# Analyzing Players and Offenses With Floor Percentage

## 1990

There are many players in the NBA who can score a lot of points, but how many really put fear into opposing defenses? Take Kelly Tripucka and Kevin McHale as examples. Both scored just over 22 ppg in '88-89, but McHale was a considerably more dangerous offensive player. This is evident in their field goal percentages: McHale shot 55% and Tripucka shot only 47%. Now look at two other players, Patrick Ewing and Magic Johnson. Ewing shot 57% and scored 22.7 ppg, while Johnson shot 51% and scored 22.5 ppg. Who's the more dangerous offensive player of these two? In the eyes of the people who know basketball, Johnson was clearly the better of the two offensively last season, winning MVP honors for the second time in his career; this despite the fact that Ewing outscored him and outshot him from the field. If Ewing's scoring stats were better than Johnson's, how is it justified to say that Johnson was a better scorer than Ewing? Did the statistics lie?

Paradoxes like this have scared people away from basketball statistics for years. But now, there need not be any paradox. A method has been developed to explicitly show how effective a scorer is. By defining exactly what it means to score efficiently, the mass of offensive statistics in use now can be collapsed into one piece of information. That piece of information is called a floor percentage.

## Floor Percentage Defined

The entire purpose of an offense is to score as often as possible while making as few mistakes as possible. When a team scores, whether just one point on a free throw, two points on a field goal, or three points any way it can, and the other team takes possession of the ball, then the first team has just had a scoring possession. Any time there is a change of possession, then one total possession is accrued. Floor percentage (floor%) is the ratio of scoring possessions to total possessions. The efficiency of an individual scorer is determined by how often he helps his team score as compared to how often he contributes to the failure of his team to score.

A floor% is just a physical measurement or observation, like a field goal percentage. (It is not a haphazard combination of physically uncombinable stats like the Tendex and Schick Pivotal Player Rating Systems.) When Michael Jordan rebounds an opponent's miss, dribbles upcourt, then goes in for a crashing slam dunk, he has both a field goal percentage and a floor percentage of 100%. (This same situation, however, cannot be represented in any meaningful way by either Tendex or Schick.) If Jordan instead misses the dunk and it is rebounded and put in by his teammate Horace Grant, then Jordan is not responsible for a possession, 0 for 0, and Grant is 1 for 1, 100%, on his possession. By counting individual possessions this way, Chicago's team floor% of 100% is preserved.

An important facet of floor% is how it counts assists. An assist does represent a scoring possession, but it cannot be counted exactly as one. Counting an assist and a field goal each as one scoring possession would sum to two scoring possessions for a team when there is only one. This is remedied by giving fractional credit to both the assistant and the assistee (i.e. - 0.35 scoring possessions for the assistant and 0.65 scoring possessions for the assistee). The amount of credit awarded depends on how easy the shot is, which is represented by a field goal percentage A point guard who makes passes to teammates in good scoring position would get more credit for his assists (and more assists) than a point guard who makes passes to teammates that have difficult shots. (For further explanation of the method, see Box.)

## Ranking Players With Floor Percentage

Let's look at the Magic Johnson-Patrick Ewing comparison made earlier. Most people would agree that Johnson is a better offensive player, but field goal percentage and points per game stats from last year don't reflect that. When all scores and all mistakes are taken into account, though, Johnson's superiority soon becomes evident. Johnson's scores last year came in the form of 579 field goals, 513 free throws, and 988 assists. His mistakes came in the form of 558 missed field goals, 50 missed free throws, and 312 turnovers. Ewing's same numbers were 727, 361, 188, 555, 123, and 266, respectively. Transform all these numbers into possessions and Johnson is shown to have scored on 1064 of 1752 possessions, a floor% of 0.607, and Ewing is shown to have scored on 839 of 1471 possessions, a floor% of 0.570. Johnson was, as now confirmed by the stats, the better offensive player.

Actually, both Johnson and Ewing scored very well last year. Each finished second in floor% at his respective position.

Second! Who's better than Magic and Ewing?

John Stockton and Robert Parish both had better scoring efficiencies than their more famous rivals. Stockton had a floor% of 0.624, scoring on 996 of 1597 possessions. Parish had a floor% of 0.575, scoring on 684 of 1190 possessions. This now raises the question of how best to rank players using this method. Johnson scored less efficiently than Stockton, but he scored 68 more times than Stockton. Ewing scored less efficiently than Parish, but he scored 155 more times than Parish.

There is really no best way to rank scorers. For teams that need a lot of scoring at a position, they might sacrifice a more efficient scorer for one who is aggressive, scores a lot, and draws the defense more, thus freeing up his teammates. For teams that already have good active scorers, they might want a position player who doesn't take many shots, but also doesn't make many mistakes. For example, look through the table of power forwards for A.C. Green and Terry Cummings. Green scored 487 times at 0.572 efficiency for the Los Angeles Lakers. Cummings scored 828 times at 0.518 efficiency for the Milwaukee Bucks. Who was better? It's impossible to say for sure. Both did good jobs filling their roles on successful teams., but performing those same roles on different teams, neither would have looked as good. Put Cummings on the Lakers and they probably would have been a less successful team. Put Green on the Bucks and they, too, probably would have been a less successful team. Cummings propensity to shoot would have taken possessions away from more efficient Laker scorers like James Worthy and Magic Johnson. Green's inability to create his own shots would have allowed defenders to work harder on other Buck scorers like Rickey Pierce and Jack Sikma.

As you can see, there is no perfect way to assess the quality of players. Likewise there is no perfect way to statistically rank them. A general manager that has some good scorers and is looking for a small forward who scores efficiently, but not a lot, may find Rod Higgins attractive. This GM might base his decision of players solely on floor%. A GM that has an anemic offense that just needs someone who isn't afraid to shoot is probably willing to pay for someone like Dominique Wilkins or Alex English. This GM would likely multiply scoring possessions and floor% together (i.e. - Scoring Ability = (scoring possessions) * (floor%)^2) to give him a better idea of what players fit his needs.

No matter how you rank scorers, there are some who will always look best. Michael Jordan is clearly the best shooting guard in the NBA; Clyde Drexler is best of the rest. Magic Johnson, John Stockton, Kevin Johnson, and Mark Price are among the top point guards in the league. Charles Barkley, Karl Malone, and Kevin McHale are the best power forwards. Chris Mullin, James Worthy, and Adrian Dantley are among the best scoring small forwards. Patrick Ewing and Brad Daugherty are two of the best centers.

But special statistics aren't really necessary to show that these are the best players in the league; many people already know that these are great players. In fact, there are better uses for floor percentage.

## The Free Throw Effect

Free throws can make a bad player into a good one, an ordinary player into a very good one, and a good player into a great one. Probably the best example of this is Tom Chambers. Chambers has been a lousy shooter for years now. His field goal percentage of 0.471 last year was his best since '85, and was still worse than league average. The season Chambers won All-Star Game MVP honors, he shot 0.456 from the field. Very few players can shoot that poorly and end up All-Stars. An interesting comparison between Chambers and his teammate Eddie Johnson, using floor percentage methods, shows just how free throws have made Chambers so successful.

In the '87-88 season Johnson outshot Chambers from the field, 48.0% to 44.8%, and from the line, 85.0% to 80.7%. Johnson also had a better assist to turnover ratio, 1.29 to 1.01. So who was the more efficient scorer? Believe it or not, Chambers was the better scorer. Chambers had a floor% of 0.523 and Johnson had a floor% of 0.517. This inconsistency comes about because Chambers went to the free throw line so much more often than Johnson. While Johnson was shooting 48% from the field, Chambers was often shooting 80.7% from the line. Johnson spent most of his time shooting tougher shots (field goals), where Chambers spent a little more of his time shooting easier shots (free throws).

This might be easier to understand by looking at a simple ten possession scenario, ignoring offensive rebounds and assists. With ten possessions, Chambers likely would have done the following: go down the court twice and hit two field goals; go down once to hit a field goal and a free throw for a three point play; go down twice to get fouled for two shots each time, making 3 of 4; and go down five more times to miss field goal attempts. Overall, Chambers would have made 3 of 8 field goals, 37.5%, and 4 of 5 free throws, 80%, converting on 5 of 10 possessions for 10 points. With ten possessions, Johnson likely would have done things a little differently: go down the court four times and hit four field goals; go down once to get fouled for two shots, making both; and go down five more times to miss field goal attempts. Overall, Johnson would have made 4 of 9 field goals, 44.4%, and 2 of 2 free throws, 100%, converting on 5 of 10 possessions for 10 points. In a ten possession scenario, Johnson would likely have had a better field goal and free throw percentage, but he and Chambers would have produced just about the same thing.

Free throws do make a big difference in the NBA. Chambers is not the only one who has made a living shooting free throws. Adrian Dantley, Michael Jordan, Magic Johnson, Karl Malone, Moses Malone, and Charles Barkley all make a killing at the line. Denver's unheralded Danny Schayes and Miami's Grant Long have starting jobs because they shoot so many free throws.

Finally, take a look at Chicago's Bill Cartwright, who took a lot of criticism last year for his uninspired play. One of the biggest complaints was that he wasn't shooting as many free throws as he had in the past. As a quick exercise, I checked the effect on the Bulls' team if Cartwright had gone to the free throw line as often as he had the year before. As a rough estimate, it looks like Chicago would have had about 50 more scoring possessions last year, which is equivalent to about 100 more points, which is equivalent to 3 or 4 more victories. That's the difference free throws make.

## Designing an Offense

Some offenses are built around one player. Some are built around the styles of more than one player. Some offenses rely on the fast break, while some can set up in the half court and take their time scoring. Some offenses have one player distributing the ball to all the others, while some offenses are built on the premise that all players should pass and shoot equally well. Some offenses incorporate the three point shot into the offense, while others ignore it unless it's necessary. Some offenses are reliant on the starters while others heavily involve bench players.

How exactly should an offense be structured to work most efficiently? Is a dominant point guard necessary to run an efficient offense? Is a dominant scoring center necessary? Is a dominant rebounder necessary? If so, is it better if that rebounder is a center or if he's a power forward? Are three point specialists necessary? Is a fast pace or a slow pace conducive to good offense?

These are tough questions, questions without definite answers. Every year, NBA coaches try to find the right answers, but they often end up finding many wrong ones. Sometimes, though, a team shows up that runs so smoothly that no one can stop them. It's those teams - teams like the '81-82 Denver Nuggets that hold the record for most points in a season, or the '84-85 Los Angeles Lakers that hold the record for best field goal percentage, or the '87-88 Boston Celtics that hold the record for best three point shooting - that help provide some clues to building a good offense.

All these great offensive teams had very little in common except for the fact that they all had at least four starters who scored very well (with floor%'s over 0.550). Some teams had good scorers across the front line and at one guard; some teams had good scorers at two guards, a center, and a forward; and some teams had good scorers everywhere but center. It didn't seem to matter what positions good scorers play, only that there were four of them who got a lot of playing time, especially in starting roles.

Even the age-old theory about needing a good center to be successful in the league appears to be only a myth. Looking at just last year's results shows this clearly. Detroit won the NBA title with Bill Laimbeer, a decent scoring center, but one who didn't play the low post offense of a traditional center. The best offensive team in the league last year, the Lakers, played with Kareem Abdul-Jabaar, a mediocre center, at best, in his final season; the Lakers, in actuality, played around Abdul-Jabaar nearly as much as they played with him. The Phoenix Suns led the league in scoring and scored on 55% of their possessions, doing it all without an established center. All three of these teams had poor low post games, but they all had at least four players at other positions playing regularly and scoring with a floor% of at least 0.538.

Other trends showed up when looking at some of the best offensive teams in history. For example, teams that ran a lot tended to be better offensively. There were exceptions, of course, particularly noting the '87-88 Celtics, whose offense was one of slow death from the low post play of Parish and McHale or from the outside shooting of Bird and Ainge.

## Conclusions

Individual floor percentage is a statistic derived from a model of the game of basketball and some of the commonly collected statistics in basketball. It serves to appropriately weigh the various offensive contributions of various players, from field goal percentage to free throw percentage to assists and turnovers. It can be used to rank players' offenses, but it doesn't suggest anything about their defenses. Because individual floor percentage is based upon a model of basketball (based upon a scoring system not outlined here), it accounts for how efficient players are at scoring, accounting for players who score efficiently by going to the line a lot. This demonstrates how a player with a lower field goal percentage, lower free throw percentage, and worse assist-to-turnover ratio than another player can actually score more efficiently, a seemingly paradoxical effect. Finally, we showed how individual floor percentage relates to the design of good offenses. Namely, if you can put together a team with three or four players who can score efficiently, the team will score efficiently.