Interaction Effects and Diminishing Returns

BACKGROUND

This continues what’s turned into an ongoing conversation between myself and Nathan Walker (aka @bbstats) of  the basketball distribution, which started with my last post, continued over at Nathan’s site, and has been supplemented on Twitter.  I started by trying to find out the effect that turnovers have had on the Michigan State offense, which I did by calculating what was essentially an opponent-adjusted version of what Nathan later more intuitively converted to:

[Pts/Possession] – [Pts/(Possessions – TO)]

This tells us how much a team’s offensive efficiency would change if their turnovers all magically disappeared.  Turnovers are a very simple case: there can be only 1 or 0 turnovers on each possession; and when there is a turnover, a team never scores on that possession.  Contrast that with rebounds: in theory, a team could gain 20 offensive rebounds in one possession, yet not score; another team could score after every single offensive rebound.  The only way I could think of to track this kind of thing is to look at play-by-play data, which can get extremely time consuming, extremely quickly.

Nathan came up with another way of looking at the efficiency impact of rebounding and the other Four Factors, though.  He published an Excel spreadsheet (in this post) that uses a regression equation to ask, for example, “What would Arizona’s predicted offensive efficiency be if we changed their eFG% to the league average value of 48.5%, and what’s the difference between that value and their actual efficiency?”

How Much Are Turnovers Hurting Michigan State?

[NOTE: Almost the exact same article can be written for Baylor, except that Baylor hasn’t played any tough games, and as a result are undefeated.  But I wanted to choose just one team to refer to throughout.  So, Baylor fans, just Ctrl+H and replace “Michigan State”/”Tom Izzo” with “Baylor”/”Scott Drew”.]

A 6-3 record against a tough schedule certainly isn’t the end of the world, and as The Only Colors pointed out, the Spartans have had plenty of success in the postseason after slow November/December starts.  But Michigan State was ranked #2 in the preseason AP poll, and the team is clearly struggling more than expected.  Taking a look at their stats page on kenpom.com, what jumps out are the big red splotches on the left: they’re ranked 322nd nationally in Turnover%, 293rd in FT%, and 298th in Steal%.  But what are those marks costing Tom Izzo’s team?  Quite a lot of offense, it turns out.

TURNOVERS/STEALS

One way to gauge the effect of turnovers is to look at what happens when a team doesn’t turn the ball over.  To calculate a team’s offensive efficiency on possessions where they managed to hang on to the ball (TOAdjOff), I used a simple formula:

TOAdjOff = Adjusted Offensive Efficiency / (1 – Turnover%)

I then subtracted this from their actual adjusted offensive efficiency, to get what I’ll call turnover cost.  It tells us how much a team’s adjusted offensive efficiency would increase if they somehow never turned it over.  Here’s the top 20 in the country:

In case you’re wondering, that value of 150.6 for TOAdjOff is 3rd in the country, behind Duke and Georgetown.  When the Spartans don’t turn it over, they’re among the best of the best.

Of course, a turnoverless team is a pipe dream; a more reasonable goal for the Spartans is to try to improve their TO% from abysmal to merely average.  This seems doable – the average MSU TO% over the last 8 years has been 21.4%, which is right in line with this year’s national average of 21.2%.  Using the same concept as above, but adjusting TO% to 21.2% instead of 0%, Michigan State ends up with an offensive efficiency of 118.7 (a gain of 6.5 over their current 112.2).  That would bump their offensive rank from 26th to 4th, and their Pomeroy ranking from 14th to 5th.  Couple that with what I can only assume would be a dip in opponent transition points, and they could rise even higher.

FREE THROWS

Michigan State is nearly as poor at free throw shooting as they are at preventing turnovers, but it’s not nearly as important because: A) a missed free throw only costs 1 point, while a wasted possession costs, as we saw above, 1.5 points; and B) there tends to be far fewer free throw attempts than possessions.

The Spartans have a 63.4 FT% so far, compared to a national average of 68.1%.  Over their 202 FTA, that amounts to a difference of 9.6 total points.  Working back from their number of possessions, that works out to 1.5 points per 100 possessions.

ALL TOGETHER NOW

If you add those 1.5 points onto the 6.5 gained from reducing turnovers, Michigan State’s offensive efficiency would rise to 120.2.  However, because the gap between the top 4 teams (Duke, Kansas, Ohio State, and Pittsburgh) and the rest of the field is so large, their overall ranking wouldn’t change.  Still, if Tom Izzo can tighten up (see also: tighten up) his leaky boat, he’ll have a good chance of floating down to Houston, come April.

How much will Kyrie Irving’s Absence affect Duke?

[EDIT: Ken Pomeroy posted a treatise on plus-minus which pointed out there’s a great deal of error inherent in the use of +/- data, something which has also been pointed out to me by John Ezekowitz.  At this point, I’d advise you to take everything I wrote below with a huge grain of salt.  And I doubt you’ll be seeing any more +/- analysis from me.]

There was a great post by the basketball distribution a few days ago about the effect of individual players on a team’s offense.  It ended up being extremely topical, given A) his choice of Duke as one of the example teams, and B) Kyrie Irving’s toe.  He calculated that removing Irving’s production from the Duke team would in theory reduce their offensive efficiency by about 3.1 points per 100 possessions, if the vacated minutes were filled proportionally by the other Duke players according to their share of minutes played so far, and if they all played at the same level.  (Obviously, those assumptions are questionable, but it’s the best that can be done with the available data.)

I thought I’d take a look at it from a different angle, one that is probably on even more tenuous footing, but that is nonetheless interesting.  I thought that perhaps, as a freshman, Irving might not be as advanced as his teammates defensively, so losing him might actually improve Duke’s defense.  The only way I could think of to investigate this was to use StatSheet’s plus-minus data to find out what has actually happened this year when Irving sits on the bench.  Before I get to the numbers, I should strongly emphasize that this data is very dependent on who all the other players in the game are, and we shouldn’t take it to seriously.  But I thought the results were drastic enough, and surprising enough, that they’d be of interest.

The Most Best On The Best [Or: Skillz]

[Apologies to Mrs. Rowland, Mrs. Akers, Mrs. Davis, and all my other English teachers for the mangled title.]

I wanted to do something to celebrate this week’s early Christmas present, the unveiling of tempo-free player stats on kenpom.com, but it’s too early, and the schedules have been too sweet, to draw many meaningful conclusion.  So I decided to do something kind of fun and interesting and statistics-oriented, but totally nonanalytic.  Something Stark-ish.  I went through Pomeroy’s top 25, and for each team, I found the one player who attained the highest ranking in one of the tempo-free stats.  I excluded % of minutes played, offensive rating, % of possessions used, and % of shots taken, because I was looking for specific skills, not overall quality.  For the most part, these turned out to not be the first player you think of when you think of a team, which is what I hoped.  There are some players below who have some potential, and need to build around a skill they already have, some that clearly are on the court only to do that one particular thing, and some who are just great at everything.

[For definitions of the stats below, see “PLAYER SECTION” here.]

1. KANSAS – Markieff Morris, 36.6 DR% (1st)

The Lesser of the Morrii gets the spotlight here.  His DR% last year was “only” 20.5% (152nd), after a 20.0% his freshman year, but both of those Kansas teams had Cole Aldrich in the middle, gobbling up opponent misses.  It stood to reason that his numbers would go up this year, but not this much.  They should drop back down to earth against Big XII opponents.

2. DUKE – Kyrie Irving, 69.6 TS% (36th)

Freshmen are not supposed to be this good.  They’re supposed to force bad shots, settle for jump shots too easily, maybe not practice free throws enough.  But Irving’s shooting percentages are 59%/45%/90% (2/3/FT), and he’s 147th in the country in drawing fouls.  And to top it off, he’s 87th in assist rate, at 31.2%.

3. OHIO STATE – Dallas Lauderdale, 16.9 Blk% (3rd)

Only 8 teams in the entire country block shots at a higher rate than Lauderdale does when he’s on the court.  And it’s a good thing he is so dominant, because the rest of team blocks basically nothing.  He has 69% of tOSU’s blocks, despite only playing 10.4% of the player-minutes.

4. PITTSBURGH – Talib Zanna, 17.0 OR% (24th)

The 2010 season was the first year since Pomeroy started tracking OR% that Pitt didn’t have a monster in the middle (DeJuan Blair 09/08, Aaron Gray 07/06, Chevon Troutman AND Chris Taft 05).  Though Zanna’s not at Blair’s level, he has helped propel the Panthers to 1st in the nation in team OR%.  Cue Radiohead.

5. WASHINGTON – Aziz N’Diaye, 19.8 OR% (7th)

All the 7-foot Senegalese N’Diaye does is block shots, rebound, and miss free throws.  Despite his impressive ranking in OR% and Blk% (35th), the number that practically leaps off the page when viewing his stat line is his 140.9 FTRate. If he had enough minutes to qualify, that would place him 2nd in the NCAA, after Memphis’s Wesley Witherspoon. Unfortunately, he only shoots 42% from the line.  Maybe somebody who watches more UW ball can fill me in – is he getting to the line because it’s so easy for him to receive a pass in close, and teams are forced to play tough defense?  Or is this the result of some Hack-A-Ziz defense?  Seems like the latter could work out pretty well.

6. ARIZONA – Derrick Williams, 75.9 TS% (4th)

Was there any doubt it wouldn’t be Williams listed here?  He’s also 6th in eFG%, 11th in OR%, 11th in FD/40, 47th in FTRate, has a shooting line of 65%/82%/79%, and is, in my book, the frontrunner for National POY.  His only weaknesses are a low assist rate (but really, why should he pass it?) and a high foul rate (5.1 per 40 minutes).  The latter has helped limit him to only 61.6% of possible minutes played, and his 5th foul in the Wildcats’ game against Kansas was the turning point.

7. ILLINOIS – Demetri McCamey, 42.7 ARate (12th)

Combined with his team-high 24.2 %Poss, this means that 66.9% of Illinois possessions (when he is on the floor) end with a McCamey shot, turnover, or assist.  Having not seen an Illinois game yet, I’m curious what happens to the team when he sits.  Do they drift, rudderless, in a sea of frustration?

8. KENTUCKY – Josh Harrellson, 17.5 OR% (21st)

Admittedly, Harrellson is a role player, using only 10.6% of possessions in his 57.9% of possible minutes.  But given that Kentucky is only 146th in the country in 2PFG% (48.7%), it’s a pretty important role.  (Outside of Harrellson, the next highest ranking for any UK player is 59th, for Terrence Jones’s 7.1 FD/40.)

9. WISCONSIN – Tim Jarmusz, 4.1 TORate (3rd)

Pomeroy notes that TORate “can be highly dependent on context.  Players that do little passing or dribbling (i.e. spot-up shooters) will have an artificially deflated TO%.”  Jarmusz has taken 27 shots this year.  24 of them are 3-pointers.  He’s only made 7 of them (29%).  Yuck.  (The next highest ranking for a Badger is Jon Leuer’s 113th in Blk%.)

10. PURDUE – JaJuan Johnson, 6.0 TORate (19th)

In sharp contrast to Wisconsin’s Jarmusz, Johnson is most definitely not a spot-up shooter.  Only 15 of his 116 FGAs have been 3’s, and he draws 5.8 fouls per 40min (244th).  Johnson and E’Twaun Moore have put Purdue on their backs this year, with each having >25 %Poss and >28 %Shots, while still ranking 2nd and 3rd on the team in ORtg.

11. GEORGETOWN – Julian Vaughn, 13.0 Blk% (13th)

Vaughn’s Blk% has nearly doubled from last season’s 7.0%, and his share of possessions has risen from 19.3% to 25.4%.  But that last increase might be bad for the Hoyas, as his ORtg is only 102.3 – only freshman Nate Lubick is lower, among players with %Min >20.

12. BAYLOR – A.J. Walton, 4.5 Stl% (67th)

This one isn’t quite fair, as LaceDarius Dunn would probably be listed for eFG%, TS%, or FD/40, if not for the fact he’s missed time due to suspension.  Walton doesn’t contribute much value beyond his steals; he might subtract value, as he has an ORtg of 93.1 while using a significant number of possessions (22.7%).

13. UNLV – Chace Stanback, 67.3 eFG% (37th)

UNLV has a difficult-to-guard weapon in Stanback, a 6’8” junior who is tall enough to compete down low, but can step out and hit a three (11 for 29 through 8 games).  The Rebels seem to know it – they let Stanback take the most shots when he’s on the flower (26.4%).

14. MICHIGAN ST – Draymond Green, 25.7 DR% (39th)

A poor man’s Derrick Williams, in terms of filling the tempo-free stats sheet: he ranks in the top 309 in everything except %Min, %Shots, TORate, and FC/40.  It’s surprising that he’s the team’s best defensive rebounder, despite being only 6’6”, but what’s more surprising is that he shoots nearly identical from 2, 3, and the FT line: 56%/54%/55% on 45/24/38 attempts.

15. VILLANOVA – Maalik Wayns, 37.0 ARate (32nd)

Can you dish out a ton of assists, avoid turning it over too much, and still have a negative effect on your team’s offense?  Apparently Wayns can.  Eyeballing the numbers, it’s almost certainly due to his 5 for 30 performance from long range.  Last year he only hit 32% on 54 attempts, so there’s no guarantee that will substantially improve.

16. BYU – Jackson Emery, 5.8 TORate (16th)

This was the battle of do-nothings, as Emery’s low TORate (the product of not doing much other than shooting on offense) edges out Jimmer Fredette’s extreme foul avoidance on defense (24th in FC/40 at 1.1).  Another spot-up jumper type (shoots over 7 threes per game), Emery also contributes a 53rd-ranked 4.7 Stl% on the other end.

17. SYRACUSE – Scoop Jardine, 43.9 ARate (9th)

True story: I turned on Syracuse-MSU last night, and the very first play I saw was Scoop Jardine making a beautiful pass to Rick Jackson for an easy dunk.  Guess I had about a 50/50 shot.  He’s Jason Kidd-esque, but that unfortunately includes the terrible shooting range, as he’s 13 of 47 (28%) on threes this year.

18. WEST VIRGINIA – John Flowers, 9.4 Blk% (48th)

If he were an inch shorter, at 6’6”, he’d be the top shot blocker for his height.  Unfortunately, the top swatter in the whole nation happens to be 6’7” William Mosley of Northwestern St, so Flowers is just another guy that’s good at defense.  He’s also a solid rebounder, and gets to the FT line enough that he’s a net positive on offense.

19. TENNESSEE – Brian Williams, 18.0 OR% (15th)

He’s mostly your typical clumsy giant – good at rebounding and blocking shots, doesn’t get very involved in the offense (17.3 %Poss), and bricks a lot of FTs (58% on the year).  But he’s cut his TORate by a third from last year, and ranks 292nd lowest.

20. SAN DIEGO ST – Kawhi Leonard, 26.9 DR% (24th)

The Aztecs’ MVP so far, Leonard’s 122.6 ORtg is 12th in the country among players with a usage rate of at least 26%.  As a freshman last year, he was a high-usage (24.6%), low-efficiency (106.5) player, but two things have changed this year.  He’s cut his turnovers in half, to 9.1% (79th), and he’s improved his 3PFG% from 21% to 38%.  The rebounding was already good, and hasn’t dipped this year.

21. LOUISVILLE – Terrence Jennings, 15.9 Blk% (4th)

According to the height/weight numbers for last year and this year on kenpom.com, Jennings lost 1 inch and 20 pounds in the offseason.  I'm not sure about the inch, but the getting rid of that 20 pounds seems to have given him some extra bounce – his block rate is up over 50%.

22. FLORIDA – Erving Walker, 1.4 FC/40 (64th)

Wow, this is a boring one.  Walker gets plenty of steals (3.4%, 263rd), so it doesn’t seem like his low fouls are due to a swinging door defensive philosophy.  Florida has the 4th lowest opponent FTRate in the country, so I’m going to give nearly all the credit to Florida’s use of zone defense.

23. VANDERBILT – Festus Ezeli, 21.3 OR% (2nd)

Festus Ezeli actually has a higher OR% than DR%, which is weird.  Maybe Festus Ezili is too busy blocking shots (9.6%, 42nd) to worry about grabbing rebounds.  Or maybe Festus Ezeli is getting his defensive boards stolen by equally-awesomely-named teammate Steve Tchiengang (pronounced ChainGang … at least when I say it).  Festus Ezeli.

24. KANSAS STATE – Freddy Asprilla, 15.7 OR% (46th)

Hmm, Asprilla has the exact same rebounding rate on offense and defense.  Maybe this is more common than I though.  The fact that Asprilla has enough minutes to qualify is probably a bad sign for the Wildcats, as he has an ORtg of only 92.9.  And commits 6.3 fouls per 40 minutes, oh dear.  Which probably means Frank Martin would like him to play even more.  This is funny: his 31% FT% is better than 3 other teammates.

25. TEXAS – Tristan Thompson, 108.8 FTRate (13th)

Getting to the line for more FTA than FGA is usually a good thing, since FT’s are usually the most efficient way to score.  But not when you shoot 48% from the FT line, and 53% from the field.  Thompson is just a freshman, so hopefully he will improve.  He’s already a slight positive on offense, even with so many missed opportunities.