FT Frequency Revised – Or Why Four Factors Should Be Six Factors

FT frequency is one of the Four Factors, the basketball analysis framework developed by Dean Oliver. The equation he uses is:

  • FT frequency = FTM / FGA

However, there are severe problems with the equation – in fact so severe that the FT factor should be split into two.

One of the problems with Oliver’s equation is that negative occurrences may cause FT frequency to rise. I.e. if the shooter misses a FG shot where he gets fouled it affects the FT frequency more positively than if he gets fouled and makes the shot. That is because a missed foul FG shot will not add to the number of FG attempts, as a made foul FG shot does, and because a missed foul FG shot provides the offense with two FTA, whereas a made foul FGS will only provide one.

Example: Say you have made one 2-point FG shot where there has been no foul. Then you take a second one, and this time there is a foul. If you make the FG shot, you earn a bonus FT. Make it, and the equation becomes:

  • FT Frequency = 1 / 2 = 0.5

Should you instead miss your second FG shot and make one of the subsequent FT attempts, the equation is:

  • FT frequency = 1 / 1 = 1.0.

So, now the FT frequency is higher even though your FT% is lower and even though you have drawn the same number of fouls as in the previous case.

The other problem with Oliver’s FT frequency equation is practical. A team’s FT frequency will not tell how they have done regarding the two basic aspects of free throws: earning FTA and making them. Hence they must have separate indicators.

This is hardly surprising since in 2007 Kubatko, Oliver, Pelton and Rosenbaum wrote: “This would imply Five Factors, but this one term [FT frequency] tends to capture the most important elements of both.” As shown above, their second claim was incorrect.

To measure a team’s ability to hit FT’s there is no better tool than FT%.

To measure a team’s ability to earn FT’s I suggest this equation:

  • FT frequency = FT Sets / Plays

As shown above, neither FTA nor FTM should be the dividend since getting fouled and missing the FG shot would lead to more FTA and FTM than getting fouled and making the FG shot. I.e. a less positive outcome would have a more positive effect on the FT frequency.

So, the only options left for the dividend are the number of number defensive fouls or the number of FT sets. The context here is Four Factors where the independent variables cover endings of plays. Since a defensive foul will not necessarily be the ending of play but a FT set will be, it makes sense to choose the number of FT sets as the dividend. Also, FT sets are more directly linked to FT frequency than the total number of defensive fouls is. In a previous blog I already turned Four Factors into Five Factors.

This splitting the FT frequency into two factors turns Five Factors into Six Factors. And this is where it ends. Hence the Four Factors turned into Six Factors are:

  1. Clean effective field goal percentage
  2. Foul effective field goal percentage
  3. Turnover percentage
  4. Offensive rebounding percentage
  5. Free throw frequency
  6. Free throw percentage

Five Factors – or Improving the Validity of Four Factors

Four Factors, developed by Dean Oliver, is a widespread concept in basketball performance analysis. Yet there is a serious flaw in it: it uses eFG% to measure the efficiency of field goal shooting. This is an invalid procedure, as shown here.

What then would be a valid indicator for the efficiency of field goal shooting within the framework of Four Factors?

Actually, two indicators are needed: eFG% of FG shots where the shooter is not fouled in the act of shooting (clean eFG%) and eFG% of FGS shots where the shooter is fouled in the act of shooting (foul eFGS%). This is the most useful way of including all FG shots  in the analysis – even those shots where the shooter is fouled and misses the shot.

The equations are:

  •                       Clean eFG% = (Clean FG + .5 x Clean 3P) / Clean FG shots
  •                       Foul eFG% = (Foul FG + .5 x Foul 3P) / Foul FG shots

Adding to the number of variables adds to the complexity of the analysis. However, the practical value of the analysis is also improved since now getting to the free throw line and hitting FG shots are measured as separate issues. At this point Four Factors have turned into Five Factors:

  1. Clean effective field goal percentage
  2. Foul effective field goal percentage
  3. Turnovers per possession
  4. Offensive rebounding percentage
  5. Free throw frequency

However, Five Factors will eventually become Six Factors, since there is a practical and theoretical problem with the factor of free throw frequency.

Blog: You Ain’t Seen Nothing Yet in Basketball

Last summer, Team USA won the FIBA world championship easily. Not one team could actually compete with them. What was that about?

To me the main teaching was that basketball is an underdeveloped sport – a work very much in progress.

That is because Team USA overwhelmed everyone with their combination of athletism and sufficient amount of technical skill. In other words, no opponent was physically capable of putting them in a position where any advanced tactical skills would have been required.

The fact that that type of one-dimensional dominance was enough to win a world championship, showed that the sport itself is underdeveloped. In more fully developed sports – say, European or American football – a combination of high-class tactical, technical, and physical capabilities is needed in order to be the best in the world.

Okay, maybe the FIBA World Cup is a bad example? Maybe it’s rather the NBA champions San Antonio Spurs that have it all: techniques, tactics, athletism?

Much has been made of the Spurs’ collectivistic team play. And yes, relatively speaking they do play collectivistically – in other words, collectivistically for an NBA team.

That is because in that league, the individualistic line of thinking is the default setting. When NBA star players work towards the common good – i.e. do the job of a basketball player – they are thought to nobly sacrifice their game.

In European high-level basketball, it is rather collectivism that is the default setting. Compared to the top European teams, the Spurs’ tactical competence nothing to cheer about. Just consider what happened in their preseason loss to Alba Berlin.

What does all this mean regarding future, then? That when it comes to basketball, you ain’t seen nothing yet. There is plenty of room for improvement. First, a combination of high-class techniques, tactics and athletism must be reached. Only after that, we can really go to work.

Blog: Much of Basketball Performance Analysis Is Invalid Because eFG% Is an Invalid Metric for Measuring the Efficiency of FG Shooting

Whenever you see basketball performance analysis where eFG% is used as the metric to measure the efficiency of FG shooting, you immediately know that the whole analysis is invalid.

Since eFG% is widely used, much of the current basketball performance analysis is invalid.

Nothing helps: not the huge amount of the data, not the sophistication of the analysis methods, not the great looks of the graphics. In a way, they only make matters worse sonce they help hide the invalidity of the underlying assumptions.

The invalidity of eFG% is due to an obvious yet ignored fact: eFG% does not consider all FG shots. The equation of eFG% is:

eFG% = (FGM + 0.5 x 3PM) / FGA

The problems is that not all FG shots count as FGA. If the shooter gets fouled in the act of shooting and misses the shot, that FG shot is not considered an FGA in the statistics.

Consequently, eFG% does not measure the efficiency of all FG shots but the sample is systematically biased. This makes all performance analysis, where eFG% involved, invalid when it comes measuring the efficiency of FG shooting.

Despite this obvious bias, eFG% continues to be widely used. Why? Probably because it is easily derived from the basic box score stats.

Thus implementing eFG% requires no extra work. Rather than ponder the validity the underlying assumptions, analysts concentrate on putting together new formulas or new graphics.

For glossary of terms, see Basketball Reference.

Blog: Theory and Practice in Children’s Sports

During the past couple of years I have been reading some scientific literature on children’s sports but also following the phenomenon as a parent. The following remarks are some of my observations on the clash between the two worlds, theory and practice.

1) The lure of early specialization and early selection is strong.

Benefits of sampling – doing multiple sports as a kid – have been well shown but the problem is that the greatest benefits become apparent only years later. And the same goes for late selection.

Yet what helps children succeed asap is early specialization, and what helps the children’s team win asap is early selection. That’s obvious to all stakeholders. That is also why early specialization is still often encouraged and why early selection is still a normal procedure.

Also, children’s coaches are often inexperienced. Hence they do not have the first-hand experience of long-term benefits of sampling and late specialization.

2) Games and competitions enhance learning

To fully enjoy the benefits of sampling, a kid should not only practice multiple sports but also compete in them. Meaning, take part in “official” competitions and games.

First, competing is an exciting and memorable activity in itself.

Secondly, the incomparable excitement and purposefulness of competing enhances learning. The games and competitions are learning opportunities as such, but kids also practice more intensely when they know that they are going to compete.

Think about it this way. In an off-season practice, children’s ice hockey team may play soccer to add variety to the training. Is it effective? Or would it be more effective if the children practiced with an actual soccer team in a different social set-up under a real enthusiastic soccer coach to prepare for real exciting games played real uniforms?

3) Changes in weather enhance learning

When it comes to motor learning variability is good, generally speaking. One of the inherent advantages that outdoor sports have over indoor sports is that outdoors, practice conditions inevitably change from practice to practice, often during a single practice. This provides the athletes and coaches an automatic form of contextual interference. Conversely in indoor sports, practice conditions remain more or less the same all through the season.

4) Motor skill teaching is still done old school

Recently, research has changed a lot of assumption about motor learning. Now coaches should consider e.g. external focus of attention, self-controlled practice, random practice, implicit learning and practicing first with the non-dominant limb.

Breakthroughs in research have not yet caused a revolution in the way children are coached. Mainly it is still internal focus, blocked practice, start with the dominant limb and so on.

Blog: Small Forward 2024 Will Handle the Ball And Pick And Roll And Pop

Say, you coach a 14-year-old boy who’ll grow up to be 6-5 to 6-7. What skills should you help him learn now so that he could develop into a high-performance small forward 10 years?

That’s a simple question, isn’t it? Just look at the characteristics of the present top small forwards, analyze what skills the 14-year-old is lacking, and there you have his curriculum. Right?


Unfortunately complex systems, such as basketball, do not change in a linear fashion. Rather “the future of a complex system is under perpetual creation. What emerges is partially something that is known and partially unknown because of the almost indefinite number of variables influencing what is going on.”

In other words, we have no way of telling what high-performance basketball will be like in 2024. That comes from the fact that “the links between cause and effect are lost because the tiniest overlooked, or unknown, variable can escalate into a major force.” Hence “the long-term future is not simply difficult to see. It is unknowable.”

Because the level of competition keeps rising, we can safely assume that top small forwards in 2024 (SF24) will be better than his counterpart in 2014 (SF14). In other words, SF24 must be able to not only execute the same skills that the SF14 executes but to execute them better.

But because the change will not be linear, there is an even more severe complication: SF24 may also be asked to execute skills that are not even in SF14’s repertoire.

The process of change is ubiquitous. Rod Higgins writes “There used to be a time when point guards would bring the ball upcourt, hand it over to their small forward and get out of the way.” “The point forward tendencies of Dejan Bodiroga and Hedo Turkoglu, among others, kept that proud European tradition alive into the 00’s.”

But “then along came the pick and roll and everything changed.” Now small forwards’ “main mission is to create space with their shooting, take advantage of space with their cuts toward the rim and take away space with their help defense.”

This brings about two answers to the question of what SF24 should be learning now.

One answer is that he should be developing general motor learning skills. Those skills will help him meet the new demands of the ever-evolving game over and over again.

The second answer is that we should construct a scenario of the evolvement of the small forward position and, based on that scenario, assess what sport-specific SF24 will need, in addition to the skills of SF14. Here’s my line of thinking on that:

1) Presently, in pick-and-roll oriented offenses, small forward tends to be an underutilized position. SF14 is usually not directly involved in PNR but he’s primarily a spot-up shooter and a slasher.

2) The small forward’s direct involvement in PNR would add to the variety and unpredictability of the offense. However, most SF14 do not have the necessary relevant skills.

3) To improve the offenses, SF24 will be required to take part in PNR both as the ball handler and as the screener. This will take the number of ball handlers and screeners on the floor from two to three.

4) In the present player development, small forwards should be taught PNR offensive skills: using the pick as the ball handler, setting the screen, popping out, rolling to the basket. PNR-related defensive skills should be taught, too.

Naturally, this line of thinking may be based wrong assumptions and thus misguided: in 10 years, basketball may become less PNR-oriented, or small forwards may continue to stay out of the PNR picture. Even if this is the case, PNR-related practice will not be a complete waste of time for SF24, since most of that practice will serve not only PNR-specific purposes but will also be useful basic basketball-specific practice.

Blog: The Future of Player Development Ain’t What It Used to Be

Developing players is a futuristic project. We need to prepare players to face the challenges of high-performance basketball as it is played in the year of 2020. Or 2025. Even 2030 is only sixteen years away…

At the moment, the game is changing at a furious pace due to e.g. the breakthrough of the performance analytics. Looking back just a few years, it was a wholly different game.

So how should we go about developing future top-performance players when we do not know what the future top-performance basketball will be like?

At least these things should be considered:

1) Variability
The tactics and techniques that the players learn today probably will not serve them until the end of their career. Everything must be varied and modified – during a career and, as a reflection of that, during every practice session. Continuous motor learning is a necessity, and hence motor learning skills should be emphasized in player development.

2) Quickness
Whatever else will happen in the evolution of basketball down the lane, the game will probably become quicker and quicker. Hence players must also become quicker – not just physically but also tactically and technically quicker. We should e.g. critically assess every single technique we teach: Is there a quicker way to do this?

3) Specificity
The higher the level of play, the more important it becomes to realize what a player’s future position will be, what the skill requirements will be at that position, and what he will need to do to excel at the required skills.

There have been arguments that in the future, positions will disappear – that all players will be interchangeable. I don’t think that’s going to happen. Here are some comments on the subject.

The next time around I’ll discuss how these predictions, if taken seriously, should affect training at… let’s say #3 position.