Ever heard of Simple Rating System (SRS)? It's a nifty little statistical system for making sense of the hundreds or thousands of games in a season of sports. Back in January, about 10 or 15 games into the season, I was a little bit obsessed with SRS. The math is a bit complex, but not all that hard for computers (some linear algebra if you're into that), but the idea is quite elegant. Let's go into it quickly.
See, when we talk about strength of schedule, usually we mean the average record of the teams played against. But consider a team in one of those tiny college conferences out west. If most of the team's games are in that conference, they're going to average about .500 in their SOS (Strength of Schedule) calculation over that conference (as for ACC teams). Even if our small-conference team plays a few decent teams out of conference and gets torched every time - they could stockpile wins in their weaker conference and end up with a great record and an excellent strength of schedule. We want a rating system that takes this into account. That rating system is SRS, and it's one very elegant solution.
How does it work? Well, this gets a little bit technical below (and if you have time, this is much better as an explanation), but I'll give an overview first. It's essentially a process for collecting all the outcomes of all the games and then using these outcomes to come up with a rating estimate that simultaneously explains every team's margin of victory, given the simultaneously solved rating estimate of their average opponent. In other words, you get "The Spurs are rated +8 because they were +7 margin of victory (MOV) against a schedule of teams that averages +1 as their rating" as the answer.
Okay, here's technical stuff (those who aren't interested can feel free to skip to the next paragraph): What you do is to take the number of games played by every pairing of teams, and then you put this number of games into a 30x30 matrix indexed by row and column for that those teams. So say the Spurs who are 27th alphabetically beat the Raptors (28th) by 10 this season in one game... in the 27th row and the 28th column, you'll put 1 in that matrix entry (for 1 game). In the 28th row and the 27th column, you'll put 1, also, for the same reason. Where does that 10 (or -10, for the Raptors) go? Well, it gets added both the Spurs and Raptors average MOV (margin of victory), which you put on the right side (a column vector) of a matrix equation. So we have a column vector that aggregates margin of victory for each team... but we also have a column vector that aggregates 30 "rating variables," one for each team. This is the catch-all variable that cuts through the strength of schedule variable completely to answer decisively questions like "Are you an average team in a crappy conference?" "Are you a bad team in a good conference?" "Are you a great team overall that towers over a crappy conference or that is still third in an incredible conference?"
Alright, technical stuff is done. Now, you've probably groaned (as I have) at the BCS using these elaborate computational methods because it always feels really shady and arbitrary. "Come on, this team already beat that team, the losing team had their chance, why can't we just switch to a 4-8 team playoff?" I understand that feeling and the unease it can create for those who distrust too much number crunching. Now I'm not promoting SRS as a substitute for understanding the team matchups involved (and it's especially no substitute for the joy of the NBA playoffs), but: a) I made a bunch of incredibly neat graphics which go far beyond simple SRS and, b) I'm aware of the limitations of such a framework and won't beat you over the head with it. It's just an estimate to see how the teams stack up...
The main problem I was trying to solve for the Spurs is working out how to account for the fact that the middle and bottom of the Eastern Conference has been historically bad for about as long as the Spurs have been contenders in the Robinson-Duncan era. Strength of schedule and strength of conference have a huge impact on margin of victory (and the individual Four Factors components that make up MOV), since about two-thirds of games are in your own conference and the 9 seed in the West is typically the 8 or even 7 seed in the East. The Spurs last season - before their injury-fueled slide - had one of the ten best starts in the history of the NBA, by record, if I recall correctly, That was great, but what made it amazing is that iis that they were doing so in by far the best conference and by far the best division (the worst team in the Southwest were the Rockets, the 9 seed with a 43-39 record). So yeah, of course strength of schedule matters, and SRS is just a tool to account for that (and to give Western teams a well-deserved boost of 1 point or so.) and the Four Factors just give us 8-12 additional variables to go a little further to see sort of where the efficiency is coming from in the offense, whether the teams are running out and getting transition buckets like the Grizz and Nuggets or if they're just eating their opponents hearts out from every offensive angle, like the Spurs.
Now, these were pretty fun to make, and I was surprised to discover that my years of watching the NBA had helped me develop an intricate knowledge of slightly different shades of blue. I was really going to town on these subtly differing wavelengths. "This one for Memphis, this one for Dallas... this one for those stupid Thunder shirts." Anyway, getting back on track...
The most important thing to note note is that there are five categories (called "Total Efficiency" and the "Four Factors" with their offensive, defensive, and total advantages). Right is good and left is bad, and the zero line is league average in every category except for Turnovers Caused, which is reversed for no good reason. For every one of these categories, there is an "advantage" variable.which is just the sum of the offensive and the defensive component. For example, Turnovers Prevented has Turnovers Caused and add them together to get the Turnover Advantage. Note that the offensive and defensive components of a factor aren't necessarily related (look at Boston's Offensive and Defensive Rebounding Rates to see the importance of systems in some of these stats).
The Four Factors and general efficiency are both well-known to the NBA's stats community The Four Factors (great link there) encode the four different ways a possession can end in basketball: Getting to the line (fouling a shooter or fouling over the limit), making a shot (allowing a make), failing to get the offensive rebound on a miss (getting a defensive rebound), and turning the ball over (causing a turnover). There are fluky events not covered here, but anything numerically tangible that happens on a court usually affects one of the four factors (even passing for assists helps shooting at the expense of risking turnovers). So the four factors put the tangible outcomes of basketball into four offensive and defensive categories.
So what? Well, besides giving us a few categories to focus on, the main importance of the four factors is that each of the factors has just one number associated with it for each team at the end of a game. We use EFG% for the shooting because that takes into account the extra point from 3-point shots, we use OREB%, a percentage of offensive misses rather than of total shots per-gamethat ended in offensive rebounds (rather than OREB/Game) because rebounding is a percentage of available misses, not a percentage of total shots. We use FT/FGA for...odd historical reasons, because that doesn't make much sense (seems like it should be FT/possession, in my humble opninon, but there it is), and we use TOV%, or turnovers per possession. I could've put those into the graph but I think the common language makes the graphs easier to read and understand that way. If you're curious, though, those are the underlying base stats for the graphs.
That just leaves "total efficiency," whose base stat is just margin of victory per game, which we've slightly adjusted to account for the number of possessions in a game. So it's a per-possession margin of victory: If you play 100 possessions against a league-average opponent, where will the final score be on average? This is Ortg - Drtg, the number of points created minus points surrendered per 100 possessions.
The numbers in the chart above are not the raw Four Factors or base efficiencies but are the schedule-adjusted Four Factors and total efficiency using the perspective of SRS. That is to say, I took the concept of SRS to modify the base stats of the Four Factors. In other words, this chart answers statistically the questions like: How well did you offensively rebound, given your raw offensive rebounding stats and the average strength of the defensive rebounding teams you went against? How well did you defensively rebound given your raw stats and the average strength of the offensive rebounding teams you went against? The SRS matrix for determining team ratings is 30x30 for the NBA. I just turned that into 5 60x60 matrices (one for each category), where each team's offense and defense in that category are separate variables pitted against every other offense and defense. Neat, right? Glossing over some basic home court advantage stuff I added (this is for a neutral court) and there you have it, a much more granular version of the SRS concept that takes into account how a team does creating and guarding the four outcomes that end a possession.
Anyway... even after adjusting for schedule, the Bulls still had a stingy enough defense to have the best efficency in the league, and I think our game against them attests to that fact well. By my count, to their supreme credit, the Bulls were the only team to really beat the drive-and-kick Parker offense not with hedges or doubles but with legitimate anticipation and steals on the kick-outs and drives. But without Derrick Rose, it's probably for naught. A sad reminder of the toll of injuries, which Spurs fans know all too well.
In any case, assuming the rest of the injuries to players either are minimal or cancel out, the Spurs do look like the best team remaining* by this adjusted efficiency, and their offensive numbers are predictably stellar. As we all know, it all comes down to matchups, though, and Memphis, OKC, the Heat, and the Lakers should all have their say before they're hopefully eliminated, just like the defending champion Dallas Mavericks have already been (unfortunately for them, the jet landed on their hopes this season).
Now... here's one way to read the chart for Spurs-Jazz, for example: you can see the Spurs and Jazz right next to each other. The thing that jumps out to me is that the Jazz foul way too much, and Tony and Manu know how to get to the line to exploit this outcome (I suspect their relatively low number is the result of increased attention to avoiding unnecessary contact during the slog season). The Jazz are a tremendous reboudning team but are fairly weak defensively overall. Part of that is the fouling, part of that is simply that their backcourt leaves quite a lot to be desired. I love Gordon Hayward's game and I could have seen him and Millsap and AJ stealing a game from the Spurs if one of Tony or Manu had had a bad night. But the Jazz didn't have much to stop the ruthless drive of penetrators at the first line, and the second line just wasn't good enough to keep up with the momentum of Tony and the craft of Manu. Turnovers were a wash, and while the Jazz are fairly good at getting to the line (better than the Spurs, actually), the Spurs legendarily avoid fouling, and so that advantage was removed.
How about Memphis-Clippers? I think this goes to the Grizzlies for several reasons: Okay, Chris Paul is one of the best ever at controlling the tempo and avoiding turnovers. But he was forced off his spots so much so that even his legendarily cerebral approach to things like clock management were pedestrian. He's a smart player and you don't bet against him, but Memphis has done numbers on our own poing guard and Russell Westbrook in the Z-Bo/Gasol era. What's more, if Paul doesn't have it in his hands, he's trusting savvy vets like Nick Young, Eric Bledsoe, Mo Williams, Randy Foye, and Blake Griffin to make good decisions with the ball. Not only is that a huge step downward to almost anyone from Chris Paul, these players are not especially good to begin with, except for Griffin, who has (in some sort of hilarious Aesopian absurdity) been unable to get around the body of the only player in the league that cannot jump, in Z-Bo. The chart shoes that the Clippers foul too much and the Grizzlies cause too many turnovers, but the Clippers (to their credit) do have better shooters. But qualitatively? I just don't see Chris Paul imposing his will on such a decent point guard defense (he's become resigned to scoring, and he's been pretty good at it in this series and in the past, but he would pretty much have to take over the rest of the series as far as I can see, and I just don't see it happening). Then again, the Clippers do have the potential for freakish comebacks...so...nah, still no. It's gotta be Memphis.
How about our second round series? Well, here the chart above is a little bit cumbersome to view (I'll filter out teams if I post this again in later rounds) so either download it as an image with the button provided or go here: Anyway, it's a bit inconclusive. Memphis can still crash the offensive boards and we all remember Bynum's 30-rebound game. But our defensive rebounding has been stellar and well above-average all season, thanks not only to Kawhi, Green, Jax, and Manu, but also to our defensive schemes, Bonner making occasionally solid box-outs, and of course, our center for the past 15 years, Tim Duncan. But the key (as in last year) is going to be how the Spurs can fight the inevitable traps and steals and closeouts and subversions of the Memphis defense against Tony's high-powered, speedy, symbiotic offense.
That's overall the biggest limitation of this chart... in every offense except for the Hawks, you can't just take the factors' individual numbers and smash them against one another, offensive free throw against defensive free throw. In the best offenses, the symbiosis between shooters, scorers, and distributors is powerful precisely because one doesn't know the outcome of a possession in advance or who will take the shot, and the best defenses mitigate several factors simultaneously (as Duncan's brilliance in the pick and roll D over his career testifies to). But a team can react to what the other side gives them, and this gives us a general overview of how well they've responded over the course of the season.
Random Credits: Neil Paine for figuring out the methodology for this system in order to produce his quite similar schedule-adjusted offensive and defensive ratings last season.
HoopData, which despite some irritating formatting choices was ultimately the only place where I could easily find "advanced box scores" that listed four factors and efficiency differential in one place with the box score.
Tableau, which is incredibly useful for stats posts and probably for many other things.
And... our dear leader jrw for patiently nodding his head with worry while I changed the central idea for this post and its previous incarnations about sixty times before finally ending up doing the absolute first thing I tried. Heh.
*Even with the Bulls at full strength, that would've been an incredible series, and given the Bulls' offensive woes and the Spurs' ability to tighten the defensive screws, I'd favor the Spurs over the Bulls in five or six games, honestly.