I should note that I tended to choose teams who were at least moderately successful, although not all were champions or finalists.  For some reason, good-but-not-great squads and awesome regular season teams which faltered in the playoffs seem to dominate this list.  Still, some NBA champs will make the list; it is hard to talk about the 2010’s without some mention of LeBron James or the Golden State Warriors.

As a small point of clarification, I considered teams from the 2009-10 season through this past year, 2018-19.  Also, a huge thank you to basketball-reference for providing most of the statistics I touch on here.

Without further ado, let’s begin!

The 2012-13 New York Knicks

I will note at the outset that this season still feels like a dream; it’s as if I have to check the basketball-reference page just to make sure it really, in fact, happened.  The New York Knicks, a basketball team from the Big Apple known for their general ineptitude, were legitimately… good.  At least for a season.

Let’s start with the top-line numbers.  This Knicks team won 54 games and weren’t just lucky; their expected wins based on point differential were 53.  The 2012-13 edition posted the 6th best regular season net rating (point scored minus points allowed per 100 possessions) in the entire league and did it by achieving the 3rd best offensive rating (points scored per 100 possessions).  How did they score so efficiently?  They did it by shooting 3-pointers before it was cool to shoot 3-pointers.

The 2012-13 Knicks attempted 35.4% of their field goal attempts from behind the 3-point line, the top mark in a season in which the league average team 3-point attempt rate was just 24.3%.  No team other than the Daryl Morey GM’d Houston Rockets was even close. And they didn’t just attempt them- they also made them. They shot 37.6% on 3-pointers, good for 5th in the league.

Everybody on the team was given the green light to hoist the long-ball.  J.R. Smith, their minutes played leader in the regular season, attempted 416 3-pointers and made 35.6% of them.  Carmelo Anthony, in his age 28 season, went from never posting a season with more than 4 3-point attempts per 36 minutes to 6 per 36 minutes.  Long-range specialist Steve Novak made an astounding 42.5% of his 351 attempts.  A 39 year-old Jason Kidd shot them. His backcourt mate Raymond Felton shot them.

Another secret to their offensive success was posting the lowest turnover rate in the NBA at 11.7%.  This team was able to usually get a shot attempt up and avoid playing too much transition defense, which was particularly important for an older club (they had the 3rd highest average age at 30.2 years).  They also managed to not be horrible on defense; they finished 18th in defensive rating.

I remember Jason Kidd being an important part of this team.  His passing, often to a rim-running Tyson Chandler, and timely 3-point shooting produced some awesome highlights.  In terms of assists per 36 minutes though, his passing was actually a good bit down from his New Jersey Nets peak.  He still had great hands on the perimeter, as his 2.2 steals per 36 minutes evidenced, and he paced the team to the 4th best opponent turnover rate in the NBA.  But this was the twilight of his illustrious playing career; the next season he was coaching the Brooklyn Nets.  Though he was arguably a better player than a coach.

No early 2010’s Knicks discussion can be complete without some mention of Carmelo Anthony.  As previously stated, Melo became more of a 3-point shooter this season.  He also posted the highest usage rate of his NBA career this year, his age 28 season.  Though I remember him taking a leap in shooting efficiency as well, this was not the case.  His 0.560 True Shooting Percentage mirrored his Denver Nuggets days.  Perhaps this was because his increased 3-point volume came at the expense of getting to the foul line; his 0.344 free throw attempt rate was at the time a career low.  He also shot a lower percentage of his overall field goal attempts at the rim.

I thought Anthony became a more willing passer this year, but it was actually the previous season where he posted his then career high assist rate.  Overall, aside from the increased reliance on 3-pointers, this Anthony year looked statistically a lot like many of his other successful seasons.  He would have one more strong statistical year in 2013-14 before exhibiting a noticeable decline.

The one truly successful Knicks campaign of the 2010’s ended with a 6 game conference semifinals series loss to the Paul George-led Indiana Pacers.  I recalled this series as being fairly lopsided in the Pacers’ favor, but this was not the case.  Each team actually scored the exact same 537 total points in the series.  This was also the season that the Knicks memorably wore “funeral black” to an elimination playoff game against the Celtics; they lost the game but held on to win the series.

Another interesting nugget: this was backup point guard Pablo Prigioni’s first season in the NBA, coming over at age 35 from the Spanish squad Baskonia.  And, even as a 35 year-old rookie, he was a useful player!  He played roughly 1300 minutes, made almost 40% of 3-pointers, and managed to post a 0.595 TS%.  Moreover, he did all this while bearing a last name which was extremely satisfying to pronounce.

As of this writing, this was the last Knicks season with a positive point differential.  The 2013-14 edition still shot 3-pointers (they were 3rd in attempt rate), but they slipped to 11th on offense and 24th on defense, in terms of points per 100 possessions.  Still, Knicks fans can always cherish their 2012-13 campaign.  For one glorious season, New York hoisted 3-pointers before it was cool to hoist 3’s and reaped the rewards .

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The photo of Carmelo Anthony was taken by Alexandra Walt on 11/23/2013. It is on Flickr and is dedicated as being in the Public Domain.

I was actually already thinking of writing about this, but now, with the Paul era in Houston coming to a premature end (hello Russell Westbrook!), I think its worthwhile to look back and evaluate the Harden-Paul pairing .

The Landscape Before Paul Went to Houston

First, a bit of context.  The 2016-2017 Houston Rockets, the edition before Paul’s arrival, were a very strong team.  They won 55 games and sported a +5.5 net rating, good for 3rd in the NBA, per basketball-reference.  They had a really good offense (James Harden was an MVP candidate, after-all) but a mediocre defense that was 0.2 points per 100 possessions below league average.

Harden, in his age 27 season, was already the free throw machine that we know and love with over 10 FTA per 36 minutes, per basketball-reference.  But this was the season that he upped his three-point attempt rate to 49%, from roughly 41% in 2015-2016.  The Rockets outscored their opponents by +6.4 points per 100 possessions with Harden on the court but were a more pedestrian +2.4 with him off, per pbpstats.  The decline was mainly due to the offense coming back down to earth without Harden on the court.

In Los Angeles, Chris Paul had a very fine statistical 2016-2017 season.  At age 31, he posted a career high 61.1% true shooting percentage, buoyed by shooting a career high 41.1% on three-pointers with a 38.5% three-point attempt rate (per basketball-reference).  His Clippers posted a +4.5 net rating that season, good for 4th in the NBA.  Continuing a trend for the lob-city era Clippers, the team was roughly 19 (!) points per 100 possessions better when Paul played than when he sat, per pbpstats.  Still, perhaps foreshadowing what was to come, CP3 played in only 61 games in 2016-2017, down from suiting up for at least 74 games in each of the previous two campaigns.

Did The Paul Experiment Work?

So, did it work?  Could Houston fully realize the benefits of having two superstars who thrive with the ball in their hands?

In short, yes, it essentially worked.  But with some caveats.

It is worth remembering that the 2017-2018 Rockets posted the best net rating in the NBA, at +8.6!  They were bolstered by the new and improved 6th ranked defense in the association.  They went from being 0.2 points per 100 possessions worse than league average in 2016-2017 to 2.5 points per 100 possession better than league average, per basketball-reference.  The 2018-2019 squad was not as dominant in the regular season as the 2017-2018 one was, but still managed the 5th highest net rating in the NBA at +4.8.

To see just how Harden and Paul made it work, it is instructive to look at their on-off stats for the combined 2017-2018 and 2018-2019 seasons.  I should note that here I am filtering to only the games in which both players played, to better highlight their effect together.  My source is the excellent basketball statistics and research website, pbpstats.com.

While Harden was on the court, with and without Paul, the Houston offense thrived. But what is fascinating to me about these numbers is that 3rd row, the 1168 minutes where Chris Paul played and James Harden sat.  Keep in mind that these are for games in which both players played, so here Paul is leading bench heavy units at the end of the 1st and 3rd quarters and beginning of the 2nd and 4th, while Harden takes a breather.

In those Paul only minutes, the Rockets’ defense was really good, posting a 103.2 defensive rating! And the 115.7 offensive rating shows that Houston was able to keep its offense afloat with Paul and without Harden.  Both numbers are very impressive. For context, NBA offense, in general, tends to be less efficient for both teams when bench heavy lineups take the floor.  This makes the Paul only offensive rating even more important. Not only did Houston’s Paul-led units lock down their opponents, but they were also able to keep putting the ball in the basket at an efficient clip.

The Rockets were able to accrue these minutes with the bench unit plus Paul by effectively staggering their stars.  They typically took Paul out a little earlier in the 1st and 3rd quarters and then put him back in at the end of the quarter when Harden was taking a breather.   You can nicely see this pattern in this excellent visualization of NBA substitution patterns by Alex Wainger.  Utilizing this stagger, the Rockets played only 171 minutes over the two seasons without both Harden and Paul, for those games in which both played. 

Of course, Houston’s on-off stats with various combinations of Harden and Paul cannot be looked at in a vacuum.  In basketball it can be hard to disentangle individual credit from team success; the supporting casts contributed mightily to these numbers.  The 2017-2018 squad relied on bench contributions from P.J. Tucker, Luc Mbah A Moute, and Eric Gordon, while the 2018-2019 bench minutes featured more Gerald Green, Austin Rivers and Gordon.  The 2017-2018 bench players in particular deserve a lot of praise for Houston’s stellar season.

In terms of individual statistics, James Harden raised his high usage, high efficiency high-wire act to new heights in the past two seasons.  An over 61% True Shooting Percentage paired with plus 40% Usage speaks for itself!  Chris Paul, on the other hand, had an efficient scoring season in 2017-2018 but experienced a drop-off in 2018-2019.  We can see this in his declining true shooting percentage.  His usage also dipped a little, particularly in 2018-2019.  Data in the graphs below is from basketball-reference.

Paul still posted an above average true shooting percentage even in 2018-2019; league average is roughly 55%.  It should also be noted that at least some of the decline in scoring efficiency for CP3 was due to poorer outside shooting; his three-point percentage declined from 38.0% in 2017-2018 to 35.8% in 2018-2019.  And he hoisted over 6 three-point attempts per game in each of his seasons in Houston, the two highest marks of his career.

No evaluation of the Harden and Paul experiment would be complete without mentioning the fact that CP3 played in only 58 games in each season due to injuries.  A potential source of worry, Paul’s health, did in fact hamper the team. This was particularly true in the 2018 playoffs.  We all still remember Houston going up 3-2 in their series with the Warriors, before Paul had to sit out the remaining two games with a hamstring injury and Golden State ultimately advanced to the Finals.

Though I have to to do more research on this in general, I think the Paul experiment in Houston is a piece of positive evidence in favor of staggering star players, especially ball-dominant ones.  A player who can effectively create efficient offense on the second unit can be extremely valuable for bolstering the offense at a time when it is typically not as strong.  This piece of advice could be relevant to the Rockets again this year with the high-usage Russell Westbrook now paired with James Harden.

The Rockets did not win a championship in either of their seasons with Chris Paul, so perhaps history will judge this experiment as a flop.  Still, I think there was a lot to like from two seasons of one of most interesting superstar combos that the league has seen.

All this turbulence and meteoric shifting of the NBA landscape got me thinking: who is actually going to win the whole thing?  This NBA season appears to feature the most wide open title chase that we have seen in years, and that’s the way Vegas sees it too.

Using historical title odds from previous seasons saved on sportsodds.com, and this year’s title odds from BetOnline (documented by OddsShark on July 9th), I plotted the title odds of the preseason title favorite for each season.  Here’s how the Los Angeles Clippers, the current favorite with a 25% implied championship probability (if the betting market were fair), stack up with their fellow title front-runners since the 2005-2006 season:

We can see that the Warriors stranglehold on the NBA has dissipated.  The 2014-2015 and 2015-2016 seasons were more like this one by this metric, with the LeBron-led Cleveland Cavaliers installed as slightly more than a 25% favorite each year.  We actually have to go all the way back to the 2008-2009 NBA season to see a Vegas title favorite viewed as weakly as this year’s Clippers.  That season the Los Angeles Lakers were given a 22% chance to win a championship. They came through, however, defeating the Orlando Magic in 5 games.

But there is more to how open the title race is than just than just the strength of the favorite, so I decided to also look at something called information entropy.  Basically, the entropy of a probability distribution (such as the distribution of title odds) is a measure of its randomness.  The maximum entropy of a distribution with 2 outcomes, i.e. the flipping of a coin, is when each outcome is equally likely.  So you can think of more entropy  meaning more uncertainty in the championship race.  As an aside, I scaled the probabilities so that they summed to 1 for each season before doing the calculation.

By this measure too, the NBA title race is uncertain as it has been since 2008-2009.

Finally, I think it is fitting that in such a topsy-turvy year, the three teams with the best title odds are not the same favorites as those of the previous few seasons.  The Clippers, Lakers, and Bucks have waited a long time to be taken this seriously, particularly the Clippers and Bucks.  Let’s hope that the pursuit of the suddenly very winnable 2019-2020 title is a blast!

I immediately went to Twitter, eagerly searching for the details of how much Los Angeles had to give up.  A day or so later we finally got the full story: the Lakers were sending Ball, Ingram, Hart, this year’s 4th overall pick, a top-8 reverse protected 2021 1st rounder (which becomes unprotected in 2022), a 2023 pick swap, and a 2024 1st rounder (with the right to defer to 2025) to the Pelicans for the one contract year of Anthony Davis’s services.

My initial reaction: wow, that’s a heckuva lot to give up!  But there is a lot to breakdown when evaluating this trade from the Lakers’ perspective, so let’s dive into the salient questions.

How Much Better Does Davis Make the 2019-20 Lakers?

The paragraph header sounds kind of silly, right?  A lot better, of course.  But I think it’s worth trying to quantify the impact Davis has more precisely, particularly on championship odds.  After all, the one sure thing the Lakers are getting with this trade is the opportunity to have one prime Anthony Davis year, paired next to a post-prime but still extremely valuable LeBron James.

It goes without saying, but Anthony Davis is a superstar.  The advanced metrics laud his impact; he’s been a top-15 BPM and top-10 RPM player over each of the past 2 seasons.  He is only 26, so his best years are likely still ahead of him.  While there may be debate about where exactly he ranks on the Mount Rushmore of the current league, I think the prevailing view is that he is firmly a top-10 player right now and maybe even a top-5 player.

Let’s try and place a ballpark estimate on the percentage chance that the Lakers win the championship this year, under two scenarios: our current one, where the Lakers have traded for AD, and a hypothetical alternative world where another team has instead acquired Davis.

The current Lakers (on June 18th) have LeBron, Anthony Davis, Kyle Kuzma, and not a whole bunch else.  They can clear up a little more cap space depending on the timing of the trade, but they appear to be unable to get enough cap space to offer the full max to a 10-year plus NBA veteran.  It seems likely, or at least plausible, that they break up their remaining cap space and acquire other role players to build around their core.

With all this being said, the 2019-20 Lakers have shot up to 3-1 odds to win the title at the Westgate Las Vegas SuperBook, which would imply a 25% chance to win the championship.  When I see a number like this, I immediately discount the true odds in my heads, so perhaps 15-20% is a better estimate.  As a sanity check, Neil Paine of 538 wrote that their super early CARMELO model projection for the 2019-20 Lakers has them as about a +5.8 efficiency team.  In previous research, I have found that a team of that strength typically has closer to a 10% chance to win the title, but there is reason to expect that a LeBron James led squad could have another gear in the playoffs.  So a 17% chance at the title seems like a more reasonable estimate.

Though 17% might not sound like a huge number, keep in mind that only 1 of the 30 teams claims a title at the end of the season.  The 83% of the time where they do not win consists of many scenarios where the Lakers make a deep playoff run but come up a little short.  Heading into free agency, Los Angeles appears among the favorites.

To quantify the marginal impact of Davis on this year though, it’s worth considering the counterfactual universe where AD is instead traded to another team.  In that universe, the Lakers would of course still have Ball, Ingram, and Hart but these players are young and have less short-term value.  LA would also have the cap space to add another star next to James, but getting a max free agent to sign would be no sure thing.  Moreover, the Lakers might not have wanted to commit too much money beyond 2019-2020 in order to keep the option open of signing Davis in the summer of 2020.  Making an educated guess (because I do not have a ready-made projection model), the pre-AD trade roster plus a lower tier star player like Jimmy Butler or Kemba Walker feels like a second tier contender with something like a 7-10% chance of winning the title.  And there is always the possibility that they would not have picked up a star at all.

Without the aid of a statistical model, I think the Lakers increased their title odds from roughly 5% to about 17% in 2019-2020 with this trade.  That 5% figure comes from averaging the Lakers’ chances in the scenario where they acquire a second tier star with the scenario where they do not.

How Much Does This Trade Increase the Lakers’ Chance of Re-signing AD in 2020?

A 12% increase in championship win probability is not the only benefit of the trade for the Lakers.  What I think has perhaps been under discussed is that this trade appears to increase the odds that Davis is in purple and gold throughout the early 2020’s.  This is of tremendous benefit because Anthony Davis is still just 26, and 27-29 are typical peak years for a player.

I think here too it is worth putting some percentages on things.  After the trade, it appears likely that Davis will resign with Los Angeles in 2020, though perhaps on a 1 year deal plus a player option.  How likely?  I would say my prior is in the neighborhood of 85-90% likely that Davis remains beyond 2020.  Things could fall apart for the Lakers this year and Davis could decide to walk, but given that Los Angeles appeared to be his preferred destination pre-trade, I think that it is likely he gives them more time.

What about the in the scenario where someone else signs Davis, most likely Boston or New York? AD could certainly still sign with the Lakers in the summer of 2020, but I think he could plausibly be tempted to remain in his 2019-2020 landing spot, particularly if that team had a successful season.  There is a lot of uncertainty forecasting a decision a year into the future; Davis’s thought process could certainly change.  I think AD would probably still sign with the Lakers in the summer of 2020 (after all, they still have LeBron under contract for the 2020-2021 season) but I would put this likelihood in the neighborhood of 65-75%.

I think quantifying the increase in likelihood that Davis signs with Los Angeles past 2020 is a really important part of evaluating this trade.  If you think the Lakers were a coin flip to sign Davis if he were traded somewhere else but now have them at 95% post-trade, that’s really different than if you had them at 95% regardless.  If this trade is not substantially increasing the Lakers’ odds at keeping Davis past 2020, then it loses a lot of its value.

AD would really boost the 2020-2021 and 2021-2022 Lakers, particularly because LeBron James is already entering his age 35 season this year. I think those Laker teams with Davis would probably be in the neighborhood of 15% likely to take the title each season.  Without Davis and with an aging LeBron, those teams would not figure to be serious title contenders unless LA acquired another max caliber player, which could of course still happen.

It should be noted, however, that all the young players and draft picks that the Lakers gave up in this trade means that they have less firepower to make moves to boost potential AD-led 2020-2021 and 2021-2022 squads.  This makes it all the more important that the trade actually increases his odds of re-signing; if it does not, they have sacrificed some trade assets in the early 2020’s for no future benefit, beyond 2019-2020.

Where Does This Leave Us?

I will again emphasize that the probabilities I offered earlier were just educated guesses, my non-model based priors.  I expect disagreement, and I could be persuaded to think differently if presented with a convincing argument.  My main point is that I think it’s important for each analyst to think carefully about these questions when evaluating this trade. To summarize, the questions are:

1. How much do the Lakers’ 2019-2020 championship odds increase in the scenario where they make this trade vs. the scenario where another team trades for Davis?

My answer is that they go from roughly 5% likely to take the title to 17%.  Another analyst could disagree; maybe they are truly now 25% favorites.  However you answer this question is extremely important because this is where the up-front value in the trade lies.

2. How much more likely are the Lakers to re-sign AD in the summer of 2020 now vs. if another team had traded for him?

This question implicitly gets at how much you think the trade helps the Lakers of the seasons beyond 2019-2020.  If being on another team for one year would have substantially hurt the chances that Davis donned purple and gold in the future, then this part of the trade provides real positive value.  If Davis was a sure thing to go the Lakers either way, than this trade looks a whole lot worse from their perspective.  I estimated (with no inside information of course) that the Lakers went from 70% to 90% likely to sign Davis long term with this trade.  So I think there is some value here.

That this trade has value for the Lakers next season and, probabilistically speaking, the few after that is a testament to how dominant a player Anthony Davis is.  The Lakers are taking a huge gamble, however, because their late 2020’s squads will likely be bereft of high-end draft talent.  Also, all NBA players have the potential to suffer injuries or a performance drop-off, so investing so many resources in one player (even a superstar like Davis) inherently has risks.  I should note that I really like the trade from the Pelican’s side; the asset haul is substantial for just a single guaranteed year of Davis.

At the end of the day, I am really fascinated to see how this trade turns out for the NBA’s most storied franchise.  The NBA Finals are not even a week old and the offseason is already in full swing.

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Photo Credit:  The photo of Anthony Davis is attributed to Keith Allison and was taken on February 22, 2014. It is used under the Flickr Creative Commons License.

To get a feel for how a series might shake out, I like to start by looking at the regular season point differentials of both competitors.  By this measure, this Finals looks pretty even.  The Warriors and the Raptors were 2nd and 3rd in the NBA, respectively, at +6.5 and +6.1.  My simple point differential only model pegs the Raptors as slight favorites (55% chance to win the series) by virtue of having home-court advantage.  Plus, the Warriors look to be without Kevin Durant for at least the first few games in the series, which hurts their odds.

However, Las Vegas really likes the Warrior’s chances to defend their crown.  As of Sunday afternoon, the Westgate Super Book had Golden State at -300 and Toronto at +240, which implies a roughly 27% chance that the Raptors win the series.  This does not seem crazy given the playoff Warrior’s tendency to take their game to another level.

With all this in mind, I decided to do a little research into one source of variability in an NBA playoff series: 3-point shooting.  The vagaries of playoff 3-point shooting caught my eye during the extremely tight Raptors vs. Sixers series in the Eastern Conference Semifinals.  Toronto eked out a series win in 7 games despite really struggling to shoot the ball from the outside.  The Raptors made just 29.8% of their 3-pointers in the series, despite being a 36.3% 3-point shooting team in the regular season, per basketball-reference.  They were probably saved in that series by the fact that Philadelphia also shot poorly on 3’s, making just 32.9%.

In the next round, the Raptors were the ones to benefit from opponent bricks.  Their Eastern Conference Finals opponent, the Bucks, made just 31% of their 3’s while Toronto shot 37.4% for the series.  This outside shooting edge was crucial considering that Toronto won a number of close games in the series and only outscored Milwaukee by 1 point per game.

So how big a deal are 3-pointers in the playoffs?  To answer this, I considered all playoff series from 2012 to 2018.  I decided not to go back earlier because I wanted to capture a representative sample of series played in the 3-point shooting heavy league of today.

Unsurprisingly, 71% of the time the team which outshot their opponent on 3-pointers ended up winning the series.  But what I was really interested in was the following: given the difference in strength between two teams and the final 3-point shooting margin of the series, what is the likelihood that each team wins the series?

To this end, I defined Series 3-Point Margin (S3-PM) as the following:

S3-PM = (Home Team Series 3-PT% – Away Team Series 3-PT%) – (Home Team Regular Season 3-PT% – Away Team Regular Season 3-PT%)

In the above equation, the “Home Team” is the team in the playoff series with home court advantage (I will use home team in this manner from now on).  Basically, S3-PM is telling us how much better the home court team shot on 3’s relative to their opponent in the series, relative to our expectation from the regular season.

As an example, take the recently completed Raptors vs. Bucks Eastern Conference Finals.  The Raptors outshot the Bucks 37.4% to 31% on 3-pointers.  In the regular season, the Raptors were also a better 3-point shooting team, 36.6% to 35.3%.  So the S3-PM of the series (calculated from the home Buck’s perspective) is (0.31 – 0.374) – (0.353 – 0.366) = -0.051.  In other words, the Bucks were outshot by about 5 percentage points more than might be expected.

I took a look at the distribution of  S3-PM and found that it is roughly normally distributed around a mean of 0 and standard deviation of 0.06.  What this means is that if two teams with identical regular season 3-point percentages are facing each other in a playoff series, our rough 95% confidence bound for the final 3-point percentage difference in the series is +/- 0.12.  Anything in this +/- 0.12 range is not really surprising.

Using S3-PM, I ran a simple logistic regression which predicted the winner of each playoff series from 2012 to 2018.  I used only S3-PM and the difference in net rating between the home team and road team in the series (I call this net rating difference).  This model is not truly “predictive” because we are using information from an already played series in our projection.  Still, it gets at the heart of quantifying the impact of 3-point shooting on a series.

As one might expect, knowing how the 3-point battle turned out in a series is helpful in determining the outcome.  Both net rating difference and S3-PM were significant predictors of the series winner, at the 0.01 significance level.

To get a feel for how much 3-point shooting affects a typical playoff series, suppose two teams with the same regular season net rating and 3-point percentage are facing off in the postseason.  The chart below gives the predicted win probability of the home team, based on S3-PM.

What we see makes sense.  If both teams wind up shooting the exact same percentage on 3-pointers in the series, then we are not really sure who will win because the two teams have equal ability.  The home team is a slight favorite with a 59% chance of winning the series in this scenario.  But if the home team outshoots their opponent by 6 points from beyond the arc, then we know they will probably be victorious.  They have a 78% chance of winning.  The visitors do make up the 3-point deficit in the other areas of the game 22% of the time in this scenario, but it’s an uphill battle.

So what does all this mean for the Raptors and Warriors in this NBA finals? Well, let’s take it at face value that the Warriors have a 72% chance of winning this series, as betting markets imply.  A typical home court team (as the Raptors are in this series) which is this big an underdog is 5 points of net rating worse than their opponent.  Using this 5 point net rating difference, we can project the Raptor’s chances of winning the series based on the difference in the teams’ 3-point percentage in the series.  This is shown below.

To interpret the above plot, first note that the “fat” part of the distribution is centered around -0.02.  The Warriors shot roughly 2 percentage points better on 3’s in the regular season than the Raptors, 38.5% to 36.7%,  so outcomes around -0.02 (from the Raptor’s perspective) are relatively more likely than more lopsided 3-point differentials.  Centered around a mean of -0.02, the Raptor’s 3-point percentage advantage is normally distributed with a standard deviation of 0.06.

If we move to the left of -0.02, we are in a scenario where the Warriors have shot even better than expected and/or the Raptors have shot worse.  Toronto is unlikely to win if this happens, as shown by the diminishing size of the red bars.

What about if the two teams shoot the same 3-point percentage?  This would actually be a small win for the Raptors because they have been the worse shooting team this year, but they would still be underdogs in this scenario.  Their win probability would be 33%, up a little from the baseline of 27%.

So how much do the Raptors have to outshoot the Warriors on 3’s to actually be the favorites?  From my model, the answer is by roughly 5 percentage points.  We should keep in mind, however, that even in this rosy scenario Toronto is still just a little over a coin flip to beat Golden State.

In this Finals clash, keep an eye on the 3-point shooting battle.  If Fred VanVleet and company are not lighting it from the outside or the Warriors are not a little colder than usual, it will be an uphill battle for the challengers from north of the border.

The draft night is so intoxicating precisely because, on this night, we can’t distinguish the stars from the non-stars.  Yes, by the time we reach 2029, the events that took place on draft night 2019 will be oh-so clear.  Team X saw the potential in player A and got an amazing player at pick #8.  Team Y thought they were getting a franchise changer at pick #2, but player B just never panned out.  But on the the actual draft night of 2019, none of this will be known.

What we can do is establish some baseline expectations for how likely each pick is to actually work out, based on historical data.  To this end, I collected data on all players drafted from 1995 to 2012.  For each player, I recorded the number of All-Star game appearances and All-NBA teams made.  Using this data, we can estimate the likelihood that a player will eventually make an All-Star game based on their draft position:

The black dots in the plot above represent the actual proportion of players from 1995-2012, at each draft slot, who made an All-Star game in their careers.  The red line is the smoothed probability given from a logistic regression.

One of the striking things to me is that, even at the top of the draft, there is really no such thing as a sure thing.  At the #1 overall pick, 12 of the 18 players in this time range made at least 1 All-Star game.  But at #2, only 28% of draftees (5 of 18) actually reached this level.  That means that only 47% of top 2 picks became All-Stars.  There are roughly the same number of Greg Odens as there are Kevin Durants.

Another thing we can see from the graph is that star potential goes down very quickly after the first few selections.  Based on the logistic regression, the #1 overall pick has a 64% chance of becoming an All-Star.  By the time pick 5 comes around, that probability is more than halved to 30%.  Pick #10 has roughly half the star potential of pick #5, at 16%.

The situation is even dicier from here.  Historically, picks in the back half of the first round become All-Stars only 8% of the time.  Hoping to snag the next Nikola Jokic in the 2nd round?  Well, only about 3% of these 2nd rounders reached All-Stardom.

Of course, the All-Star threshold is not the only marker of player value.  There are plenty of extremely useful players in the NBA who have never made an All-Star team.  Ask the Rockets how important P.J. Tucker has been for them.  Getting a player who will someday be a league-average starter is extremely valuable at, say, pick #15.

But the NBA is a league built around stars.  The quickest path from watching the playoffs on the couch to advancing far enough to be beat by the Warriors is to acquire at least one franchise-changing contributor.  Every team is hoping on draft night that they will snag an All-Star of tomorrow.  But for selections made after the top 2 or 3, that is unlikely to happen.

For reference, here is a table of the estimated probability of making an All-Star team by draft pick:

How Often Do Teams Play Bench Majority Lineups?

For the purpose of analysis, I call lineups which have 3 or more starters starter majority lineups and those with 2 or less starters bench majority lineups.  The bench majority lineups are not a perfect proxy for what we might consider true “bench” minutes; after all, Curry and Durant plus 3 reserves is technically considered a bench lineup by my definition.  But still, I think it’s a logical place to start an analysis.

To orient ourselves, here are some basic facts: Starter majority lineups have played about 63% of the minutes across all teams, and thus bench majority lineups account for the remaining 37% of minutes.  The bench majority lineups play a minority of the minutes, but it’s not a tiny minority.  True “bench mob” lineups, those with 0 or 1 starter, have played about 22% of all minutes.  Of course, some of these minutes are coming at the end of lopsided games and are thus less important.

The statistics cited in the previous paragraph are totals across all teams; some teams deviate from these base rates in interesting ways.  The Sixers, for example, have staggered their substitution patterns so that 2 or more starters are on the court for 92% of their minutes.  Their most common lineup composition has 3 starters.  The Raptors, on the other hand, like playing all 5 of their starters together.  At 38% of their total minutes, the Raptors are second only to the Mavericks in terms of proportion of minutes playing all 5 starters.

How Effective are Starter and Bench Majority Lineups?

Of course, the teams not only vary in how often they deploy starter and bench heavy units, but also how effective these units actually are.  To measure this, I simply calculated the net points (team points minus opponent points) per game for each team, at each number of starters from 0 to 5.  Then I aggregated this information to determine which teams have the best and worst starter majority and bench majority lineups in terms of net points per game.

In the graph above, you can see that something is going right for the Raptors and Bucks when they play 5 starters and 3 starters, respectively.  The Raptors (the orange line) have outscored opponents by a staggering 7.5 points per game when they deploy all 5 of their starters, almost 3 points per game higher than second place Oklahoma City.  The Bucks, meanwhile, have been leaps and bounds better than every other team when playing 3 starters, at about +5 net points per game.  That spike in the green line at 3 starters jumps off the page!

You can also clearly see where the Spurs excel.  For each lineup composition from 0 starters to 3 starters, the Spurs are solidly above average.  When the Spurs are playing 4 or 5 starters, however, the story shifts.  They are in fact the 3rd worst team in the entire NBA in terms of 5 starter lineup net points per game, at almost -2 points per game.

To give you an idea of where the best and worst teams stand in terms of starter majority and bench majority net points per game, here are the top 5 and bottom 5 teams in both statistics.  You can see the full table of teams here.

How Important Are Bench Majority Lineups?

Scanning the tables above, we can see that the best starter majority lineups have higher net points per game than the best bench majority lineups.  The Bucks and Raptors are outscoring teams by more than 8 points a game when they play starter dominated lineups, while the Pacers and Spurs can’t crack +3.0 with bench majority units.

In fact, the marginal value, in terms of points per game, between above average and below average starter play is greater than the marginal value between above average and below average bench play.  To see this, look at the graph below which plots each team’s starter and bench net points per game.  The gap between the 7th best starter majority team (the Pacers) and the 7th worst starter majority team (the Nets) is roughly 6 points per game.   For the bench majority units, that same gap between 7th best and 7th worst is about 4 points per game.  Over the full 82 game season, I have found that 1 point of point differential is worth about 2.5 wins on average, so the difference between 6 points per game and 4 points per game could be 5 wins.

This gap between 7th best and 7th worst (roughly the interquartile range) is actually understating just how much the top 4 starter teams have separated themselves from the pack.  The Bucks, Raptors, Thunder, and Celtics have all outscored their opponents by at least 6 points per game when playing 3 or more of their starters.  To be really upper echelon, at least this season, you need to dominate the starter minutes.

Though having dominant starter majority lineups is the path to the top of the standings, benches can make a difference too.  Two teams stand out as prime examples: the Pacers and the Magic. The Indiana Pacers, leading the league at about +3.0 bench majority net points per game, would be expected to win about 7.5 less games out of 82 if they merely had a +0.0 bench.   The Orlando Magic, owners of the worst bench in the league at -5.1, would actually have a positive point differential if they could just survive those bench majority minutes without losing so much ground.  They are middle of the pack at +1.7 starter majority net points per game.

The best teams have differentiated themselves from the field with their stellar starter majority lineup play, which is unsurprising given that these lineups play roughly 63% of the minutes. But the difference between a solidly above average and solidly below average bench could plausibly be 3 or 4 points per game, which is still quite substantial.

This really simple insight actually has a lot of value as a framework for evaluating everything that happens on the court.  Each action that a player takes, be it good or bad, has to have its effect traced back to the scoreboard to be properly measured.  Of course, some actions, like made jumpers and rebounds, are neatly recorded in the box-score and others, like contesting a shot or moving the ball quickly to keep an offensive action going, are not.  But, at the end of the day, we really need to tie everything back to points.

I should point out that this framework for thinking about an NBA game was, of course, not invented by me.  Lots of really smart people have thought about the game in this flavor, including Dean Oliver in his seminal Basketball on Paper.  What I am trying to do here is present the idea in a way that I personally find appealing and intuitive.

Defining Expected Points Gained (EPG)

When I discuss relating the actions on the basketball court back to the basic currency of points, I am talking about much more than simply counting the points scored by each player at the end of the game.  What I am really getting at is something I am calling Expected Points Gained.

Expected Points Gained (EPG) = Expected Margin of Victory After an Action – Expected Margin of Victory Before an Action

An action in the above definition is just what you might expect: something that takes place on the basketball court.  Let me give you an example:

Say a player makes a 10-foot jumper.  What is the EPG from this action?  Well, currently in the 2018-19 regular season, the average team offensive rating (points per 100 possessions) is 109.7.  This means that the offense is expected to score about 1.10 points from 1 possession.  The made jumper was worth 2 points so, from the perspective of the team which made the jumper, the expected margin of victory has increased by 2.00-1.10 = 0.90 points.  Their EPG from the made field goal is 0.90 points and their opponents have a commensurate -0.90 EPG.

Simple, right?

It Gets Complicated Fast

The thoughtful reader might look at my previous example and feel like I’m leaving a bunch of stuff out.  I started with the assumption that an offensive possession was worth an expected 1.10 points.  But what if the possession was in the half-court? Half-court possessions score less points than fastbreak possessions, on average. And what if the possession belonged to the Golden State Warriors rather than, say, the Chicago Bulls?

Also, that made 2-point jumper effects more than just that one offensive possession, right?  I mean, the opponent is taking the ball out of their own basket and not sprinting down the court for a juicy transition look.  That’s got to be worth some expected points as well.

And we can go deeper and deeper.  Why use the expected margin of victory at the beginning of the possession as our baseline?  Why not consider the fact that there were 5 seconds left on the shot clock?  Perhaps the offense was only expected to make 0.90 points on average that late in the shot clock, making the EPG higher than we initially calculated.

So what’s the right level to calculate EPG at?

This is a tricky question, but in the end it really depends on context.  Evaluating an offensive (or defensive) possession for a team, we would probably want to compare the expected margin of victory after the possession has ended with the expected margin of victory when the possession began.  It makes sense to view things at the zoomed out possession level because we are evaluating the entire team’s performance, rather than that of a single player.

However, in the context of evaluating an individual player’s action, we might instead be interested in the baseline expected margin of victory immediately before their action, rather than at the beginning of the possession.  To see this, let’s think about an offensive rebound.

The Value of a Rebound

Say that our hypothetical 10-foot jumper is missed instead of made, but the center then secures the offensive rebound.  How does this fit into our EPG framework?  Well, the offensive rebound rate (the proportion of missed shots which are rebounded by the offense) this year is about 0.23, per basketball-reference.  Let’s assume for a moment that the offense will score an expected 1.10 points (the same as an average possession) if they do in fact secure the offensive rebound.

Now we can compute the expected value of the possession before the offensive rebound but after the missed shot as

Expected Points Scored Before Offensive Rebound = (Expected Points Score Given a Defensive Rebound) * Probability of Def. Reb. + (Expected Points Score Given an Offensive Rebound) * Probability of Off. Reb. = 0 * 0.77 + 1.10 * 0.23 = 0.25

After the offensive rebound, our expected points scored are 1.10, so the EPG of the offensive rebound is 1.10 – 0.25 = 0.85.  On the flip side, if the defense had instead secured the defensive rebound, their EPG would have been 0.25 because the value of the opponent’s possession would have fallen from an expected 0.25 points to 0.

A cool consequence of this calculation is that we have determined, from an EPG perspective, that an offensive rebound is more valuable than a defensive rebound.  This is really a direct consequence of the fact that a missed shot is more likely to be rebounded by the defense than the offense.

The Approximate EPG of Some Common Actions

Having already computed the EPG of a made 2-point jumper and an offensive and defensive rebound, let me display a handy table of the EPG of some of the other common, box-score recorded actions on a basketball court.

I will say from the outset that I am computing these under a few simplifying assumptions.  I am assuming that each offensive possession begins with at 1.10 expected points scored, as I did in the made 2-point field goal example.  I am also ignoring the value an action has on possessions after the current one, i.e. the value a forced live-ball turnover has from the fastbreak which proceeds it.  I am making these assumptions mainly to the make the calculations simpler.

Conclusion

My main goal in writing this was to encourage you, the reader, to evaluate actions on the basketball court in terms of points.  Specifically, Expected Points Gained (EPG).  Using EPG, we can assign a value to things like offensive rebounds and made 2-pointers.  Unfortunately, actually calculating EPG can get a bit messy and is inherently tied to the context we want to consider the action in.  I plan on using the concept of EPG in future posts to make some points about the value of certain things happening on the NBA court.

Inspired by Ben Falk’s Predict challenge on his website, Cleaning the Glass, (a really cool website if you’re an NBA fan) and filled with intrigue about year 1 of the LeBron led Lakers experiment, I decided to tackle this question.

So, how should we go about answering it?

Well, I could build a complicated plus-minus based model.  But I’m lazy. Others have already built really good models.  I wanted to try a simpler approach.

Let’s start by looking at the betting markets.  According to Vegas Insider, on October 10th the Lakers were -400 to make the playoffs and +300 to make the playoffs.  What this means, for non-bettors, is that if you want to bet on them to make the playoffs you have to risk $400 for the possibility of winning $100.  Likewise, if you bet on them to miss the playoffs, you risk $100 to possibly win $300.

What this means is that you would have to believe they have a greater than 80% chance to make the playoffs to bet on the former or believe they have less than a 75% chance to bet the latter.  So maybe Vegas thinks the true probability of LA making the playoffs is somewhere in the 75% to 80% range?

To establish my own probability, I looked at how each team performed relative to their pre-season season win total over/under line, since the 2012-13 regular season.  As it turns out, if you run a linear regression to predict regular season wins based on the over/under line you get the following equation:

Predicted Wins  =  4.22 + 0.89 * Season Win Total Over/Under Line

This means that teams win, on average, about what the over/under line is set at, with a little regression towards the mean.  The plot below shows how each team in the dataset fared relative to the prediction from this equation.

The really important part of this regression is actually not the equation but something called the residual standard error.  The residual standard error basically tells us how much variability there is in the actual wins of a team around our predicted value.  The residual standard error of our regression was almost exactly 8 wins, which means that our 95% confidence interval for predicted wins is the prediction from the equation plus or minus 16 wins.  

That’s a huge amount of variability, which really surprised me!  This mean that if we predict a team will win 41 games then we can only be 95% confident that they will win somewhere between 25 and 57.  This agrees with our data.  Since the 2012-13 regular season, 6 of the 179 teams have won or lost at least 16 more games than we would expect based on the regression equation.  6 divided by 179 is about 3.4%, not far off from the 5% we would expect.

So what does all this math have to do with the Lakers and the playoffs?  Here’s what:  to estimate LA’s playoff odds, I started by taking each team’s season win total over/under line, from Westgate.  Next I computed expected wins from my regression equation.  Then, I estimated that each team’s true win total is normally distributed about this expectation with standard deviation 8 wins (the residual standard error from before).  I used this estimate to run 100,000 simulations and recorded how many times each team made the playoffs.  Here are the results for the West:

* According to Westgate, on October 10th.

** Found using the equation from the linear regression: Expected Wins = 4.22 + 0.89 * Season Win Total O/U Line

*** Computed via 100,000 simulations, assuming win total is normally distributed around expected wins with standard deviation of 8 wins.

If you want to see the derived playoff probabilities for the Eastern Conference teams too, you can go to this google sheet.

So this method tells us that the Lakers have a 73% chance to make the playoffs and a 27% chance to miss the playoffs.  That’s about what I would expect.  You could argue that this year’s Lakers squad has even more variability in win total than your average NBA team, which would increase their chances of winning many more games than we would expect but also increase their chances of falling short and missing the playoffs.  So maybe their chances of missing the playoffs are a little more than 27%.

On the other hand, you could argue that the real possibility of Jimmy Butler being traded to the Eastern Conference means my method is undervaluing their playoff odds.  I think Westgate is already pricing the Butler trade possibility into their lines, as the T-Wolves opened at a 44.5 and are now down to 41.5.  Still, if you think the Timberwolves are really more of a 38 win over/under team without Butler (which is probably too low) and run the simulations than the Laker’s probability of missing the playoffs falls from 27% to 25%.  It’s not a big difference.  You could you could argue that the Timberwolves will be, on average, much worse than a 38 win team without Butler, but I’m not quite buying that.

Answer:  I estimate that the Lakers have about a 27% chance to miss the playoffs, about the same chance as flipping tails twice with a fair coin.

Q2: When is it safe to leave an NBA game at the start of the 4th quarter?

Say it’s a blowout at the start of the 4th quarter.  You want leave the arena and go home, (or more likely turn off the TV) but you don’t want to wake up and find out that the trailing team ended up coming back and winning.  How large a lead do you need to safely go home?

To answer this question, I used basketball-reference data from the past two regular seasons.  I built a (logistic regression) model to predict which team will win the game based on the score at the start of the 4th quarter, which team is home, and the difference in ability between the two teams, in terms of points of net rating difference.

So, if the two teams are roughly equal in skill, then a 15 point home lead or 18 point away lead is needed to be 95% confident that we won’t miss a comeback.  If one team is a bit better than the other, then you should add (or subtract) a few points from these numbers, depending on who is leading.

Answer:  You can be 95% confident that you won’t miss a comeback by the trailing team if the home team is leading by at least 15 points or the away team is leading by at least 18.  If one of the teams is substantially better than the other, then you should adjust these thresholds by a couple points.

Q3: Say I’m a Kings fan.  Will they win a championship in my lifetime?

Alright tortured Kings fans, here’s a question for you.  I feel for you guys- I’m a fan of the Brooklyn Nets.

To give us somewhere to start, let’s say that you are an 18-year-old Kings fan.  Not to be too morbid, but for 18-year-old males the Social Security Administration estimates that you will live, on average, another 59 years.  If you are a female, then you live an extra 4.7 years on average.

Now, we know the Kings are almost certainly not going to win it all this year (Bovada has them at 500 to 1).  But in 2050?  That far in the future, we might estimate that they have as good a chance as any other team, that is 1/30 ~= 3.33%.

To account for this high likelihood of near-term futility but high uncertainty in the long term, this is what I decided to do: let’s give the Kings have a 1/500 chance to win the championship each year for the next 5 seasons, a 1/100 chance for the following 5 seasons, and then a 1/30 chance (i.e. league average) in each subsequent year after that. (I assume each season is an independent event).  This gives your 18-year-old male Kings fan a 1 – ((499/500)^5 * (99/100)^5 * (29/30)^49) ~= 82% chance to witness a Kings championship in their lifetime.  A female 18-year-old has about an 85% chance.  Have hope Kings fans!

This is just a rough estimate that tries to account for two ideas: they are almost certainly not winning a championship in the next few years, but have as good a chance as any other team in seasons far in the future.  You can of course disagree with my estimates. Maybe you instead want to say the Kings only return to ‘league average’ championship odds 20 years from now, rather than 10.  Then you arrive at a 77% chance of a King’s finals victory in the lifetime of the 18-year-old male fan.  That’s not too large a difference.

What about if the NBA expands and each individual team thus has lower championship odds?  What about possible relocation? What about the chance the NBA isn’t even around in 30 years?  If you want to factor these possibilities into your analysis then you are more dedicated than I am.

Answer:  Probably, especially if you are relatively young.  An 18-year-old male Kings fan has about an 82% chance of seeing the Kings win a championship in their lifetime.

References:

Data used in this post was from basketball-reference.com.

I dived right into some small projects inspired by this discussion.  My first post examined whether the shooting ability of the players actually taking the 3-pointers against a particular defense had some ability to explain variability in 3-point percentage defense.  I looked into whether the Celtics’ sustained run of top-5 3-point percentage defenses under Coach Brad Stevens could be a fluke of randomness (it’s highly likely it’s not).  I also analyzed which team statistics were most likely to carry over from the first half of the regular season to the second, and found defensive 3-point percentage was low on that list.

Now, I have tried quantify exactly how many points of defensive rating (points per 100 possessions allowed) are subject to opponent shooting variability.  Besides simply considering 3-pointers, I also looked at free throws and ‘deep’ 2-point attempts, where I defined deep as greater than 16 feet.

Defining Net Shooting Points

Question: How many points would Team X’s defensive rating change if their opponents shot an ‘average’ percentage on 3-pointers?  Well, the answer seems simple enough.  Basketball-reference tells us how many 3-point attempts a particular defense allowed, per 100 possessions, and what percentage opponents shot on those attempts.  We can simply move this percentage to league average and calculate how many points would be gained (or lost), right?

As it turns out, there is one other small adjustment we should make.  Every missed shot has an opportunity to be rebounded by the offense.  So a made 3-pointer that magically turns into a miss does not simply subtract 3 points from a team’s score; we have to add back the expected points that could be gained by an offensive rebound leading to a new possession.  The percentage of missed shots which were offensive rebounded in 2017-18 was 22.3%, and the mean points scored per possession was about 1.086 (per basketball-reference).  Multiplying 0.223 by 1.086 we get about 0.24, meaning that each missed 3-pointer yielded 0.24 points in value from potential offensive rebounds. (As an aside, one could use the precise offensive rebounding percentage on missed 3-point attempts and the expected points per possession after an offensive rebound, but the original numbers will do for my purposes.)

With this idea in mind, I will explain how I compute Net Shooting Points, the points a team’s defensive rating would increase if they allowed a league average percentage on 3-pointers, free throws, and long 2-pointers.  To do this, I start by defining Net 3-Point Shooting Points.

Net 3-Point Shooting Points = New 3-Point Shooting Points – Original 3-Point Shooting Points

= [(3 * 3-PT % Avg. * 3-PT FGA_per_100) + ( 3-PT FGA_per_100 * (1-3-PT % Avg.) * OReb % Avg. * ORtg Avg./100)] –

[(3 * 3-PT % * 3-PT FGA_per_100) + (3-PT FGA_per_100 * (1-3-PT %) * OReb % Avg. * ORtg Avg./100)]

where 3-PT % Avg. is the league average 3-point percentage for the particular year, 3-PT FGA_per_100 is opponent 3-point field goal attempts per 100 possessions, OReb % Avg. is the average offensive rebounding percentage of that year, and ORtg/100 is the average offensive rating divided by 100 (i.e. points scored per possession).

Net 3-Point Shooting Points attempts to answer the question of how many more points per 100 possessions would a team have given up if they allowed the exact same number of 3-point attempts, but opponents shot a league average percentage.  A positive value means a team would have given up more points had opponents shot the league average percentage, and thus had a worse defense, while a negative value means that their defense would have improved.

Similarly, we can define Net Free Throw Shooting Points and Net Deep 2-Point Shooting Points:

Net Free Throw Shooting Points = [(FT % Avg. * FTA_per_100) + ( FTA_per_100 * (1 – FT % Avg.) * 0.114 * ORtg Avg./100 * 0.553)]  –

[(FT % * FTA_per_100) + ( FTA_per_100 * (1 – FT %) * 0.114 * ORtg Avg./100 * 0.553)] 

Net Deep 2-Point Shooting Points = [(Deep 2-PT % Avg. * Deep 2-PT_per_100) + (Deep 2-PT FGA_per_100 * (1-Deep 2-PT % Avg.) * OReb % Avg. * ORtg Avg./100)]  –

[(Deep 2-PT % * Deep 2-PT_per_100) + (Deep 2-PT FGA_per_100 * (1-Deep 2-PT %) * OReb % Avg. * ORtg Avg./100)]

If you stare at these formulas, you might ask what the 0.114 and 0.553 represent in the Net Free Throw Shooting Points equation.  The 0.114 represents the fact that 11.4% of missed free throws which had the opportunity to be offensive rebounded were, in fact, offensive rebounded in 2017-18 (11.4% is close to the 11.5% figure Seth Partnow found in 2015).  The 0.553 is there because only the second free throw in a 2-shot foul (or the third in a 3-shot) can be offensive rebounded.  By sifting through play-by-play data, I found that 55.3% of free throw attempts had the opportunity to be offensive rebounded in 2017-18.

With all of the above definitions, we can define

Net Shooting Points  =  Net 3-Point Shooting Points + Net Free Throw Shooting Points + Net Deep 2-Point Shooting Points

In other words, Net Shooting Points are simply the estimated additional points per 100 possessions that a defense would have given up if their opponents shot a league average percentage on 3-pointers, free throws, and deep 2-pointers (greater than 16 feet).

Net Shooting Points for 2017-18

Let’s dive right in and see where each team stood in terms of Net Shooting Points in the 2017-18 regular season. The link below goes to a spreadsheet showing where each team stacks up in each component of Net Shooting Points. An important reminder: Net shooting points represents the additional points per 100 possessions that a defense would have given up had opponents shot league average on 3-pointers, long twos, and free throws.  So a positive Net Shooting Points value means that the defense would have gotten worse had opponents shot league average (opponents shot poorly in actuality) and a negative value means that the defense would have gotten better (opponents shot well).

Table of 2017-18 Team Net Shooting Points

The following graph displays Net Shooting Points visually:

To interpret the graph, think of the red dot as where we might expect each defense to be, after accounting for Net Shooting Points, and the blue circle as where they actually were.  The Net Shooting Points value is the red dot value minus the blue circle value.  If the red dot position is greater than the blue circle position, than the team had positive Net Shooting Points (and vice-versa).

We can see from the table and graph that the three teams with the most positive Net Shooting Points, the 76ers, Celtics and Rockets, each allowed about 2 points per 100 possessions less than would have been the case had opponents shot league average.  If we simply recorded the number of 3-pointers, free throws, and deep 2-pointers that opponents attempted against these teams, but did not know the percentage that went in, we might expect these teams to allow about 2 points per possession more than they actually gave up.  The three bottom teams, the Hawks, Hornets and Kings, each allowed about 1.5 points per 100 possessions more than expected thanks to above average opponent shooting.

So how big a deal is 2 points per 100 possessions? Well, according to a regression I ran previously, every point of net rating is equal to, on average, about 2.5 wins over the course of the 82 game season.  So a +2 net rating team is usually around 46 wins while a +0 net rating team is often about average (41 wins).  2 points of net rating is a big deal!

One fairly intuitive observation you will make by scanning the table in the link above is that Net Shooting Points tend to be dominated by Net 3-Point Shooting Points.  This makes sense given the high volume of 3-point attempts and the fact that 3-pointers are worth more than deep twos and free throws.  To further illustrate this, the average absolute value of Net 3-Point Shooting Points in 2017-18 was 0.72 points, while this number was 0.21 and 0.17 for Net Free Throw Shooting Points and Net Deep 2-Pointer Shooting Points, respectively.

Analysis

So, what should we make of all this?  The Sixers ‘gained’ 2.3 points of net rating last season from opponent poor shooting, as the title of the post implies.  So were they just lucky?  And what’s up with all these really good teams like the Celtics, Rockets, and Warriors benefitting from opponent bricks from outside?

The story is probably a bit more complicated than just pure luck.  After all, we can imagine a good defense effectively contests outside shots and does not allow as many easy open looks as a poor defense.  I need to do more research to study the quality of the outside shots given up by each team.  Moreover, for the Sixers in particular, we might suspect that a strong interior defense could scare opponents away from the paint and entice more bad outside jumpers.  And the Celtics, the league’s best 3-point percentage defense, have been near the top of the league in this stat for a while, stubbornly offering a point against the theory that 3-point percentage defense is mostly luck.

Examining the graph above, it stands out that each of the 10 worst defenses in the NBA would have been improved had their opponents shot merely league average on jumpers, while many of the top defenses would have fallen off.  Perhaps this is a point in favor of the idea that defending the perimeter is something which the defense exerts a good deal of control over.  Of course, it also makes some sense that the worst defenses in the NBA actually performed that way because opponents made a lot of outside shots.  The causality probably runs in both directions.  That is, bad defenses allow opponents to hit a higher percentage of jumpers but, also, good opponent outside shooting can lead to a poor defensive rating.

Because I was curious how predictive Net Shooting Points from one year were of the next year, I went back to the 2005 regular season and computed this value for each team.  I then normalized each Net Shooting Points score by subtracting the mean and dividing by the standard deviation of each particular year (giving us a z-score for those statistically inclined).  Next I used a linear regression to predict the next year’s Net Shooting Points from the previous year.

The result was that the next year’s Net Shooting Points was, on average, .244 times the previous year’s value (i.e. about 25% of previous year).   The intercept term equaled 0. The coefficient from this regression was, in fact, significant (even at the 0.01 level), meaning that previous year Net Shooting Points has an association with the next year’s value which is probably not due to sheer chance.

It might be reasonable to start, at the beginning of the next season, with the baseline ‘expectation’ that each defense’s Net Shooting Points will be about 0.25 times the Net Shooting Points of the previous season, on average.  The uncertainty around this estimate is really high though. The standard error from the regression was almost 1 point, indicating that the 95% confidence bound is 0.25 times previous season Net Shooting Points plus or minus 2 points.

The result of the regression makes some sense to me.  Perhaps there is an element (maybe even a large-ish element) of opponent outside shooting which is fairly random.  But there is some part of this which the defense is actively influencing.  A good defense might hamper opponent outside shooting by not allowing open looks from good shooters, force teams to settle for bad shots after stalled possessions, and do other important things well which cause opponents to shoot a poor percentage.

We should perhaps begin with the belief that the Sixers will be closer to a +0.6 Net Shooting Points defense in 2018-19, rather than the +2.3 that they put up in 2017-18.  Interestingly, the Sixer’s Net Shooting Points for 2014-15, 2015-16, and 2016-17 were -0.3, -1.3, and +0.1, respectively, though the previous year’s Sixers, especially the 2014-15 and 2015-16 editions, bore little resemblance to last year’s squad.

It should be pointed out that my analysis is limited by the fact that there is more to perimeter defense than just allowing a low percentage of makes.  It also matters the volume of shots that opponents are taking from long range.  And perimeter defense is obviously heavily intertwined with the other parts of defense, such as interior defense.  It makes sense to look at all the parts of good NBA defense together.

Still, I think it is good to start quantifying the effect opponent outside shooting has on overall defense.  I hope Net Shooting Points can be useful in this regard.

References:

Data for this post was obtained from basketball-reference.com.