Steve's Thoughts on Stats: The Basics

There are some basic concepts that have greatly refined my knowledge of basketball over the last few years, and I wish to share them with you on the off chance you haven’t been exposed to them yet. Even if you already subscribe to the logic of these ideas, I hope you still read along to help me refine my arguments to overcome the strong biases most people hold against advanced statistical analysis in sports. I will be sure to check the comments regularly for any input or feedback you have on the subject, so please give me your thoughts.

(1)   Possessions are the indisputable essence of performance analysis in basketball. The singular goal in every game of basketball is to outscore your opponent, and each opportunity to score points (or to prevent the other team from scoring points) comes in the form of a possession. Possessions always alternate between teams within a game, so in a head-to-head matchup each team will use roughly the same number of possessions. Therefore, the team that uses their possessions more efficiently in a given game will always win that game.

None of the statements above may seem very controversial at first blush, but many people still mistakenly rely on per game measures of offense and defense when attempting to assess and compare the effectiveness of different NBA teams. The problem with relying on per game measurements (points scored per game and points allowed per game) to assess effectiveness is that teams play at a variety of different paces when not in direct competition, and thus per game measurements inadvertently obscure true team efficiency. Here is an example that highlights the problem:

Example: Team X is a run and gun team that averages a stunning 108.8 points per game, which is the second highest points per game average in the NBA. Meanwhile, Team Y is a plodding team that thrives in half-court sets and averages only 98.1 points per game, which is twenty-first highest points per game average in the NBA. Team X appears to be a superior offensive team based on per game numbers, but we intuitively know that Team X has more opportunities to score in each game because they play at a much faster pace than Team Y. So how much bias does style of play introduce into the comparison? Let’s see how each team grades out on a per possession basis.

Despite the lofty per game scoring numbers, Team X really only scores 1.054 points per possession, which is the fourteenth most efficient in the NBA. Meanwhile, Team Y scores 1.080 points per possession, which is the seventh most efficient in the NBA. Team Y is actually has an offense that is significantly more efficient than the offense of Team X! Although the difference seems small when expressed on a per possession basis, it is often expressed on a per 100 possession basis (usually called Offensive Efficiency and Defensive Efficiency) to put the important differences in efficiency in a more comfortable and recognizable form. Team X has an Offensive Efficiency of 105.4, while Team Y has an Offensive Efficiency of 108.0. Even though Team Y plays at a slower pace than Team X, Team Y clearly superior offense because Team Y uses its possession more efficiently.

Note: Team X is the 09-10 Golden State Warriors (25 wins - 56 losses). Team Y is the 09-10 Portland Trailblazers (50 wins – 32 losses).

Here is the ultimate point I am trying to make: the only reason we take the effort to make comparisons between the offensive/defensive numbers of different teams is to help us determine which team actually has the better offense/defense. Per game measures of offense/defense are inaccurate measurements because they obscure true efficiency by failing to account for pace. Per possession measures of offense and defense precisely capture team efficiency because effectiveness is measured with regard to each opportunity a team will have. If we make a comparison between teams, why not take the effort to use the measure that most precisely expresses what we are actually interested in? Offensive Efficiency and Defensive Efficiency give us the precision we desire to make meaningful comparisons between teams, and that is why these measurements should be used in place of any per game stats.

(2)   Advanced metrics are often materially superior expressions of player efficiency in comparison to the traditional box score measures.

Traditional box scores record many meaningful events (made/missed FG, made/missed FT, assist, steal, offensive/defensive rebound, foul, turnover, etc.) that take place during a basketball game. Prevalent back-of-the-basketball-card stats (Pts/gm, Reb/gm, Ast/gm, FG%, 3PT%, FT%, etc.) are familiar to everyone and are certainly a comfortable point of reference for basic player comparisons, but in some cases we can use advanced metrics to get a better snapshot of player efficiency. Let’s take a look at a few of the most valuable advanced metrics:

 *Effective Field Goal Percentage (eFg%) = (FGM + 0.5 * 3PTM) / FGA). A made three-point field goal is worth more than a made two-point field goal, right? Of course it is, but both shots only use one possession, and eFG% is a metric that adjusts for the added value of a three point make. We now have a single shooting percentage to compare players who might have opportunities to shoot from very different places on the floor, instead of being forced to make informal (and probably inaccurate) adjustments between FG% and 3PT%. We try to make these informal adjustments based on position and opportunity all the time (we expect big men to have higher FG% because they shoot closer to the rim, and we expect guards to have higher 3PT%), but the ultimate goal is to have your team allocate the majority of their possessions to their most efficient offensive players, regardless of position. Since we really want to know about the shooting efficiency of given player, let’s use the metric that does all the work for us instead of trying to guess our way to the right answer. If we know made three-point shots are worth more made than two-point shots, then we should use eFG% to make sure we do not undervalue three-point shooting. Consider this example:

Example: Player A shoots 7-15 on his FGs with five of those makes being 3PT shots, while Player B shoots 9-15 on his FGs with no 3PT makes. Assuming neither player attempted a FT, which had the more efficient shooting night? Wrong.

When looking at a traditional box score and seeing that Player A was 7-15 on FGs and say 5-13 on 3PTs (remember that 3PT attempts are also counted as FG attempts) it just doesn’t as visually appealing as Player B going 9-15 on FGs and 0-0 on 3PTs. A quick glance at a box score would probably make us think that Player B had a better game shooting, but really that is because we aren’t very good at making all the necessary adjustments on the fly to account for the added value of the made three-point shot. eFG% accurately makes these adjustments for us: Player A scored 19 points and had an eFG% of 63.3%. Player B scored 18 points and had an eFG% of 60%. Therefore the answer is Player A, as he had the more efficient night shooting. eFG% helps us understand this fact much better than any traditional stats.

*True Shooting Percentage (TS%) = PTS / (2 * (FGA + 0.44 * FTA)). If you like the logic behind eFG%, then you will love TS%. Why? Because TS% takes into account FGs, the added value of made 3PTs field goals, and the value of free throws. Free throws are still shot attempts, so it makes sense to include these shots in a metric that seeks to express shooting efficiency. However, a single free throw does not typically use a full possession, because many times a player is awarded two free throw shots (the .44 multiplier is used because it is estimated that 44% of free throw attempts represent the end of a possession). Like the three pointer, the free throw is another high efficiency shot that tends to be undervalued by traditional box score metrics. Consider a twist on the previous example:

Example: Player A still shoots 7-15 on his FGs with five of those makes being 3PT shots, but he also shoots 1-2 on FTs. Meanwhile, Player B still shoots 9-15 on his FGs with no 3PT makes, but he also shoots 4-4 on FTs. Which had the more efficient shooting night? This time the answer is Player B.

TS% makes all the adjustments to allow a meaningful comparison between these two players who scored their points in very different ways. Player A scored 21 points and had a TS% of 59.8%, but Player B scored 22 and had a superior TS% of 65.6%. TS% reveals that Player B clearly had the more efficient shooting night.

This is the value of TS%. It allows us to make an accurate comparison of shooting efficiency between players who score their points in very different ways. When we want to compare the shooting efficiencies of different players, TS% ensures that the comparison will be a fair apples-to-apples comparison, regardless of what position the players play.