3 point FG Attempts vs Offensive Efficiency

Submitted by ehatch on March 8th, 2012 at 3:05 PM

[Ed-Ace: Bumped on a slow day. I'm working on the initial Big Ten recruiting rankings for the class of 2013, which should be up later today.]


I have never played basketball at any level, outside of a few pickup games.  I'm not all that good at statistics, so I apologize for any and all statistical errors.  However, as a former actuary, I am good at finding trends and patterns in data.  Last week, Maize N Brew had a good article on whether Michigan lives and dies by the three. The conclusion was that the offensive efficiency was not really dependent on hitting 3 pointers.  When looking at it the data presented, it looked as though the more three point shots UM takes the worse the offensive efficiency.  I decided to take a closer look.

3 point Attempts vs Offensive Effiency.

I went throught the game by game box scores and looked at the 3-point attempts and plotted it against the offensive efficiency.  [I removed Ferris St. since they aren't a D-I opponent.]  What I found was slightly disappointing.  The correlation was -0.15 (the negative means the higher the number of 3-point attempts the lower the offensive efficiency) and the R-squared was a low 0.02.  However, when I took a closer look, I noticed that two of our lower offensive efficiency numbers came against Ohio and MSU, which is no surprise considering that they are the #1 and #2 best defensive efficiency teams in the country. 

So to adjust for that I looked at the amount the offensive efficiency exceeded the opponents average adjusted defensive efficiency from Kenpom.  The result was more in line with what I expected.  The correlation drops to -0.49 and the R-squared rises to 0.24. 

Looking at the results, when U-M shoots 20 3-pointers or less, Michigan is 10-0 (4 of them RPI Top 50 wins, 5 more Top 100 wins).  Shooting more than 25, Michigan is 6-3, but those wins came against Arkansas Pine Bluff, Oakland, 2 overtime wins against Northwestern, Bradley and Iowa St (the only quality win in regulation).  The 3 losses were the 3 worst performances of the season, @Iowa, @Arkansas, and the loss to Purdue. 

Other Teams

So is this unique to Michigan?  I looked at Northwestern, a team I think is most similar to Michigan's style of play (in the B1G).  They spread the floor, shoot a ton of 3s and look for back door cuts.  And I found they have a positive correlation between 3 attempts and offensive efficiency.  A correlation of +0.17 (after adjusting for defensive effiency).  The R-squared is a pathetic 0.03, but I think it is important to note that the correlation is the opposite sign. 

I also looked at Wisconsin.  Ohio relies on Sullinger and MSU relies on the offensive rebound so much that I didn't think that they would be good comparisons to Michigan.  For them it doesn't seem to matter if they shoot a lot of threes or not.  A correlation of -0.1 and an R-squared of 0.01. 

Free Throws

One of the 4 factors is Free Throw Rate.  I think this may be the most important of the 4 for Michigan.  Michigan is 10-0 vs RPI Top 100 competition when their FT Rate is greater than 25%. Michigan is 2-7 vs RPI Top 100 when the FT Rate is at or below 25%.  How does this relate to 3-pointers?  My theory is that Michigan is at their best when driving the basket and drawing fouls and not settling for jump shots of the 3-point variety (I'm looking at you THJ).  It might also explain why Northwestern gives us fits.  Their zone forces us to take a bunch of 3 point shots (like 38 of them). 

So as we go into the post season:

  • Cackle with knowing glee if Michigan is driving the basket
  • Worry if we draw a zone team that forces us to shoot a lot of 3 pointers. 

If anyone has a team they would like me to look at, let me know. I'm going to try to figure out how to add graphs so you can see the dramatic downward slope of Michigan's efficiency against 3 point attempts.



March 8th, 2012 at 1:13 PM ^

Great analysis. Thanks. You do a good job of not confusing correlation with causation. In this case, it doesn't seem too surprising, given Beilein's offense, that this would hold true. M tends to either get back-door cuts and easy shots or 3s. If a zone team forces us to shoot 3-pointers (ala NW), our best strategy may still be to take the open 3 rather than force something inside. I don't think the answer is to necessarily drive more (though in some cases *cough* THJ *cough*  yes, we should) but to take the best look we can get, acknowledging that we're at our best when able to take more 2s than 3s.


March 8th, 2012 at 3:32 PM ^

I did actually take a look at 3PA vs. Offensive Efficiency and pretty much came to the same conclusion that you did. Games like the last one at Northwestern where we shoot a bunch of threes and only make a few are less than ideal. Given our 3 point and 2 point percentages, our value of a three point shot is 1.071 points per shot, and our two point shot is worth 1.094 points per shot. Since I'm assuming that there's lower variance for two point shooting on a game-by-game basis, putting up more twos (which are often easier looks, particularly in the context of our offense) is the optimal strategy. Interestingly, we shot the fewest amount of threes all year at home against Ohio State, and won. We only made three.


March 8th, 2012 at 3:57 PM ^

I arrive at slightly different numbers:

Michigan shot 46.02% from 2-point range this year.  That equates to .920 points per attempt.

Michigan shot 35.55% from 3-point range.  That equates to 1.066 per attempt.

Did your analysis factor in foul shots by chance?


March 8th, 2012 at 3:42 PM ^

You need to somehow account for the end of game hack fest action that occurs when we are leading by a couple possessions. That could dramatically increase the percieved importance of FTR in wins vs. losses.


March 8th, 2012 at 3:52 PM ^

-# of FTs attempted increases greatly for the team ahead in last few minutes of a game.I'm no actuary but I suggest two FT Rates:1 before last 3 minutes of game and 2 Rest of game          

 - An often overlooked stat is Reb Effiency  ie  % of missed shots rebounded by offense.Mich is woeful at both ends of the floor in this area.I'm curious if this is a "Beilins offense thing" or "Mich is a small team thing"  

Vacuous Truth

March 8th, 2012 at 11:54 PM ^

I'm pretty sure M's poor reb% has a lot to do with beilein's style. reb% is tired directly to style of play, specifically with regards to the fast break. If you crash the offensive glass, you're more susceptible to giving up fb points. And if you crash the boards on d, it's tougher to get points in transition.

So I think beilein see's that, with our small lineups, we're not going to be great on the glass anyways, so we might as well surrender some rebounding chances in exchange for winning the transition game


March 8th, 2012 at 4:02 PM ^

You can't draw conclusions from data with such low R2.  The R2 is telling you that the percentage of the variation you're accounting for with this variable is 2-3%.  So of all the wild outcomes that can occur on the basketball court, the 3pt attempts can explain less than 3% of the result.

Don't get mislead by the fact that the conclusions line up in a way that you can rationalize - this data isn't conclusive at all.


March 8th, 2012 at 5:22 PM ^

I don't disagree, the R squared of Wisconsin and Northwestern are really too low to draw any conclusions.  Michigan's R squared of almost 25% is much better, but still very difficult to ascribe many conclusions.  The 25% explains more than any of the individual 4 factors. 

There are a number of things that could explain the correlation.  Maybe they are forcing a bunch of turnovers, and are getting easy layups.  Maybe we are getting the ball into Morgan (seems unlikely).  Maybe we are shooting a bunch of long twos. 


March 8th, 2012 at 5:11 PM ^

Thanks for the comments on FT Rate.  I went back through the play by play to see how free throws came in the final 2 minutes of the game.  While it did have an impact in lowering the FT rate across the board, it didn't change much outside of that. UM went 8-0 against Top 100 teams with a FT rate greater than or equal to 25%, 4-7 with less than 25% FT rate.


March 9th, 2012 at 12:02 AM ^

I have watched them a few times this year, and saw the game against UConn today.  So the story goes in the Big East, limited scouting is done and you play how you play against everyone.  That seems to hold true with Syracuse.  They do something against everyone and they do it very well (primarily because it's practiced and practiced and practice); they run a 2-3 zone the majority of each game and do it well, forcing a team to be consistent at one thing (shooting 3's and getting to the middle and getting looks from there with a big man/more "outside" good shooting looks).  It's tough to beat them because it is hard to do that for an entire game and score more points than they're equally/greater quality offense.

As I was watching them today, I thought to myself, "How would Belein do with this matchup?".  I don't know why, but I would love to see a Beilein/Boeheim game.  I think THIS Michigan team, and I may be wrong and totally naive to Cuses' talent advantage(?) and quality of team they are, could hang and surprise people against that vaunted 2-3 Zone.  I think Michigan could hit "enough" shots, and I think if THJ was efficient playing aggresive ball and Smotz had a good rhythm they could give them fits, andTrey has the ability to attack that zone to propel the offense.  It may get a bit scary down low but I've seen these guys over-achieve enough against bigger teams that their size doesn't scare me.

Sorry, long post, but March gets me excited with all the many potential matchups.  Hope this was all relevent enough to the OP in regards to shooting.  Main point, against a tough defense like 'Cuse, I think Michigan's shooting efficiency (plus smart basketball Beilein can make them play) can play up to other teams.


March 9th, 2012 at 3:53 AM ^

Is that, like free throws, the numbers can be very different in the first 35 minutes and in the last five minutes. If you are 7 points down with 2 and change to play, you are likely to hoist a three, even if that's out of your offense. In other words, it could be that it was because Michigan was losing that they shot 20+ threes. Correlation does not imply causation!


Trimming the data - either by dumping the last shots taken, or by only including shots taken when the game was close - might provide some additional insight, though off course it may be really difficult to get that information. I kind of think hoops stats will be much better in another 10 years than they are right now.