Not All Possessions Are Created Equal: A Four Factors Memoir
With advances in technology and thought, the toolbox for evaluating a basketball team on paper has never been larger or more diverse. Built on the foundation of rate statistics (frequencies and per-100 stats), lenses such as the Four Factors, shot location data, playtype data, and more allow us to look at NBA offenses from different angles. I’m not here to re-invent the wheel; rather, to take another look at the Four Factors, their proper interpretation, and hopefully fill in some of the gaps that were left behind.
Essentially, the Four Factors measure two different areas: efficiency and opportunities. EFG% and FTAr (effective field goal percentage and free throw attempt rate) measure efficiency, while OREB% and TOV% (offensive rebound percentage and turnover percentage) measure opportunities, or how well a team maximizes it’s shot attempts. EFG% and FTAr are a natural pair - fouls are the byproduct of shot selection and offensive strategy, which are already related themselves. Opportunities, on the other hand, are a little weirder. A simple footnote that some may not really think about (at least I didn’t until very recently) is that 1 possession ≠ 1 shot attempt. That is key to all of this. But how does it manifest? Well, I think I may know the answer.
Summarize the Four Factors into the two different areas I talked about, and we get TS% as the ultimate measure of efficiency and TSA as that of attempts.
I got TSA from TSA = ORTG/(2*TS%), with TS%, of course, as a decimal. If you’re still lost, then I’ll explain it in reverse: 2*TS% = PPA, or points per attempt, or points/attempt. TSA, or attempts (TSA includes FGA and FT trips), is in this case per 100, so TSA = attempts/100. Doing simple math, (points/attempt) * (attempts/100) = points/100 (attempts cancel out), which is ORTG! Are these now the Two Factors? IDK.
Looking at where each teams’ efficiency (TS%) and opportunity (TSA) percentiles slot in (stats per pbpstats) yields fascinating results (I didn’t just throw in an adjective there; the findings are genuinely intriguing, at least to me). First, I’ll present the graph of TS% percentile (I couldn’t use z-scores because teams played different amounts of games) vs TSA percentile, and where more red equals a better offense, and more blue means a worse one; for visual reference, Toronto and Philly have most average offenses. Then, I’ll talk about some surprising conclusions (visualization from rawgraphs).
(Before that, though, let me give you a little preview of where the league is currently, or rather, was, during the 2019-20 season - the league-average TS% was 56.4% (an all-time high), and the league-average TSA per 100 was 98.58. Also, keep in mind that TS% is solely responsible for the massive ORTG jump (106.7 to 111.2) from the 2015-16 season to the 2019-20 one, with the year-by-year increases containing a 0.97 correlation with TS%.)
And for some added clarity, here are the specific values:
Ok, now I’ll fire away:
Dallas’s hue is a stronger red than any other team’s by a mile; yes, their offense, fueled by Luka, was that much better than everyone else’s.
It turns out that this season, two teams filled out each of the absolute extremes - Miami (efficiency) and New York (opportunities). However, Miami was 7th in ORTG, and New York was 27th, bringing me to my next point which is that…
Percentiles fail to capture the true value of each category, as opportunities can only be worth so much if you have the worst TS% in the league. They amplify or diminish the impact of a team’s efficiency, but efficiency (which can come about in many different ways) is the backbone of your offense. Further confirming this: for the 2019-20 NBA season, the correlation between ORTG and TS% was 0.88, while the correlation between ORTG and TSA was 0.17. A bias to consider is that better offenses generally make more of their shots, leading to less offensive rebounds, hence reducing their total opportunities. However, this is a subtle skew and almost certainly has no effect on the conclusion we ultimately draw. And finally, a DYI method to better understand this while thinking for yourself - focus exclusively on the top half of the graph, and find some trends on your own!
However, if you didn’t, I still got you. Interestingly enough, 4 of the top 5 offenses’ TSA percentile is higher than their TS% percentile, with the outlier being the Clippers; also, in keeping perspective, note that 1.06 points per 100 are all that separate Boston (4th) and Utah (10th). This leads to another insight, that being…
That, when dealing exclusively with the top 15 offenses in the league, the correlation between ORTG and TS% (0.28) is significantly lower than the correlation between ORTG and TSA (0.64). When dealing with the top 10 offenses, those numbers deviate further to -0.03 and 0.70, respectively, reinforcing that idea. Wow:
Just in case you were wondering, even if I take out MIA, MIL, and UTA, who are chilling at the top left of the graph, ORTG still correlates stronger with attempts among top-15 and top-10 offenses (although the gap does narrow a bit).
This is essentially telling us that among the more efficient offenses, maximizing opportunities became more important for offensive success. While acknowledging this, it’s also important to understand why certain teams ended up where they did; think of each team’s personnel, their collective strengths and weaknesses, and how they contributed to the team’s ultimate ranking.
Adding another layer of intrigue: to check the validity of my findings, I found the same correlation values from each season dating back to 2015-16 (when 3-point attempts began to rapidly increase), and not one season replicated the trends found within the 2019-20 season. The ORTG-TS% correlation was consistently higher across all groupings, even when taking GSW out of the equation (as they were ridiculous outliers every time). That being said, I’m now unsure what to make of the previous conclusion. I could accept this season as a fluke, but even a season cut short by Covid is still a very large sample size. Perhaps it has something to do with teams adjusting to the new shot clock rule implemented in 2018, or some stylistic shift that’s flown under the radar, or simply the chance alignment of certain players on certain teams that fit a certain way. Could it be (gasp) a fluke? Alternatively, we may be approaching the current ceiling of shot efficiency, one where there are multiple ways to build an efficient shot-generating machine, which in turn makes the shot attempt game the more ‘winnable’ battle where more ground could potentially be gained. Regardless, it gives me yet another reason to closely follow the 2020-21 NBA season (not that I needed any in the first place). I hope you don’t mind me thinking out loud, to an extent; I always want to make my thought process as transparent as possible when reaching conclusions.
So, whether you decide to take these findings with a grain of salt or not, there’s at least one person out there who seems to agree with me:
Alright. Now, we have a logical launch point for going deeper, back into the Four Factors, and ultimately jumping back into the crux of the article, as alluded to by the title. Measuring opportunities is admittedly an oversimplification, because not only do different opportunities vary in quality (aka, expected points or PPP), but the unique frequencies of their endings (turnover, make, miss) hold value as well. Huh? Now is the perfect time to introduce the data that serves as one of the foundational linchpins of this article: Inpredictable’s Possession Profile Stats (which is a nice name), as well as a section of pbpstats here (pbpstats has higher values across the board, so I’ll do my calculations once for each site’s values, despite pbpstats having more detailed breakdowns). They each measure the efficiency (PPP - points per play) of possessions, stratified by what preceded the possession. Inpredictable organizes the different ways a possession can start under 3 umbrellas - a made shot/dead ball turnover (1.06 PPP), a defensive rebound (1.10 PPP), and a live ball turnover (read: steal) (1.25 PPP), with their overall PPP set at 1.10. As you can see, how a possession starts is incredibly relevant, and the quantification of these discrepancies is what allows me to write this. Pbpstats has much more detail, so I’ll let you check out their groupings here; the same discrepancies across values hold steady, albeit pbp (that’s their new nickname from here on out) is working with a league-wide PPP of 1.11, rather than 1.10 (the final cherry on top is that pbp gives the totals behind each number, and thus access to the exact values we need). And finally, just keep in mind that this is an exercise in correlation, not causation; giving the defense more time to set is what decreases efficiency, and how a possession started is merely a way to distinguish between the different contexts.
Ok, time to get down to the nitty-gritty of things. As you might have imagined, offensive rebounds and turnovers add (or subtract) value in two different ways - with the extra shot attempt (or rather, the opportunity for one) provided by each, and how the end result of that opportunity dictates the subsequent possession’s value, relative to what it would have been had the turnover or offensive rebound not occurred. The meat of the value, predictably, lies in the extra shot attempt (not possession; possessions are always strictly back and forth, but only hold value if you’re able to get a shot off). Committing a turnover or grabbing an offensive rebound gives the benefiting team two consecutive shot attempts when it would otherwise have one. Important to note is that we are strictly measuring the expected point swing after the event has concluded - think of this in terms of net rating, not ORTG or DRTG, although each still get affected. We’ll start with the value coming from the additional possession generated by a turnover or offensive rebound. For a turnover, that value is 1.16 per Inpredictable or 1.18 per pbp. (To note: starting now, I’m going to very deep into the numbers. If this type of stuff gets you excited, then read all of the following italicized text blocks. If not, then skip them, and go straight to the answers).
How I got it: per inpredictable, a possession following a live ball TOV has a PPP of 1.25, and a possession following a dead ball turnover is the same as one coming after any made shot (1.06 PPP). Per pbpstats, 52.61% of all TOVs are live ball ones. So (0.5261*1.25) + (0.4739*1.06) = 1.16. Per pbp, we would do (0.5261*1.28) + (0.4739*1.07) = 1.18
For an offensive rebound, that value is 1.08.
How I got it: the gray area between offensive rebounds and second-chance points is a tough one to navigate, so if you know of a better value estimate, please reach out to me on twitter and share it with me so that I can make my calculations more accurate. I decided to go with a more conservative estimate by attempting to incorporate the offensive rebounds that don’t end in widely-measured putbacks or 2nd chance points. Per CTG, the average PPP for a half-court play is 0.959, while that of a putback is 1.14. Also, it maintains that 16.9/25.9 offensive rebounds per 100 offensive rebounding opportunities become putbacks (which it classifies as shot attempts before the defense is reset), so 19.3 points from putbacks/16.9 putbacks is how I got 1.14 earlier. Therefore, the value of an offensive rebound is (19.3 + (0.959*9))/25.9 = 1.08 PPP.
Ok, now for the tricky part. In order to find the expected PPP after an OREB, I tallied up the different possession endpoints occurring after an offensive rebound (using pbpstats’s 2nd chance stats as our guidelines; it’s close enough, and not to mention the best option out there), and used the average PPP for each possession start type to paint a full picture of the PPP following an offensive rebound playing out. Then, we’ll look at if offensive rebounding holds any serious defensive consequences (and just to be clear, this is completely unrelated to the crash vs get back on D debate; nothing of the sort is being measured here). As always, I’ll put the detailed counting below for those who are interested; if not, skip to the next paragraph.
(Disclaimer: There will be (some) rounding, approximations, and ambiguity here and there; don’t worry, it annoys me as much as it may annoy you, but unless you want to re-watch and hand-track the 2019-20 season, this will have to do for now.) Ok. There were 26380 offensive rebounds this season. Based on pbp’s 2nd chance stats, adjusting for and-one’s (meaning removing and-one FGM, as they don’t end a possession), there were: 10822 FG missed, 10118 FG made, 2447 turnovers, 1762 FT made, and 517 FT missed (only counting the final free throw, as there were 2279 trips to the line - just FYI, I’m only given FT points, so I used the league-average FT% and 0.44 coefficient to estimate FT trips, and worked backward from there). These all add up to 25666, so I’m 714 possessions short, or missing 2.9% of all possessions. Some of those missing possessions can be attributed to estimation error (using FTA*0.44 = FT trips, league-wide and-one rates or FT% in a specific context, etc.). On the other hand, if there was a second offensive rebound and shot attempt on a given play, I probably counted it as two different possessions. Regardless, I’m simply going to ignore those 714 missing offensive rebounds and pretend that they don’t exist, because there’s isn’t anything that can be done about it. Now, I’m going to look at how all 25666 subsequent possessions begin. To cater to Inpredictable’s counting methods, we have 11339 misses (defensive rebounds), 13039.6 dead balls (makes + dead ball TOs), and 1287.4 live ball turnovers. So, based on Inpredictable’s stats, the opposing team’s expected PPP after an offensive rebound plays out is 1.087, vs what would otherwise be 1.1 (the PPP off of a defensive rebound), so an offensive rebound reduces the expected PPP of the subsequent possession by 0.013 - the defensive impact of an offensive rebound. However, doing the same calculus via pbpstats allows us to go even deeper, as they break down PPP off of missed shots by zone - rim, midrange, corner 3’s, above the break 3’s, and FT misses (which are surprisingly inefficient). Missed middies and all 3’s are worth 1.11 PPP on the other end of the floor, while rim misses turn into 1.15 PPP opportunities. I’m going to assume that all 2-pt and-ones came from rim shots, because there’s no further stratification of that data, and rim and-one’s just make the most sense. Going through the same process, I get 1.114, 0.011 PPP below pbpstats’s off FG miss PPP, 1.125.
Per inpredictable, the expected PPP following a typical offensive rebound playing out, for the opposing team, is 1.087, down 0.013 PPP from their expected 1.1 off of a defensive rebound. Per pbp, that value is 1.114 PPP, 0.011 PPP below the alternative of 1.125 PPP following any defensive rebound. While we’re admittedly dealing with small numbers and slightly uncertain counts, the fact that both calculations gave similar values in the same direction is very encouraging. I never really had a plan in mind for reconciling the two counts, but because they seem to agree, I’d say that an offensive rebound is worth around 1.092 net points.
Now, for turnovers. Turnovers are tricky, and one of the reasons why is that we are essentially measuring two totally different events: live-ball turnovers and dead-ball ones. Like offensive rebounds, the concept for the secondary value added from turnovers stems from the idea that the aftermath of your extra shot attempt puts the opposing offense in a slightly worse position than they would be in otherwise, given that the turnover or offensive rebound never occurred. But first, what’s the average value of plays that turnovers interrupt?
I’m gonna break the rules here (but only because I think it will make my calculations more accurate; nevertheless, I’ll provide both potential values) and use CTG’s play context PPP values while using raw nba.com/pbpstats for turnovers, because CTG doesn’t include TOV% in their play context stats. Per CTG, a half-court play is worth 1.084 points (as previously discussed), while a transition play is worth 1.228. There were 30794 turnovers this season, and 4620 of them came in transition, per nba.com, meaning 26174 non-transition ones, so the PPP of the play that a typical turnover disrupts is ((26174*1.084) + (4620*1.228))/30794 = 1.106 PPP, marginally below the expected PPP of the average possession interrupted by a turnover, a tiny little bit below CTG’s ORTG (110.9) and pbp’s (111.2), but, because transition plays have a TOV% of 12.5% vs the league’s overall TOV% of 14.5%, I definitely put stock in that negative discrepancy.
Turnovers disproportionately occur during half-court possessions, if ever so slightly, and hence we end up with an average PPP of 1.106 (per CTG’s transition and non-transition #’s). Now, what’s the value of the play following the turnover playing out?
I started by looking at plays off of live-ball turnovers, 52.61% of our equation. I’ve already detailed what the in-depth process looks like above, so I’ll spare you this time. Anyway, I was able to come up with 15627 possession ending actions, versus 16200 steals this year (which is 96.5%, although pbp’s total possession count for off-steal plays is 15798, much closer to what I got); either way, it’ll have to do. Essentially, I just looked at shot attempts, free throw trips, and turnovers, and then adjusted for and-one’s and offensive rebounds (meaning that misses rebounded by the offense don’t count as possession endpoints). All put together, the average PPP following a live-ball turnover is 1.112. Following a dead-ball possession, that number is 1.113. So, the play following a turnover is worth, on average, is worth 1.1122 points per pbp (if this looks a little funny, just know that I show the rounded numbers here while still working with full numbers), and 1.087 from inpredictable. The 1.106 for the interrupted play falls between the two, so I’d say that a possession outlook before vs after a turnover hasn’t changed much.
So, per pbp, the possession following a live-ball turnover playing out has a PPP of 1.112, while that which follows a dead-ball turnover is worth 1.113. Very similar numbers, but the bigger takeaway here is that turnovers do, in fact, more or less reset one’s possession, and don’t present any clear statistical advantage (0.5 points per 100 possessions non-withstanding). However, in this particular case, the numbers may not tell the full(y accurate) story. Working off the assumption that steals are more or less synonymous with transition (64% of them are, at least), it would be fair to assume that a quick miss or turnover out in transition doesn’t hold the same defensive consequences that it would in the half-court, as a part of your team is already back on defense; this isn’t accounted for because the majority of the numbers used to approximate PPP (PPP following a rim miss, middy miss, etc.) come from the half-court. However, there were only 1178 consecutive steals this year (about one every two games), so maybe I’m getting a little reserved. On to inpredictable, where our value is 1.087 (read: below the typical possession), leading me to conclude that a team, after turning over the ball and then getting it back, is likely somewhere between a little worse off or not at all, offensively, than it previously was. Because pbp’s data gives more detail and showed no change, I don’t feel like I have enough evidence to assume a difference. So, I’ll be working with value estimates of 1.092 points for an offensive rebound, and 1.18 for a turnover.
Ok, so what does this all mean? What’s the point of it? A part of doing this, I must admit, was for myself - to get some practice fiddling around with numbers, gathering and filtering them to answer a statistical question. However, you probably didn’t come here to cheer me on as I play with some spreadsheets. You want answers. Well, I’ll try.
Rather than presenting the divine truths of the Four Factors, what I hoped to highlight here is that we need to think deeper about certain actions and the extent of their consequences. I used league-average values throughout, so that is where findings can be applied: league-wide (although, it’s definitely possible that a team with certain strengths and weaknesses could adjust aspects of their approaches to score some marginal points here and there, simply because the numbers work out that way for them). An offensive rebound is more valuable than it’s basic on-paper PPP because it also has a negative effect on the opposing team’s subsequent possession. That brings it a little closer to a turnover, but not by too much; turnovers (the live ball ones) are still incredibly valuable. As I mentioned above, for the first time in the modern era, possessions mattered more than efficiency (relatively) among the better offenses in the league. You can either preserve your own opportunities (by keeping opponent OREB% and TOV% low) or take some from your opponent (by keeping OREB% and opponent TOV% high). Now I’m going to look at what I’m calling Net Adjusted Possessions Gained Per 100, which is what it sounds like. Basically, I’m subtracting extra possessions gained from extra possessions ceded. Possessions Gained Per 100 is calculated by the following:
(Opponent TOV% * 100) + (OREB% * (league average # of available rebounds on one end per 100 possessions, or 49.6)).
Possessions Lost Per 100 is calculated in the same way, except using TOV% and opponent OREB%. The “adjusted” comes from me looking at how many offensive rebounds a team would get or cede assuming they had a league-average amount of rebounds to play with. Simply using total offensive rebounds skews towards worse teams, as their offensive rebound totals oversell their proficiency because, being bad, they generally have more missed shots to work with (and the flip side of this is true on defense). And a final warning: this list may overstate some teams’ apparent ability, so PLEASE CONSIDER CONTEXT (for example - Chicago generally won the possession game by a mile, but they frequently blitzed the P&R this year, which, while generating more turnovers, also gave up more efficient shots, a consequence not recorded here).
Now, let’s take a look at what factors into the composition of those values:
As a supplement to the data, you should probably keep in mind that the average team gets just over 25 consecutive shots up per 100 (offensive rebounds + forced turnovers). That’s about a quarter of all NBA offense (duh) coming in a non-traditional way!
So, finally, which teams “win” the possession battle? Possessions are only useful if you’re able to score. I calculated each team’s PPP for the four events listed above (forced turnovers, committed turnovers, offensive rebounds, and opponent offensive rebounds - keep in mind that these are pure PPP values, not taking into account the potential effects on the subsequent possession) and then looked at overall points added and overall efficiency. Throughout the different realms of basketball, volume and efficiency have a complicated relationship - here, not so much. The correlation between points and opportunities is 0.90 vs 0.21 between points and efficiency, which is why the next graphic will look at teams’ success through the lens of total points (per 100 possessions, of course).
No rush; take some time to look over the table and observe different teams’ strengths and weaknesses.
One cool aspect of the list is that good teams can be found all over. The Lakers, despite re-affirming general assumptions about the quintessential contender building block (stars), won the championship in part due to being the best in the league at squeezing out value on the margins, as opposed to, say, a high-octane offense, showing that the different ways to construct a winner are as diverse as ever; you simply need to look a bit deeper.
I really hope you enjoyed reading this as much as I enjoyed writing it. More importantly, though, I hope that you’re able to walk (or click) away with a new insight, perspective, or, at the bare minimum, a teensy little tidbit of information you weren’t aware of beforehand. If you really (or even just moderately) enjoyed the article, a great way to show your support would be by sharing it on Twitter. Oh, and while you’re still here, in the case that you haven’t already, I’d strongly recommend you check out my previous piece, a 4.2k word (and multi-clip) profile of Luka’s scoring, including his two biggest areas for improvement this upcoming season. And for my most avid readers (mom and dad), what to expect next: an all-in-one season-preview/off-season review, eventually followed by a breakdown of one of my favorite young guards.