I know what you’re thinking: why did this guy decide to write about formulas and theory when the Spurs just completed their epic quest for redemption and revenge. This has nothing to do with Heat-Spurs; you want to read about Gregg Popovich’s monosyllabic zingers and the size of Dwyane Wade’s cheeks. Seriously, what has he got stashed in there? At this point, I wouldn’t have been that shocked if he produced an actual gun and shot Tony Parker in the knee if it would have helped the Heat get back into to series. I promise there will be plenty of time for all this and more. I’ll even throw you a nugget right now—unnamed sources inside the Heat locker room confirm that Chris Bosh is experiencing particularly heavy flow this month. They expect him to be ready for the 14-15 season opener, but he can’t provide another win guarantee. That’s not what this is about, but really, this actually is all about Heat-Spurs after all. Sure, everyone loves a cheap laugh about Delonte West and Lebron’s mom, but at the end of the day that won’t leave you any closer to understanding what’s happening on the hardwood, why the Spurs and Heat made it to the finals again (and again, and again, in the case of Miami) and why the Carmelo Anthonys and George Karls of the world remain perennially bewildered losers. Right. So where do wins come from? What are a basketball team’s objectives? At the highest level, these can be summed up as just three:
- Gaining and keeping possession of the ball.
- Maximizing the rate at which you turn possessions into points.
- Minimizing the rate at which the opponent turns possessions into points.
That’s it! If players’ primary goal is to win games, everything they do on the court should be with these three things in mind. (Analyzing what they should do if they want to maximize the size of their wallet is an interesting and relevant question that we will disregard for the time being). But ok, you knew that those things were important, kind of. But do you know how something as simple as taking a shot affects these three factors? Here’s a picture of a Dwyane Wade’s cheeks you can admire while you think about it. 
- Before the shot, your team (Team A) has possession. The value of this is determined by the answer to (2), which will be Team A’s points per possession. But after the shot, possession is uncertain. The shot has a certain probability of going in, fg%, in which case the other team (B) certainly gains possession. It also has a probability of missing, 1 – fg%, after which possession remains uncertain. Now Team A has a certain probability of grabbing the offensive board and retaining possession, ORRa / (ORRa + DRRb), and Team B has a probability of securing the defensive rebound and completing the defensive possession successfully, DRRb / (ORRa + DRRb). So the probability of team A retaining possession after the shot is given by (1 – fg%)*ORRa / (ORRa + DRRb) and the probability of Team B having possession after the shot plays out is just one minus the aforementioned monstrosity.
Ok, so the first part is self explanatory, of course the field goal % (as a function of player, shot location, defenders, etc), is the probability that the shot will go in and the only other outcome is that it will miss so we can represent that as 1 – the field goal percentage. Offensive and defensive rebound rates (ORR, DRR), while possibly a new term, are just as simple. A team (or player’s) offensive rebound rate is the percentage of offensive rebounds it secures out of the total possible offensive rebounds it could have gotten. The defensive rebound rate is the exact same thing for defensive rebounds. However, we can’t just say that the probability of team A snagging the offensive board in this case is ORR_a and be done. In that case the probability of team B getting the defensive rebound would just be DRR_b. What if team A is the old Doc Rivers Celtics team (rip…just kidding, good riddance) that notoriously didn’t even try for offensive rebounds and team B is, say, the Bulls with the Noah and Gibson in. So then ORRa might be .05 and DRRb might be .85…so the other 10% of the time the arena gets blown up by an army of black homophobic gay terrorist Donald Sterlings. As exciting as that might be, simply dividing by the sum of the two provides new probabilities that actually do add up to 100% and represent the real probabilities of each team ending up with possession. And that was just #1. Whew (wipes forehead) .
- As alluded to earlier, how taking a shot relates to turning possessions into points is essentially embedded in (1). The shot has a certain probability of going in and corresponding probability of missing. That much is obvious, but those probabilities will vary widely depending on the player taking the shot, the location the shot is taken from, the defending player or players, and so on. For example, for wide open fast-break layups you might be looking at 95% makes compared to 50% on 18 ft jumpers by Kevin Durant or 15% on the same 18 ft jumper but now its JJ Barea defended by Lebron. Of course, the value of the made shots differ as well.
- Here we basically have the flip side of (2) as viewed by the defensive team. Team A taking the shot wants it to be that wide open fast-break layup while Team B wants to get into situations more like the third example above. There have been some takes on this from the view of the offensive team as well; Phil Jackson famously discouraged corner threes because he thought they led to his defense being in disarray, but this has been shown not to be the case. I can’t find the study again; sue me, but basically they found that teams’ defensive efficiency after missed corner threes was significantly similar to their overall defensive efficiency. In fact, a good rule of thumb is that the corner 3 (along with layups) are the two best shots in basketball for trying to maximize (2).
This is just one small action; over the course of a game there may be 115 shots not to mention fouls, passes, steals and many other actions. For any of these actions, though, by examining how it affects each of the three big objectives we can see how the action helps or hurts a team’s chances of winning the game. With statistically derived values of points and possessions relative to wins, this allows us to find, in turn, the value of any box score statistic relative to wins. Wins Produced (wp, wins per 48, wp/48) is designed with this in mind, wrapping up all of a player’s box score statistics into one metric that measures how well a player achieves these three objectives, and thusly how much he helps his team win. Now let me be clear, as clueless basketball fan Barry O. from Hawaii would say, the thought exercise above gives us only the intuition behind the formula. The details of the statistical derivation can be found here, but essentially, what the possibly murky math does is conduct that type of analysis for every event that took place on the court within the given time frame. The reason to bother with all this is that wins produced is empirically validated to explain actual wins in actual NBA games where people actually said “We got the W and that’s what counts” or maybe the classic “both teams played hard”. Between the 1977-78 and 2011-12 seasons, there have only been 2 seasons in which the correlation between Wins Produced (sum of minutes weighted wins per 48 of players on a team) and actual wins has been less than 90%. Unfortunately, not many people grasp the implications of this concept. Maybe it hasn’t been explained in a relatable way, which is why I’m making an effort to do so, albeit one that is likely futile. To this end, I will address the popular critiques of Wins Produced which come in three primary categories. The first camp agrees that wins produced is the best metric to capture a player and team’s productivity and simply suggests small tweaks in the way some detail is handled, such as how much to deduct from a scoring player and award to an assisting player when a basket was assisted or how to account for the fact that players take away their teammates rebounds. While these details are interesting to me I will disregard this camp for now as these people agree that wins produced is better than other metrics which don’t even account for these things at all. The other big WP critique comes in the form of “I can’t buy a metric that says player X is better than player Y.” Of course, this is never followed up with a deeper look into what parts of those players’ games correspond with the numbers that result in player x producing more wins, or anything rational like that. Instead, it has three subgroups itself: they either cite conventional statistics without bothering to consider quantitatively their impact on wins, or they cite the so-called experts that cite these conventional statistics on TV or in print, or worst of all, they don’t back it up at all; their point should be self-evident since it is the conventional wisdom in the first place. I dream of a day when we will be able to disregard these critics as well, but alas that day isn’t here yet. For those who cite alternate box-score stats like OMG PPG or the ‘experts’ who do, I would counter with an examination of how that metric relates to wins and explains them worse than WP. If they still “don’t buy it”, which is much more likely than not, or are in the third group, then this shows they are simply not interested in a metric that tells you about what players are contributing towards their team winning the game. Rather, they are looking for a metric to confirm what they already thought they knew. So then I would go on to discuss the point of doing research in the first place: finding the objective unbiased answer to a question. If that question is how much value does each player contribute to his team, where value is defined as on court actions that lead to wins, then if the best answer to that question is different to what we expected we don’t go back and change the question to get the answer to meet our expectations. Sadly, this occurs all too often, even at the highest levels of academia, but not here, damnit! This aggression will not stand! This doesn’t mean that player evaluation based on WP has no similarities to conventional wisdom. Lebron, Durant, and CP3 are still the best players. Kevin Love, Steph Curry, and James Harden are still clear-cut all-stars, to name a few. But when I tell you that Brandan Wright had the 8th best 2013-14 season on a per-minute basis or that Trevor Ariza ‘produced’ 13.3 wins for the wizards this year, 11th most in the league, my hope is that maybe, instead of automatically discounting the possibility that these guys had excellent seasons because Mike Wilbon, Reggie Miller, and the like didn’t say so you might look a little deeper into why WP ‘likes them’ and what traits they have that their more-hyped less productive counterparts lack. The final main critique is regarding what WP doesn’t take into account. These critics mention everything from issues off the court to player health to “intangibles” such as leadership. The first thing I would tell one of these critics is that I agree that each of these factors is important and should be accounted for when determining a player’s worth. But why are these factors important? When a player plays drunk or through an injury, that player’s team being more likely to lose is more than one step down on the causal chain. The issue causes the player to play worse, which in turn causes his team to be more likely to lose. The effects of these issues are in fact manifested in the wins produced output via their effect on that player’s actions on the court. Unfortunately, this alone doesn’t allow us to quantify these effects precisely, which would certainly be valuable. However, they are not unaccounted for in WP, or, by the same logic, any other metric. None of this is to say that WP is a perfect metric. As the first type of critique implies, there is debate among which version of WP is best. At best, all but one of them is wrong; more likely, none is precisely correct when we’re talking about picking how to weight factors that can’t be measured directly out of a continuous distribution of possibilities. The correlation with wins is very high, but not 100%. The difference tends to be attributed to parts of team defense that isn’t measured (team defense is incorporated in the formula, though), but this is only a logical hypothesis. Furthermore, we don’t really have any data on teams constructed with only WP in mind. In order to give an example, it is necessary to show some concrete examples of players’ win produced numbers. I was going to do that eventually anyway, so this is as good a time as ever. Wins produced is normalized such that the average WP per 48 is .1 at each position. Some players that had average seasons in 2013-14 include JJ Hickson (.099), John Henson (.099), Kyle Singler (.1), and, more surprisingly to mainstream fans, Al Jefferson (.1), and Luol Deng (.101). When multiplied by their minutes played and divided by 48, these players produced 3.8, 3.8, 4.8, 5.3, and 4.6 wins respectively. To give you an idea of the high end of the range, among players who played 500 or more minutes, Chris Paul led the league on a per-minute basis the last 2 seasons with WP per 48 of .348 and .335. In terms of total wins produced, Durant and Lebron have led the league the past 2 seasons with 20.1 and 19.7 this year and 20.6 and 20 in 2012-13. If you want to look up someone in particular or just see them all, go here. In between the very best players and the average ones, some notable examples are Tim Duncan (.201), Serge Ibaka (.2), Dwyane Wade(.193), Lance Stephenson (.215), and, more surprisingly, James Johnson (.216), Terrence Jones (.203), and Kyle Korver (.2). On the low end, we have Al Harrington (-.146), John Lucas III (-.137), and the first pick of the draft (link) (-.126), and Dwyane Wade’s cheeks (-.125). So yes, you can contribute negative wins to your team, as mistakes like missed shots and turnovers are penalized. Just ask Andrea Bargnani, who had one of the best years of his career posting -.049 WP per 48. Obviously a team can’t win less than 0 games, but just we don’t have data on the extreme end of low WP for this to become an issue. As much as I’d like to see a lineup of Harrington, Lucas, Bennett, Bargs, and Wade’s Cheeks and as stupid as most NBA general managers are I don’t think they’ll ever be quite stupid enough for us to get this treat. But maybe someday they’ll be smart enough that we get to see the other end of this. If we do, though, we aren’t going to see a team with a rotation full of Lebrons and KDs, even in the era of Big 3s, who may or may not actually be the best 3 players on their team. Instead, it would be a team full of guys that are underrated by conventional statistics but not WP. These are players who don’t have high raw PPG numbers but, whatever they do contribute on offense, they contribute efficiently and good defenders. Indeed, PPG correlates strongly with salary but getting those points efficiently does not. So imagine the following lineup made up of players that would be very easy to acquire. Position Player 13-14 WP / 48 C Chris Anderson .279 PF Jeff Adrien .244 SF Trevor Ariza .234 PG Pablo Prigioni .216 SG Danny Green .188 How would this team fare against: C Demarcus Cousins .157 PF Blake Griffin .169 SF Carmelo Anthony .161 SG Demar Derozan .096 PG Russell Westbrook .163 I’m the guy writing to advocate this metric and it’s still pretty hard to pick the former. In this case, I think my thought process is similar to what anyone else’s would be: the WP All Stars would never score! Even against the mediocre defense of the Yay Points All-Stars, the WPAS will be unable to create the high percentage opportunities that they are accustomed to. The WPAS wouldn’t give the YPAS open looks, but the YPAS are used to jacking up low percentage and some of them will go in. Probably more than those of the WPAS. But the YPAS could never be a real team due to salary considerations. Let’s replace a few of the players and give us the following theoretical but possible team: C Jonas Valanciunas .139 PF Tyler Zeller .125 SF Carmelo Anthony .161 SG Demar Derozan .096 PG Russell Westbrook .163 Now this team is more realistic. I don’t think it’d be all that great in the real NBA—the Thunder as currently constructed are pretty much a strictly better version and while they are very good, they’ve only made one finals and that was with James Harden as well. Yet I think I’d still have to take these five against the WPAS. Maybe I’m wrong. Maybe I’m letting myself be blinded by convention the same way I might say someone is who claims Melo is better than, say, Nic Batum or Andre Iguodala. But right now, I truly believe that it’s true just like those “idiots.” And if that first listed team wouldn’t beat the last, clearly WP isn’t the end all be all statistic and some balance amongst actual basketball functions must be sought as well. Wins Produced is just the start of the analysis; of course we must dig deeper to see how different players are producing wins and group them coherently so that the team can actually perform the basketball functions it needs to. But it’s the best starting point we have right now. So while I don’t want my Bulls to go out and build the example WPAS team just yet, I also don’t want them to trade all their assets for one of about equal value as any one of them in Carmelo Anthony either. I promise I don’t mean to target you, Melo, you’re just a good example of being overrated and cut down to size by a little math wisdom. If Kobe hadn’t been injured all season it’d be him instead. So back to the Bulls, I’m not saying to ditch Derrick Rose for Pablo Prigioni even if Rose comes back to his old, solid but overrated form (.161 WP per 48 in 2010-11, his MVP season). I’m just saying to think a little bit before you think you can replace Kyle Korver with Marco Belinelli and then Mike Dunleavey just because they’re all white and you can save some salary. And to give Ronnie Brewer some minutes once in his life! And so on. Oh and about those Spurs? Wins produced thinks they had some pretty good players this year. Kawhi Leonard .294 (6th in the league) Tim Duncan .201 Danny Green .188 Manu Ginobili .184 Tiago Splitter .158 Patty Mills .157 (71st) These rankings might not seem so impressive to at first, as only the well deserving finals MVP truly shines, but as we know the Spurs do it as a team. And having ¾ of your entire rotation in the top 16% of the league is actually pretty impressive to me when I look at it that way. WP also thinks some guys weren’t as important as we think.... Tony Parker .085 (he did put up a much better .18 in 12-13, though) Boris Diaw .093 (have to admit, doesn’t seem to do justice to his finals contribution) Of course, there’s much more to why the spurs won the title than simply listing their players and performance, but that will have to wait for another time.