TENDEX for TEAMS and PLAYERS

Published in 1997 in the basketball guide: 10+1 years of A1, parts also were included in an article published in weekly magazine TRIPONTO (29/3/1994, no 281) and the 1993-94 Greek Championship Guide.

1. Introduction

Many people doubt its validity, everyone involved in basketball is familiar with it, all coaches take a quick look at its results, but tendex has something, which cannot be denied by the scientists. It is based on the alternation of ball possession, a basic rule of the game and rewards scoring, which after all, is very important for a team to win a game.

In this study we will attempt to clarify some concepts related to tendex, such as strength difference between teams, pace of the game, attacks, shots, shooting accuracy, and we will realize, that we can securely rely on the results we take back from it. Let’s always keep in mind that for the last 13 years, where official stats are kept in first (A1) basketball division, in 96% of the games the winning team appears to have better tendex rate than the loser.

Finally, we will refer to line up performance, which, however, is the subject of another study of ours, to be found in www.galanissportsdata.com/mainsite/lineup.htm, based, though, in this present text, and can be used by coaches during the game in order to test the correctness of a player substitution.

2. Ball Possession Mechanism

A player, holding the ball, organizes the attack of his team, which may end up in three ways:
a. goal b. missed shot c. error
where a foul by the defenders should lead to one of the above possibilities.
As the ball belongs either to one team or the other, we can write without going into details at this stage:
Ball Possessions of Team A = Ball Possessions of Team B
where this equation is going to be analyzed and rewritten properly in paragraphs (6) and (7).
The start of each attack originates from two different reasons:
a. the team got hold of the ball by default, or
b. won the ball from the opponent after a fight

For example, if a team concedes a basket or the opponent violates the rules, we then talk about the first case. If possession of ball comes from a defensive / offensive rebound or steal then we have the second case.

Let us allocate a value of one point for the possession of the ball. In case the ball is lost, then this point moves from one team to the other. Therefore possession of the ball is either 1 or 0. In other words the ball belongs to one team only, either to team A or to team B.

A simple example may clarify this mechanism. Team A has ball possession (+1). A player shoots, thus possession becomes zero, since the ball does not belong to him, and the ball misses the target. If a player of the same team regains the ball then possession becomes +1 again, if not, possession remains zero for this team and becomes +1 for the opponents.

3. TENDEX POINTS and Possession Points

This plus / minus one point mechanism, which governs all actions during a basketball game is obviously clear for one attack. What happens if we sum up all attacks of one team?

We are going to take into account all parameters involved in this mechanism. Thus, we need to know, which actions give possession to the opponents and which contribute to scoring.

In other words we need to know, which are the positive and which are the negative actions.

Over the years basketball experts decided that positive actions are 1p-2p-3p goals, rebounds, assists, blocks and steals, whereas negative actions are turnovers (errors) and missed shots. Turnover is a general term, which includes all rule violations, and loss of ball possession is involved. For example a foul is not a turnover, if the ball belongs to the opponents, but it is a turnover, if it is an offensive one, as the ball belongs to the attacking team and it is lost.

However, not all positive parameters belong to this mechanism. Assists for example speed up an attack, but are not involved in a +/- change of ball possession. Of course, they are something better than simple passes, which are not taken into account anyway. The same applies to blocks, which distract shots, but in order to match the number of missed shots, we need to accompany them by a rebound, defensive or offensive, depending upon the player who gets hold of the ball after the block. In this sense the blocking hand is considered as the backboard.

Having all these in mind we can look at the expression, which includes all positive and negative actions. This sum is the sum of all positive and negative Possession Points, which are called Tendex Points, and denoted by TP, thus:

TP = Points - Missed Free Throws - Missed Field Shots + Rebounds + Assists + Steals + Blocks - Turnovers

Looking at this equation we will notice that missed shots are divided in two parts, field shots and free throws. Apart from this, instead of having total number of goals, we see points, which means that 2p and 3p goals are counted as 2 and 3 tendex points respectively.

Well, this is because we define tendex points in such a way, that we include scoring as well.
We thus can conclude saying:

when a team has the ball, possession (=1) cannot be increased, but its Tendex Points can (after a goal) when a team does not have the ball, both possession (=0) and Tendex Points can increase (after a defensive rebound, steal, opponent turnover).

It will be very helpful to clarify, why the above Tendex Points definition separates free throws from field shots.

It is obvious that free throws are different, as they do not belong to field play, but the last of them, if missed, allows a rebound to be claimed, therefore acts as a missed field shot. Many people add one half of free throws to field shots in order to count all shots. It is obvious that this is an estimation of the true number. Anyway, in the next paragraph we are going to see that we are going to distinguish first and last free throws, in order to make our lives easier.

Finally, note that the term shots is not used in the tendex points definition. Missed Shots, however, are, but we need to understand that shots are included in score, as for each goal scored, independently if it is 1p, 2p, or 3p there is a successful shot involved.

4. Three Boxes of TENDEX POINTS

The Tendex Points equation consists of a sum of eight parameters, which can be divided into three groups: the SCORE group, the BONUS group and the POSSESSION group.

Before we express these groups mathematically let’s separate Missed Free Throws into two kinds: the first ones, i.e. those, which cannot be claimed by a rebound and the last ones, i.e. those, which can. The latter ones are similar to Missed Field Shots and we could include them in this group, but we are going to keep them separately, thus:

SCORE = Points
BONUS = Assists + Blocks - First Missed Free Throws
POSSESSION = Rebounds + Steals – Last Missed Free Throws – Missed Field Shots – Turnovers

We should think of these groups as being piggy banks, moneyboxes or tendex point boxes, where after each action we insert points to the appropriate slot.
Let’s rewrite the above equation as follows:

TP = SCORE + BONUS + POSSESSION

When a team scores, the first group is affected. In case of an assist, a block or a first missed free throw, the BONUS group is affected and according all we explained in paragraph (3), we can understand, that the contents of this group do not have anything to do with the +/– change of possession mechanism.

The last group is POSSESSION. In reality it reflects the change of possession in the game except for the moment of scoring, where we have a change of ball possession by default.

If we want to be more precise, we should arrange things as follows. In case of a goal, one point has to be taken out from the POSSESSION group, as the ball is given to opponents, but we need to understand that TENDEX rewards positive and punishes negative actions.

Actually, the total number of ball possessions will be expressed mathematically later, in paragraph (7) and we should not confuse them with the term POSSESSION of this paragraph. An attempt to express ball possessions as:

POSSESSION – [ Successful Shots – First Successful Free Throws ] of opposite Team

where this extra summand in brackets expresses the default possessions due to goals, is not correct, as, for example, opponent turnovers (those not matched to steals) are missing.

Closing this paragraph, we can say a few words about ball possessions. According to our experience the average possessions of a team during a game is very close to its total number of points. That means that teams translate each possession to 1 or 1.2 points. In other words, the total number of ball possessions varies between 60 and 90 per team for scores of 60 to 110 points.

Ideally, of course, each possession should result in a 2p or 3p goal, thus the above number should be larger than 2. As said, though, it is half of it, meaning that teams achieve only 50% of what they could do, a percentage met in many popular team sports.

At this point, it is necessary to clarify that we try continuously to keep statistics in such a way that the +/– mechanism is not violated. Thus, air balls for example are taken into account, as they are followed by an offensive rebound, an opponent team defensive rebound, a turnover or they are simply considered as missed shots, depending upon the judgment of the statisticians, similarly to what we commented in the previous paragraph for blocks.

5. Pace of the Game and Strength Difference

We watch a game, where we realize that many baskets are scored for both sides and automatically say that the game is fast. In the case of both teams being close in score, we can say that we watch two equally strong teams, whereas in the opposite case we say that the strength difference is big. Therefore we can simply say:

The sum of both teams’ scores displays the pace of the game
The difference displays the difference in strength between teams

Certainly, by pace we mean scoring frequency, since the duration of the game is constant. We will see how all these are related to tendex and how can tendex help, so that we get a picture of team performance during the game. Before we proceed, let’s recall the expression, which is used for the computation of tendex:

Points - Missed Free Throws - Missed Field Shots + Rebounds + Assists + Steals + Blocks – Turnovers / Time Played

which is similar to the equation given in paragraph (3), except for the fact that Tendex Points are divided by Time Played of a player or a team.

This mathematical expression defines actually NINEDEX, not TENDEX, since it takes into consideration all nine parameters shown above. In reality the origin of the name of the terms NINEDEX and TENDEX is NINE INDICES (9 times index) and TEN INDICES (10 times index) respectively, having nothing to do with TENDENCY etc. Prior to these terms, we have seen indices with names such as FIVEDEX, SIXDEX etc.

If we look carefully at the formula, we realize, that it takes into account only one team or player. Thus, the inclusion of the opponent’s data is the TENTH element. How do we do this?

We simply calculate the sum: NINEDEX of TEAM A + NINEDEX of TEAM B and then we divide our expression by this sum:

TENDEX = NINEDEX / ( NINEDEX of TEAM A + NINEDEX of TEAM B )

In order to make things simpler, lets ignore rebounds, assists etc. and look only at the points of a player of Team A. Let’s assume that the score of the game is 60-70, i.e. team A scored 60 and team B 70 points and a player 25 points. These 25p should be divided by the sum of 60+70=130 to define his contribution to the game and not only to his team.

It is obvious, that if we do not examine a whole tournament, but only one game, and we follow this procedure for all players of both teams we can drop this division to their performance, as the denominator is common for all of them. In this case we can work with NINEDEX, as if it were TENDEX without committing any mistakes at all.

So, why is the tenth element important? Imagine we compare two games: a fast (100- 120) and a slow (70-60). If a player scores 25p in the first and another player 25p in the second, who do you believe is the better one? But of course the guy of the slower game, because he had less attacks to take advantage of (!). Let’s compare 25/(100+120)=0.104 and 25/(70+60)=1.923. The slower game guy has better ratio (1.923) than the fast (0.104).

Finally, if we compare the performance of teams and not players we can even drop TIME, the ninth parameter, and work safely with EIGHTDEX, since time is definitely common for both teams (i.e. 200 minutes = 5 players x 40 minutes for a game without overtime).

6. Ball Possession, Attacks and Shots

Is chess similar to basketball? In chess we have a player moving a piece and waiting for the reply of his opponent. In basketball, each move is similar to a ball possession. Therefore one team attacks and independently of the outcome, the opponents reply with their attack.

Every move in chess has an evaluation. It may be good or bad, it may even be decisive for the game. Similarly, in basketball each ball possession is translated into a goal, a missed shot or an error. Even if it is a goal it may have a value of 1p, 2p 3p or even more. The only difference is that, checkmate, is signaled by the game clock showing 00:00.

It is certain that in chess the number of moves of a player is equal to the number of moves of his opponent, taking into account that white pieces play first. In basketball this advantage of the first move belongs to the winner of the jump ball.

A ball possession is defined as the uninterrupted possession of the ball, even if a missed shot intervenes, but the ball is regained by means of an offensive rebound, therefore:

Ball Possessions of Team A = Ball Possessions of Team B ( ±1 per quarter )

but, naturally, one has to be careful because the starting jump ball, like white chess pieces, may lead to an advantage of one more move / ball possession.

Since this is clear we can see that the only difference between ball possessions and attacks is the number of offensive rebounds for each team, so:

Attacks = Ball Possessions + Offensive Rebounds

Attacks end either with a shot or a turnover, therefore we can write:

Shots – First Free Throws = Field Shots + Last Free Throws = Attacks – Turnovers

which fully agrees to what we mentioned in paragraph (1), i.e. an attack leads to a goal, a missed shot or an error.

Note, that shots include both field shots and free throws, thus we need to add last free throws or equivalently subtract the first free throws from them, as they can be claimed by a rebound if missed.

Mathematics are sometimes hard to understand and lead us to wrong conclusions, especially if we draw them when using percentages. For this, let’s give an example, which will help us understand both the meanings of attacks and shots and conclusions associated to them.

Imagine team A has the ball and shoots ten times and gets nine offensive rebounds, but succeeds in their tenth shot. First of all we talk about ONE ball possession, as the ball during all these attacks belongs to them, but we also talk about 10 attacks, even if the nine out of then are simply renewing the preceding one.

Their shooting percentage will appear to be very poor (1/10=10%), but according to what we said before, they are going to have one goal per one possession.

After the conceded basket, team B takes the ball and succeeds in scoring. Their shooting percentage is very good (1/1=100%), but they have also one goal per one possession (!).

Thus, percentages are sometimes misleading, and he who looks at the numbers without being experienced may end up with funny questions, like:

how is it possible to have better shooting percentages and yet lose the game?

7. The Basic Equations

This is the moment to formulate the equations, which are the basis of tendex points analysis all of them based in the ball possession equality of the previous paragraph.

According to the mechanism described previously in parallel to the example of the previous paragraph, we can express ball possession for both teams mathematically:

Ball Possessions of Team A = [Shots – First Free Throws – Offensive Rebounds +Turnovers] of A
Ball Possessions of Team B = [Shots – First Free Throws – Offensive Rebounds +Turnovers] of B

It is useful to note that we define Ball Possessions in terms of parameters of the same team exclusively. This is not always the case as every time we can use both teams to define a parameter. Many of the parameters included in the Tendex Points equation of paragraph (3), are linked to both teams. For example a missed shot of a team is connected to a defensive rebound of the other. The same applies to a steal and a turnover, a successful shot and a goal etc. Thus, one can always rewrite any equation according to the purpose of his research.

We can now rewrite the ball possession equality of paragraph (6) as basic equation no 1:

[Shots–First FT+Turnovers–Off.Rebounds] A = [Shots–First FT+Turnovers–Off.Rebounds] B                      (1)

Similarly, we can write basic equations no 2, if we look at the basket of each team, thus:

[ Missed Field Shots + Missed Last FT ] of Team A = Def. Rebounds of B + Off. Rebounds of A                      (2)
[ Missed Field Shots + Missed Last FT ] of Team B = Def. Rebounds of A + Off. Rebounds of B

Both equations added and subtracted give as a third set:

[ Missed Field Shots + Missed Last FT ] [ A + B ] = Rebounds [ A + B ]                                                                    (3)
[ Missed Field Shots + Missed Last FT ] [ A – B ] = Off. Rebounds [ A – B ] – Def. Rebounds [ A – B ]

This last equation shows clearly what described in the example of the previous paragraph, i.e.:

offensive rebounds allow the improvement of shooting accuracy of a team
in terms of both: goals per possessions and goals per shots

Players, therefore, who are capable of getting offensive rebounds, keep their teams’ attacks alive. The same applies to players who steal the ball, and charge opponents with turnovers.

in both cases these players do not increase the number of possessions of their team, as these remain the same, but they increase the number shooting and scoring chances

We can now count the number of attacks of a team according to what we said above:

Attacks = Shots – First Free Throws + Turnovers = Ball Possessions + Offensive Rebounds

Of course we can count the number of attacks by examining the moments of their start, i.e. the conceded goals, the defensive rebounds and the turnovers of the opponent:

Def. Rebounds A + Successful Shots B – First Free Throws B + Turnovers B =

                                                                                            Def. Rebounds B + Successful Shots A – First Free Throws A + Turnovers A

in which, replacing Defensive Rebounds from equations (2) we obtain the same result as (1):

Missed F.Shots B + Missed Last FT B + Successful Shots B – First Free Throws B + Turnovers B – Off. Rebounds B =
                    Missed F.Shots A + Missed Last FT A + Successful Shots A – First Free Throws A + Turnovers A – Off. Rebounds A

8. Turnover without Ball Possession

A steal of a player corresponds to a turnover of a player of the opposite team, but this is not the only case where a turnover is counted. There are a number of rule violations, like: out of bounds situation, fumbling of the ball, traveling, 3 seconds, 8 seconds, 24 seconds etc.

In these cases the ball is given to the opponents, although no steal is involved, therefore:

Turnovers A = Steals B + Rule Violations A and Turnovers B = Steals A+ Rule Violations B

Except from these cases a statistician has to consider a TECHNICAL FOUL, even originating from the bench or the coach, as a turnover, as it gives the ball to the opponent and in case the ball belongs to the team which commits the technical foul then we need to add an extra turnover, in order to match the number of possessions.

However there is a very fishy, hidden turnover, not mentioned previously, which requires special attention. Imagine a player attempting a 2p or 3p shot, which succeeds, but at the same time is fouled by a defender. What happens then? Instead of the ball going to the team which conceded the goal, remains in the hands of the scorer for an extra free throw.

So, there is the interference of an extra turnover performed by the defender, who has no ball possession. It looks peculiar, but we have to charge the defender with a turnover without possession, as he offers the ball to his opponents and violates the possessions equality of paragraph (6). In our stats page, we keep this parameter separately, in order to help coaches understand the difference.

9. Game Pace = Sum of TENDEX POINTS of both teams

We referred to Game Pace in paragraph (5) and we connected it to the number of attacks, or not anyway equivalently, to the sum of both scores.

Let us denote with TP(A) and TP(B) the Tendex Points of teams A and B respectively, thus:

TP(A) = Points - Missed Free Throws - Missed Field Shots + Rebounds + Assists + Steals + Blocks - Turnovers
TP(B) = Points - Missed Free Throws - Missed Field Shots + Rebounds + Assists + Steals + Blocks - Turnovers

Remember, that examining Tendex Points of teams is equivalent to examining Tendex of teams, as time is common for both (200 minutes for example). Anyway, the sum results in:

TP(A)+TP(B)= Total Points – Total Missed Free Throws – Total Missed Field Shots + Total Rebounds

                                                                     + Total Assists + Total Blocks + Total Steals – Total Turnovers

Taking basic equations (2) of paragraph (7) and equations of paragraph (8) we obtain:

TP(A) + TP(B)= Total (Points – Missed First Free Throws – Rule Violations + Assists + Blocks)

This equation reveals that Game Pace is dependent upon the sum of Tendex Points as:

The bigger the sum of total points (score) the bigger the sum of Tendex Points

Finally, we need to underline that in paragraph (5) we gave the examples of a slow and a fast game. It is obvious that a game, where many baskets are scored is a fast game. It is not obvious, though, that a game where score is low is a slow game. It may be a fast one, but between teams with many missed shots. This information though, is missing, as missed shots are eliminated by rebounds.

10. Strength Difference = Difference of TENDEX POINTS

We will follow a similar procedure in order to examine the difference of Tendex Points, thus:

TP(A) – TP(B) = Points [A–B] + Rebounds [A–B] + Assists [A–B] + Blocks [A–B]

                                                        + Steals [A–B] – Turnovers [A–B] – Missed FT [A–B] – Missed Field Shots [A–B]

Since rebounds = offensive rebounds + defensive rebounds:

TP(A) – TP(B) = Points [A–B] + Offensive Rebounds [A–B] + Defensive Rebounds [A–B] + Assists [A–B]

                                                        + Blocks [A–B] + Steals [A–B] – Turnovers [A–B] – Missed FT [A–B] – Missed Field Shots [A–B]

Replacing defensive rebounds by using the second of basic equations (3) of paragraph (7):

TP(A) – TP(B) = Points [A–B] + Assists [A–B] + Blocks [A–B] + Steals [A–B] – Turnovers [A–B]

                                    + 2 * Offensive Rebounds [A–B] – 2 * Missed Field Shots [A–B] – Missed FT [A–B] – Missed Last FT [A–B]

and taking into account turnover equations of paragraph (8):

TP(A) – TP(B) = Points [A–B] + Assists [A–B] + Blocks [A–B] + Rule Violations [A–B] – 2 * Turnovers [A–B]

                                              + 2 * Off. Rebounds [A–B]  – 2 * Missed Field Shots [A–B] – Missed FT [A–B] – Missed Last FT [A–B]

With the help of basic equation (1), we replace turnovers and offensive rebounds, thus:

TP(A) – TP(B) = Points [A–B] + Assists [A–B] + Blocks [A–B] + Rule Violations [A–B]

        + 2 * Shots [A–B] – 2 * First Free Throws [A–B] – 2 * Missed Field Shots [A–B] – Missed FT [A–B] – Missed Last FT [A–B]

Let us add and subtract missed free throws and replace shots – missed shots with successful shots and missed free throws – missed last free throws with missed first free throws, so:

TP(A) – TP(B) = Points [A–B] + Assists [A–B] + Blocks [A–B] + Rule Violations [A–B]

                                                        + 2 * Successful Field Shots [A–B] – Missed First Free Throws [A–B]

This is a very strange equation showing that Difference of Tendex Points consists of three parts: the points (score) difference, the assist / block part and the part which contains rule violations, free throws and twice (!) the successful field shots.

First of all, let us give ant interpretation of TWICE: If I have a coin and you have also a coin, the difference is zero. Now, if I take the coin from you, then I have two coins and you have nothing, thus the difference becomes 2.

Exactly the same happens if a team attacks and shoots and the opponent does exactly the same, resulting in a zero difference between shots. If, however, team A attacks and shoots and team B, when trying to reply, miss the ball instead of shooting, then, all of the sudden team A attacks for the second time.

In this sense, every turnover from a team allows the creation of a gap of two goals or shots, and that is what above equation tells us. This is the consequence of ball possession equality, which states that the ball belongs to you or to me.

The Tendex Points difference equation requires a little bit of analysis. As said in previous paragraphs: assists and blocks are not part of the ±1 possession mechanism. These parameters though are included in order to reward players for there efforts.

There is a possibility, that losers have more assists than winners, and in case score is close, winners appear to have worst tendex ratio than losers. The same applies to blocks or to the combination of both.

Let us now concentrate on the Rule Violations difference. We know that a steal corresponds to an opponent’s turnover, but not vice versa. Each extra turnover because of violations of the rules allows the opponent to start an attack, which may end up in a shot. Therefore rule violations cannot be treated like assists or blocks, which do not belong to the possessions mechanism, but in an extreme case, can be considered as opponent’s shots.

As the above equation is complicated, depending upon many parameters, we are going to look at different possibilities, separately. Assume that assists, blocks and rule violations are equal for both teams, therefore all above differences are zero. Thus, the difference between TP(A) – TP(B) and Points [A–B] reduces to:

2 * Successful Field Shots [A–B] – Missed First Free Throws [A–B]

When this expression is positive, we can say that the winner has better tendex that the loser, since if Points [A–B]>0 then TP(A)–TP(B)>0.

It is obvious that one can find examples of games where this expression is negative, but as said in our introduction of paragraph (1), this is very rare.

Another witty question is: If two teams have the same number of successful field shots, but team A scores 3p goals, whereas team B scores 2p goals, what happens? Well, the answer is simple: Points [A–B]>0 thus TP(A)>TP(B). But, if things are not exactly like that?

Imagine: Successful Field Shots of Team A = 10 where all of them are 2p goals, and
Successful Field Shots of Team B = 7 where all of them are 3p goals

and for simplicity there are no free throws, no blocks, no assists, rule violations at all, yet. The difference between successful shots is 10–7=3, and the points difference is (2*10)–(3*7) = 20–21 = –1 (negative, i.e. team B wins). Tendex Points difference, however is:

TP(A) – TP(B) = Points [A–B] + 2 * Successful Field Shots [A–B] = 3 + 2*(–1) = 1 ( i.e. team A wins)

a result, which contradicts the previous one, but as said before these cases are rare.

Anyway we can conclude saying: the winner has generally better tendex ratio than the loser

It is easy to examine the conditions, which mathematically can reverse this conclusion, but this is not important. The most important dimension here is for someone to understand that Tendex analysis includes not only a comparison between final score of both teams, but also parameters, which measure the quality of the game (assists, blocks), contribution of players in terms of ball possession alternation etc., which with the help of time played depict a good picture of a player performance.

Finally, we need to underline that we have to be very careful, when we combine stats. Are these stats correct? Have these stats been collected according to the rules described in all previous paragraphs? We have been examining all stats rules and we included them in our web site under: www.galanissportsdata.com/mainsite/basketr.htm

In order for someone to get an idea of how easy it is to err, we only need to mention that each game involves 500 entries per team. If we allow a reasonable 3% error we can result in a total of 15(!) tendex points difference per team, which can lead to reverse conclusions.

11. Difference and Sum of Attacks

Since the mechanism of attacking and shooting is clear we can proceed with writing the attacks equation of paragraph (6) for both teams, which subtracted give:

Attacks A – Attacks B = Offensive Rebounds of team A– Offensive Rebounds of team B

which looks surprising and simple, but it is true.
Imagine there are no turnovers and rebounds at all. This means, that all shots are on target. What would we have then? Each attack would end in a goal, thus we would see a cascade of successful attacks. In this case the difference of attacks would be 0 or 1.

If we examine instead the difference of possessions then things are even simpler, since as said this difference is 0 or 1, as the number of possessions is almost equal for both teams.

Performing the sum of attacks (see paragraph 7) we obtain:

Attacks A + Attacks B = [Shots A+B] – [First Free Throws A+B] + [Turnovers A+B]

where in reality [Shots A+B] – [First Free Throws A+B] is what we call Final Attempts.

12. Tendex Analysis for Line Ups

Since Tendex Analysis gives safe results for players and teams, it can be used also for any selected line up during the game. In other words tendex can be a useful tool, not only after the game, but also for the evaluation of any line up at any moment, in order to check the correctness of a substitution.

The main idea behind this approach is that, averages of a team can be foreseen or predicted after a small part of total team data, while the game is in progress. Naturally, the spectator looks at the scoreboard and sometimes guesses the score of the next minutes. This can be properly performed by an analysis based on real data, in a similar way to what is done during elections, where a sample of results gives a picture of the future.

All these are included in LINE UP PERFORMANCE ANALYSIS AND PREDICTION, which is also presented in http://www.galanissportsdata.com/mainsite/lineup.htm. Even if this analysis is presented at its simplified version, it explains step by step the mechanism of line-ups study and substitutions comparison.

13. Conclusions

Even, if all above mathematics seem to be confusing, the conclusions drawn are very easy to understand, thus tendex points and ratio, which most of basketball people are familiar with:

1. display player, but also, mostly important, team performance

2. are based on ball possession alternation between two teams, and tendex points reflect teams’ and players’ contribution to scoring and ball collecting, as, both their sum and their difference correspond to game pace and strength difference, respectively

3. can be used as a starting tool for other studies related to line up performance, prediction, ranking in order to help coaches take fast decisions during or before the game