan is in the top left quadrant – meaning they take a lot of threes (more than anyone in the conference) but make them at a below average rate. Michigan obviously wants to move toward the top-right quadrant of the graph where most of Beilein’s West Virginia teams fall.

Michigan appears to be moving in the right direction, they saw about a 2% increase in their three point shooting percentage from Beilein Year 1 to Year 2. But, their three point shooting percentage on the year was still over 1% lower than Beilein’s worst three point shooting team at West Virginia.

The upshot is that there are a lot of guys who have shown that they can shoot that just need to be more consistent. Stu Douglass, Laval Lucas-Perry, and Zack Novak all had multiple hot shooting games last year but they also had their fair share of 0-4 or 0-6 games.

The encouraging part about freshmen is that they become sophomores, I think it’s fair to expect all three to make substantial strides in their consistency and overall shooting percentages.

Freshman Matt Vogrich has widely been proclaimed as one of the top shooters in the incoming freshman class and judging from early practices, he will be able to contribute. If Douglass or Lucas-Perry are cold, it’s always good to have one more shooter to try off the bench.

Manny Harris’ shot continues to improve as well,  and an uptick of a few percentage points on Manny’s three point percentage could be worth 10-15 spots in the NBA draft.

Last year’s team resembled a Beilein team statistically in many ways but three point shooting will be the difference between a good and great Michigan team this year. Douglass, Lucas-Perry, Novak, and Vogrich hitting threes consistently continues to open up the offense and has a bit of a snowball effect. Forcing teams to play pressure defense on the perimeter opens the backdoor cut and also prevents teams from stacking the paint against penetration from Manny Harris and Darius Morris.

Without saying a word this site has ended up in the middle of a debate: who’s the better point guard, Michigan State’s Kalin Lucas or Michigan’s Manny Harris.

John Gasaway started the debate on this very site with this comment on Manny Harris:

In fact, I want to pipe up on behalf of one of your players. I read the interview you did with KJ of The Only Colors and I have to take issue with your statement that Michigan State’s Kalin Lucas “is easily the best point guard in the conference.” Really? What about a certain Manny Harris? Oh, I know last year there were always other Wolverines on the floor alongside Harris who proudly wore the “point guard” label (Kelvin Grady, C.J. Lee, Stu Douglass, etc.). I for one don’t buy it. Harris had by far the highest assist rate on the team and, more importantly, he ran this offense in the literal Beilein-ian sense. Plus Lucas is hapless inside the arc, making an anemic 40 percent of his twos last year. I’ll grant you that Lucas made Sherron Collins look really bad at a propitious moment (less than a minute left in a tie game) in the Sweet 16 and is clearly superior to Harris when it comes to nailing threes. I’m just sayin’. Not open and shut from my chair.

KJ ran the numbers to try to determine a winner. Looking at only conference numbers, KJ concludes that Lucas has the advantage in the point guard battle because he turns the ball over less and shot much better from three point range. The other two stats that KJ looked at were assist and free throw rates, which turned out to be roughly equivalent.

The most interesting point that KJ makes is that Kalin Lucas morphs into whatever Michigan State needs him to be based on the opponent:

Against non-Big Ten foes, Lucas fits the mold of the traditional pass-first point guard.  He distributes the ball to his teammates, minimizes turnovers, and scores at a relatively modest rate.  And it isn’t just a case of padding the ball-handling stats against weaker opposition; the numbers don’t change much if you restrict the sample to nonconference opponents from BCS conferences.

Against Big Ten adversaries, meanwhile, Lucas morphs into a shoot-first point guard.  The assist number drops substantially, with an uptick in turnovers, and the scoring average shows an offsetting increase.

Let me state my theory on Lucas in broader (and less emotionally-detached) terms : Kalin Lucas does what his team needs him to do to win games.  Against faster-paced opponents, he runs the fast break with superb efficiency.  Against more plodding opponents, he finds ways to score in the half-court offense.

I think the moral of the story is that Kalin Lucas and Manny Harris are very different players who somehow come away with similar stat lines because of the role each plays for his team.

Lucas is a pure point guard in every sense of the phrase. Luckily for him, he plays in an offense that relies on a guy like him to control the ball and make plays in the half court offense. When MSU runs, he is able to shift gears and turn into a pass first player, distributing the ball to MSU’s stable of wings in transition.

Michigan, on the other hand, runs a two guard offense that was designed to eliminate the need for a true point guard. Beilein’s offense revolves around spacing and doesn’t call for one player to dominate the ball in the half court set. Manny Harris does a little bit of everything for Michigan but it prevents him from falling into any traditional role. He plays the three but distributes like a point guard, scores like a wing, and attacks the defensive glass like a big man.

I concede that Kalin Lucas is a better point guard than Manny Harris, especially in Big Ten play when Lucas snapped out of his early season funk. But I think the most impressive point here is that Manny had a higher assist rate in conference play than one of the top point guards in the country. Not to mention that Harris’ defensive rebounding percentage in conference games was in the same league as Big10 rebounding elites such as Joe Krabbenhoft, Mike Davis, and Paul Carter.

The obvious argument against Harris’ remarkable statistical well-roundedness is that he is forced to do everything as a product of his teams’ flaws. For example, Brian Cook points out that his rebounding is merely a function of being the second tallest player on his team. Maybe so, but I have a hard time believing that Harris wouldn’t be a tremendous defensive rebounder for any school in the country.

Villanova by the Numbers has been investigating the effect that moving the three point line back a foot had on last year’s college basketball season. Nova by the Numbers focused on how Luke Winn’s predictions from a little over a year ago look in retrospect. Winn’s hypothesis was that the biggest winners from the move would be teams that don’t rely on the three point shot or defend the three point line well. The losers would be perimeter oriented teams that shoot a lot of threes and teams that make a low percentage of their three point shots in general.

The hypothesis makes so much sense that it almost seems rudimentary. Judging by Michigan’s 2007-2008 statistics, they should have been negatively affected by the move (and that’s probably an understatement). The 2007-2008 Michigan team was one of the worst in the country at making (31.2%) and defending (38.1%) three point shots yet they still shot 40.7% of their field goal attempts from behind the arc.

So how did Michigan deal with the move? They shot even more three point shots at a slightly higher percentage. (They also made a dramatic improvement in three point defense — their opponents shot 31.1% compared to 38.1% in 2008.)

Michigan kept on chucking and somehow found success, going from 10 to 21 wins in only a season.  The three point shot is obviously a staple of the Beilein offense.  Therefore it’s not surprising that Michigan was more reliant on the three point shot than any other NCAA tournament team.

Top 10 3FGA/FGA for NCAA Tournament Teams (National Rank to the left, NCAA seed in brackets)

  7 Michigan[10] (B10)               47.9
 11 Arizona St.[6] (P10)             45.3
 13 Butler[9] (Horz)                 45.2
 15 Portland St.[13] (BSky)          44.8
 26 Oklahoma St.[8] (B12)            41.3
 29 Chattanooga[16] (SC)             41.2
 38 Akron[13] (MAC)                  40.0
 40 Mississippi St.[13] (SEC)        39.7
 54 Utah[5] (MWC)                    38.4
 58 American[14] (Pat)               38.1

That list is an eye opener. There are very few high major teams in that group, only Arizona St., Oklahoma St., and Mississippi St, and none of the top ten made it passed the second round.

This clearly isn’t a strategy that is replicated often with success at the high major level. Of those four high major teams, Michigan’s 33.4% three point shooting percentage was the worst among the group by a pretty significant margin. It’s clear that perimeter oriented teams were adversely affected by the three point move.

Nova By the Numbers points out that three of the ten interior oriented offenses that Winn identified before the season ended up in the Final Four (UNC, UConn, and Michigan State). Perimeter oriented offenses didn’t perform so well but I’m not sure John Beilein is too concerned as his tournament success is well documented. Despite the success of interior oriented teams, John Beilein’s teams still perform better against their seed than any other college coach.

Michigan’s three point shooting numbers are even more shocking when you realize that Manny Harris and DeShawn Sims combined to take 64% of Michigan’s 2 point field goals. Stu Douglass (80.3%) and Zack Novak (77.8%) took the highest percentage of their shots from long range on the team with more than 3 out of every 4 field goal attempts coming from behind the arc. Seven players on the Michigan roster took 65% or more of their field goal attempts from three point range. Only Jevohn Shepherd, Zack Gibson, DeShawn Sims, and Manny Harris took more than half of their shots inside the arc.

I’ve mentioned high variance strategies in the past (explained here) and there is no doubt that relying on the three point shot qualifies as a high variance strategy. To most in the college basketball world, three point shooting is typically thought of as an underdog  strategy marred with desperation. The common thought is that truly great teams will pound the ball inside rather than shoot away.  However, John Beilein’s best teams actually appear to shoot more three point shots than his teams that struggle.

 Michigan      2009 21-14 (7)      47.9
 Michigan      2008 10-22 (42)     40.7
 West Virginia 2007 27-9  (5)      49.0
 West Virginia 2006 22-11 (2)      51.4
 West Virginia 2005 24-11 (7)      45.9
 West Virginia 2004 17-14 (25)     40.1
 West Virginia 2003 14-15          37.6

John Beilein coached teams play their best when they favor a strategy that is generally frowned upon in the basketball world. The numbers tell the whole story last year: Michigan succeeded by shooting a lot of threes (7th) even while making a low percentage (195th).

The question is what happens going forward — does Michigan continue to shoot so many three point shots or do they revert toward a more traditional style of play. Looking at John Beilein’s history, it is hard to imagine Michigan relying on the three ball any less than they did this year.

The first place potential change would come from would be the incoming freshmen class. Of the four scholarship players and two walk-ons, three players would be described as shooters first and foremost (Vogrich, McLimans, and Bartelstein). Jordan Morgan gives Michigan a big guy that they were lacking last year, but after knee surgery his impact is questionable. Eso Akunne is without a position, but he possesses a well rounded versatile game.

The one guy who has to potential to redefine the offense is Darius Morris. Darius has the ability to create for himself and others in a way that none of the point guards on last year’s roster could. If Darius can provide a threat to drive and score it would go a long ways toward making Michigan’s offense multi-dimensional and giving Michigan three guys who are a threat to score inside the arc rather than just two.

However, relying on a freshman point guard to reshape an offense is probably too much to ask for. I wouldn’t be surprised to see Michigan shoot over 50% of their shots from long range next year but they need to improve their shooting percentage. When you shoot more three point shots than just about every other high major team in the country, you’re going to want to rank higher than 195th in percentage made.

The three point shooting issue is one that has confronted Beilein teams for years and there is no firm answer about what is right and what is wrong. For example, the three point shot was the reason Michigan trailed by 20 points versus Indiana at Assembly Hall (3-18 first half) but it was also what enabled the comeback (7-17 second half). The success that Michigan had last year despite not shooting a very high percentage says one of two things: the strategy really works or Michigan got very lucky.

The topics for discussion on this subject are endless, so let’s hear your thoughts in the comments and then maybe we can revisit this subject in a couple weeks with some follow up.