Chauncey Billups , true shooting & skill curves | Scoring efficiency (NBA Stats 101, Part 2)

In part one of this series, we looked at how the per-game slash line of points, rebounds, and assists can be drastically misleading, and how in 1991 those per-game averages made Michael Adams look like an all-time level point guard. The biggest issue with those numbers is that they miss a lot of the game, they lack context. Take points for example, Adams scored 27 per game that year, 8 more than Magic Johnson, but we don't know how he came about scoring those points. The most basic way to contextualize points in basketball is to look at shooting efficiency, how many shots did it take him to score those 27 points. For decades, field goal percentage was the traditional measuring stick for efficiency in basketball. In 1991, Adams only shot 39% from the floor, one of the reasons he didn't even make the all-star team that year despite those big numbers. But field goal percentage doesn't paint a very complete picture of scoring efficiency. To understand why, take a player like Chauncey Billups. Billups shot 42% from the field in 2006, well below the league average of 45%, so through this lens, Billups was an inefficient scorer. But field goal percentage fails to account for whether those shots were twos or threes. Since threes are worth 50% more points than twos, a player only needs to shoot 33% from downtown to match the number of points he would score on 50% shooting from two-point range. That's worth repeating, 50% on twos is equal to 33% on threes. So what if someone took a bunch of threes, dragging down his overall field goal percentage while simultaneously driving up his points per shot? It turns out that's exactly what happened with Billups. Chauncey took nearly half of his attempts from downtown, and as a 43% long-distance shooter, he racked up about 7 points per game from three and 6 points per game from two. He scored those 13 points a night on 12.5 shots, good for a 1.02 points per shot attempt, or the equivalent of 51% two-point shooting. Coincidentally, his teammate Ben Wallace shot far better from the floor that year with a 51% field goal percentage. Only Wallace made zero three-pointers, so he also averaged 1.02 points per shot. This number, points per shot, is captured as effective field goal percentage, or EFG, and it provides far more accurate information about a player's scoring efficiency on his shot attempts than raw field goal percentage alone. Effective field goal percentage takes the number of points scored on field goal attempts and converts them to the two-point percentage needed to generate that many points. But what about free throws? Free throws never register as a shot attempt, so imagine a game where someone shot one of five from the floor, but nearly every time he went to the basket, he was fouled and made, say, all 18 of his free throws. Field goal percentage tells us he scored his 20 points on 20% shooting, which makes it look like he wasted a bunch of possessions trying to score those 20 points. But there's no functional difference between making nine layups and making 18 free throws. Each of them ended nine possessions with two points. In total, our hypothetical player had 14 scoring attempts, sometimes called shooting possessions, those five shots from the field and the nine trips to the free throw line, and he scored 20 points on those attempts, which is good for 1.43 points per attempt, incredibly efficient offense. Put another way, he would have to shoot 71% on two-point shots to generate the same 20 points on those 14 attempts. This number is called true shooting percentage, which is points per scoring attempt converted to the quote-unquote true two-point field goal percentage needed to score that many points per attempt. It's a name that has confused many of us over the years, but it was intended to convert all shot types to the familiar two-point field goal percentage. Returning to Chauncey Billups and Ben Wallace, we can now get the complete picture. Billups took about six free throws per game at nearly 90%, six free throws eats up about three possessions. Meanwhile, Wallace used about a possession and a half to shoot 42% from the line. All told, Billups scored his 18.5 points per night on roughly 15 scoring attempts, and Big Ben scored his 7 points per game on roughly 7 scoring attempts. This gives Billups a 60% true shooting percentage. Again, that's his equivalent two-point field goal percentage based on the value of all those threes and free throws. Wallace, meanwhile, scored about a point per attempt, giving him a 50% true shooting percentage. Billups generated far more points per scoring attempt than Wallace, making him a vastly more efficient scorer. If our goal is to know how efficiently a player is scoring, we need to be looking at true shooting percentage, not field goal percentage. Overall field goal percentage actually clouds the picture by blending threes and twos and ignoring ones altogether. Back in 1991, Magic Johnson shot around league average from the field, but counting his threes and free throws made him one of the most efficient scorers in the game. At 62% efficiency, he was well ahead of Michael Adams' 53%. If we look at a distribution of scoring efficiency across all players in the league, we can appreciate just how far ahead Magic's true shooting was, pushing the league leaders in the category. By the way, this normal distribution, with most players clustered around league average and standouts 8 or 10% ahead of the league, has held constant throughout every NBA season in history. This is strong evidence that shooting efficiency is dependent on league norms, and that we should compare players across seasons by using their percentages relative to the league, as outlined in another video on this channel on stat inflation. Now, some people have wondered how true shooting handles things like and ones. After all, if I take two shots in a game and am fouled for an and one both times, I would finish 2 for 2 from the floor and 2 for 2 from the line for 6 points. But I scored those points in 2 possessions, not 3. My true shooting percentage should be 150%. That sounds weird, but remember, it would take more than 100% shooting on 2-point shots to average 3 points per attempt. So, does true shooting percentage really know about my and ones? The answer is essentially yes. Most true shooting percentage you'll encounter accurately estimates the number of and ones for a player. In a single game, the estimator can be off by a bit, but over the course of many games, a player's estimated true shooting attempts will start to match his actual true shooting attempts almost perfectly. In 2019, 99% of players were within 1% of their quote unquote real true shooting percentage, and about 90% of players were within half a percentage point. Adding in efficiency is a huge step when contextualizing that scoring, but teammates and opponents still matter, and so a difference in efficiency of 1% isn't material when we make inferences about performance. Similarly, there's a classic debate about interpreting efficiency based on scoring volume. Is it better to score 25 points per game on 55% true shooting, or 20 points per game on 60% true shooting? As players are asked to score more, their efficiency often goes down because they are less discriminant about shot selection, and defenses also tend to load up on them. Current Washington Wizards assistant coach Dean Oliver, a founding father of the analytics movement in basketball, coined the term skill curves to describe some of these volume efficiency relationships. The idea is that some players can increase their scoring volume before they see a severe drop in efficiency, while other players won't receive a huge bump in efficiency even if they taper down their volume. So which is better, more volume or more efficiency? Well, the answer seems to be it depends. Sometimes a team might benefit from scoring volume despite bleeding some efficiency. Allen Iverson was often blasted for inefficient chucking, largely because he shot around 40% from the floor, but in his MVP year in 2001, his overall efficiency was actually right around league average, which isn't great, but it helped provide value for Philadelphia because the Sixers lack scoring and an offensive focal point. Those kinds of players can keep defensive teams like this afloat, and they're often referred to as floor raisers. Speaking of teams, you might be wondering if true shooting also measures efficiency at the team level, and the answer is not quite. What we've discussed here does apply to teams too, so field goal percentage doesn't do a great job capturing how efficient a team is. For instance, the Rockets were the second most efficient offense last year, but 24th in field goal percentage. But true shooting percentage isn't great for measuring a team's offense either, because a team's scoring attempts are just every time they have the ball as a unit. For a team, a possession can end not only with a scoring attempt, but with a turnover, or it can be extended by an offensive rebound. So true shooting percentage doesn't quite capture the full picture. In the next installment, we'll talk about how we formally define offensive efficiency for teams, but for now, the key takeaways from part two are this. Basketball is a game of limited scoring opportunities, so we care about how efficiently we rack up points in those opportunities. Field goal percentage is misleading when judging that scoring efficiency, and as a result, there's never a good reason to reference it. Effective field goal percentage is better, but only relates to shots from the floor, leaving out free throws. True shooting percentage is the gold standard for player efficiency, because it calculates points per scoring attempt by incorporating free throws and three-pointers. Finally, there's a non-linear relationship between volume scoring and efficiency that varies from player to player. High volume and high efficiency scoring is ideal, but volume scoring at a round league average can help non-elite offenses too. Of course, there's even more context we could add to these scoring numbers and other stats, and that's exactly what we'll explore in part three. If you're interested in diving deeper into some of these areas, I've added a few relevant resources in the description box below, including episode number 24 of the Thinking Basketball podcast, which examines skill curves and the volume efficiency relationship deeper. If you want to support this channel, you can subscribe at patreon.com slash thinking basketball for access to historical data and insider articles. Thanks so much to everyone for fueling this series with all your questions, and I hope you're having a great day.