Individual Floor %

When I started my research over three years ago, one of my original goals was to come up with a points created formula for players, something that would indicate how many points a player contributed to his team by scoring, rebounding, assisting, stealing, blocking shots, or whatever else there could be contributing to points scored. It was a fruitless task that, in retrospect, was rather stupid. The 'points created' by a rebound or blocked shot was hard to define or to get a grasp on. Someone may score points because of a rebound or blocked shot, but what percentage of those points should be credited to the person getting the rebound or blocking the shot. How does one define such a percentage? It's very possible that a rebound or blocked shot does not lead to a score, so assigning an 'average value' to all rebounds and blocked shots may be inaccurate. It is hard to say, in fact, whether defensive rebounds or blocked shots really can 'create' points. Even offensive rebounds don't 'create' points if no one can make a basket.

I left my 'points created' research behind about a year and a half ago, deciding to approach the game from a different point of view. That point of view was based on possessions and is used in this book. Concentrating on scoring games and on how teams worked together, I devised the formula for team possessions and found out what the floor % formula, which had been sitting around getting used without any physical meaning to it, meant in a game. Points per possession came immediately from all this and the first methods of ranking offenses and defenses were born.

It took a year or so before the idea hit me to try to define possessions and floor %'s for players. When a player ends his team's possession, it would be a possession charged to him. When a player scored or assisted on a score, a scoring possession would be charged to him. Problems occurred in trying to 'conserve' possessions so that they would add up to the team total. Also, I ran into the problem of trying to determine how much value is placed on an assist. Like my earlier troubles with rebounds and blocked shots, I had to try to arbitrarily assign a weight to assists that would give credit to the 'assistant' and simultaneously take the same amount of credit away from the 'assistee'. Assists, though, unlike rebounds or blocked shots, have a definite scoring possession associated with them; there are no assists without points scored.

These problems kept me away from pursuing individual offensive rankings until about a third of the way through this book. Then, I came to the Philadelphia comment, which was an attempt at assigning Charles Barkley's place among the league's best players. The time came for individual floor %'s. Things started falling into place and ideas kept coming on how to improve it. Finally, on a long walk around the neighborhood, I collected all my thoughts together in my head and realized that an individual floor % could be an outstanding way for not only ranking the offensive efficiency of players, but also for calculating something similar to points created.

To start again, an individual's floor % would be his scoring possessions divided by his total possessions. A player's scoring possessions would be his field goals that weren't assisted on, plus a certain percentage of his field goals that were assisted on, plus a certain percentage of his assists, plus his free throws made that represented a team scoring possession. A player's total possessions would be all of his scoring possessions, plus his missed field goals and free throws that weren't rebounded by his team, plus his turnovers.

The work came in devising formulas that fit what I wanted. Those are given below.

Scoring possessions= FG - 0.37*FG*Q/R + 0.37*AST + 0.5*FT

Possessions= FGA-(FGA-FG)*OR%+0.37*AST-0.37*FG*Q/R+TO+0.4*FTA

Q= TMAST/TMMIN*5*PLYRMIN - AST
R= TMFG/TMMIN*5*PLYRMIN - AST
OR%= TMOR/(TMFGA-TMFG)
FG= Player's field goals made AST= Player's total assists
FT= Player's free throws made
FGA= Player's field goals attempted
TO= Player's total turnovers FTA= Player's free throws attempted
TMAST= Team's total assists
TMMIN= Total minutes played by team (i.e. 19755 in a season)
PLYRMIN= Minutes played by player (i.e. 2600 in a season)
TMFG= Total field goals made by team
TMOR= Total team offensive rebounds
TMFGA= Total field goals attempted by team

Once certain things are understood, the above formulas, as complex as they may look, make some sense. Starting with the scoring possession formula, the first two terms represent an approximation of how many field goals a player scores that are credited to him, subtracting out the credit given to 'assistants'. The Q term approximates the number of assists made by a player's team while he's in the game that aren't made by the player himself. (TMMIN is given in box scores as 240 for a 48 minute game, because 5 players can play 48 minutes each, 5*48= 240. The 5 in both the Q and R formulas adjusts for this.) The R term is an estimate of the number of field goals scored by a player's team while he is in the game that aren't assisted on by the player. Therefore, the Q/R term is an estimate of the percentage of a player's field goals that are assisted on by his teammates; multiplying by FG then gives an estimate of the number of a player's field goals that are assisted on by his teammates. This Q/R term is usually less than 0.5 for point guards, but can be higher than 0.6 for centers or power forwards who rarely pass. FG - FG*Q/R would then be the total number of a player's field goals that aren't assisted on.

What does the 0.37 mean? As I said before, only part of the credit for assisted baskets should be taken away. Essentially arbitrarily, I said that 63% of an assisted basket is credited to the player who made the basket and the other 37% goes to the 'assistant'. This 0.37 came from score sheets of games I had scored. Long shots, I decided, should be mostly credited to the shooter because the shot is usually considerably more difficult than the pass that becomes the assist. Long shots then were credited 75% to the shooter and 25% to the 'assistant'. Short shots, as I had scored them, were usually layups or shots within five feet of the basket - relatively easy shots. These are shots that most anyone could make, not requiring someone with jump shooter skills, and half (50%) credit was given to both the shooter and 'assistant'. Medium range shots would have the credit split up with shooter getting 62.5% and 'assistant' getting 37.5% (values halfway between those given for long and short shots). For several games, I counted assists and assigned credit based on the lengths of the shots. Dividing total credit by total assists, I came up with 0.39 as the proper average credit for assists. There was plenty of uncertainty to the measurement and I judged that 0.39 was a little too high and lowered the figure to 0.37. This has produced very satisfactory results.

Moving on with the scoring possession formula, the 0.37*AST comes from the above measurement giving 37% of the credit for assisted baskets to the 'assistant'. This is saying that 37% of a scoring possession goes to the player who assisted on the score. The 0.5*FT approximates half of every made free throw as a scoring possession. When a player is fouled and is sent to the free throw line for two shots, then makes them both, that is one scoring possession and the multiplying factor on FT is 0.5. When a player makes only one of two free throws, that is still one scoring possession, but the multiplying factor is now 1.0. When a player makes a free throw to complete a three point play, the scoring possession has already been counted in the FG and the multiplying factor is 0.0. I assumed that everything balances out so that 0.5 is the average multiplying factor. This is the part of the formula I'm most unsure about, but I don't think that it causes major problems.

The total possessions formula incorporates all of the scoring possessions fairly obviously. Parts of the scoring possession formula are in the total possessions formula, but parts have been replaced. The first two terms of the possessions formula represent an estimate of the number of a player's shots that aren't rebounded by his own team (made shots or shots missed that are rebounded by the defense). OR%, as defined above, is something that will probably be changed in future versions of the formula, but stays put this year. A better formula for OR% would be TMOR/(TMOR + OPPDR), where OPPDR is a team's opponents defensive rebounds. I should have used this in the first place, but have done too much this year to replace it until later. My formula for OR% is not too different from this and doesn't make significant differences, but will eventually be replaced.

The rest of the total possessions formula has been explained before. The middle two terms come from the scoring possession formula and the final two terms come from the team's total possession formula (in Introduction to Methods).

Individual floor % is then just a player's scoring possessions divided by his total possessions. This statistic takes all areas of a player's offensive contribution, with the possible exception of his offensive rebounds (they are indirectly counted in the total possession formula). Many times, field goal percentages and free throw percentages are quoted as measures of a player's scoring efficiency. For guards, assist to turnover ratios are often quoted. Individual floor % sums it all up into one meaningful number.

As noted for teams, the league average floor % is around .540. This is true for all players as a group, but that average varies for positions. Most notably, point guards have an average floor % close to .570. This makes sense when you think about it, though. Most coaches want the ball in the hands of their point guard because point guards are usually the most efficient players at finding the best way to score. Point guards generally bring the ball up because they're the best ball handlers and because they will pass to the open man or to the team's top shooter. On teams like Boston that don't have a dominant point guard, the team's best combination ball handler and scorer (Larry Bird, Dennis Johnson, and Danny Ainge) will bring the ball up or players will share the duty.

Another important part of the formulas is that they involve a player's team's statistics. It has always been my belief that the most accurate measurements of a player's effects are measurements that involve his team's numbers as well as his own. It is impossible to completely separate a team's effects on its players from its players' individual stats; these formulas show some of those effects. I have toyed with the idea of trying to maneuver the stats so that all player's can be shown in the context of an average offense (using league average team stats), but that hasn't been done yet. It may become a valuable procedure, but it is going to take some thought and probably won't be very simple.

We can use these formulas for a 'points created' formula because, in the NBA, the scoring possessions calculated average about 1.96 points and don't vary widely from player to player. By far the most common score is a two point basket. One point on a scoring possession, when only one free throw is made, is not uncommon. Three point plays and three pointers are only somewhat less common than one point scoring possessions. A player's scoring possessions can thus be multiplied by 1.96 (or 2.0 or whatever is close and convenient) to get an approximation of his points created. This, I've found, can be 'unfair' to three point specialists because many of their scoring possessions are of the three point variety. There are ways to correct this, perhaps by using adjusted field goal percentages in some way in the above formulas or by adding points to players who make a lot of three pointers and subtracting points from players who don't make three pointers and have poor free throw percentages.

I'm very excited about individual floor % and what it can possibly do. It often points out who should and should not be controlling the ball in an offense. It shows why offenses built around Terry Cummings or Karl Malone aren't very efficient; offenses with an inefficient player using many of the team's possessions cannot be that good. In studies where we might like to find out the effects of replacing one player with another, we can just replace scoring possessions and possessions instead of estimating field goal and free throw percentages. Individual floor % has shown how much free throws play a part in a player's scoring efficiency (See Chambers/Johnson comment in Small Forwards ratings). I'm sure that the uses of individual floor % will become very numerous as research continues on how to improve the offensive efficiency in the NBA.


Basketball Hoopla, 1988, L. Dean Oliver