Biorhythm in soccer - Research paper

REVIEW OF THE INFLUENCE OF BIORHYTHM

ON PERFORMANCE OF SOCCER PLAYERS - PARTICIPANTS

OF THE 20TH WORLD SOCCER CHAMPIONSHIP

BRAZIL 2014Research workDrago Mari, B.Sc (Psychology) and Journalism

Boris Mari, B.Sc.Business AdministrationVladimir Mari, Media Analysis Experthttp://biorhythminsoccer.blogspot.com/SUMMARYIn modern age, being successful in almost any activity business, sports and even personal life decision making - dominantly depends on the level of success in forecasting.

In the environment of dominant neoliberal limitlessness, biorhythm becomes one of old-new possibilities of predicting behaviour and success. Nowadays, every computer and/or smartphone application worth mentioning enables a user to calculate more than ten biorhythm indicators.

It is not surprising that biorhythm has intrigued coaches and athletes alike.

The topic of this research is a review of biorhythm theory on a specific sport sample the last FIFA World Cup in Brazil (2014). The research plan focused on five segments, each with its own hypothesis.

Research covered 55 matches each having a winning outcome (out of which 78% of victories were achieved in regular time including referee time, and 22% in the course of extended time and in the course of the elimination rules valid for the final phase). There have been calculations for 1,460 individual biorhythm sets.

Testing of statistical significance of differences in number of plus, minus and C days of four primary and three secondary biorhythm cycles conducted in pairs of soccer players and coaches as selected by research plan - has confirmed all five initial Null-hypothesis (Ho). Despite biorhythm theory related controversies (which, as we believe, became more articulated with results of our research), we find that biorhythm, to a certain extent, can increase motivational capacities of athletes, in this case, soccer players.Keywords: biorhythm, biorhythm cycles, plus and minus phase, C- days, motivation of athletesAbbreviations and terminology used in this research workBiorhythm abbreviations

A. PRIMARY BIORHYTHMS

PcPhysical cycle

EcEmotional cycle

IcIntellectual cycle

INTcIntuitive cycle

Plus (+)Sign for active, more favourable days of each cycle

Minus (-)Sign for passive, unfavourable days of each cycle

"C"-daysDays of each cycle when biorhythm shifts from active to passivephase (and vice versa) the most unfavourable period

B. Secondary biorhythms

MsBBinomial combination of Physical and Intellectual cycle (Pc+Ic)

PsBBinomial combination of Physical and Emotional cycle (Pc+Ec)

WsBBinomial combination of Emotional and Intellectual cycle (Ec +Ic)

Research terminology

HoNull-hypothesis

HAlternative hypothesis

pHoNull-subhypothesis

pHAlternative subhypothesis

X -scoreSingle Chi-square statistics, calculated value for subhypothesis level (one biorhythm cycle)

X -scoreAggregate Chi-square statistics calculated value for subhypothesis level (all four - or three - biorhythm cycles)

DfLevel of freedomintegral part of the procedure for determination of X -score significance.

The base for Contingency table (table with statistically analysed frequencies), and is calculated according to the formula = (number of rows-1) x (number of columns-1) of this table

GVMarginal value for determination of significance of obtained results

= 0.05Given value of significance with 5% probability of error

PEmpirical (calculated) value which indicates (percentual) error probability for making a decision regarding substantiation of formulated hypotheses

NNumber of cases in a sample

INTRODUCTIONAmong all human aspirations, two of them have accompanied human development for the longest period of time. The first one is summarised in the message to man, coming from ancient Greeks: Know thyself. The second powerful human aspiration is being able to predict future events. Its genuine source is human primordial fear of uncertainty as the main feature of each upcoming unit of time, whether we speak about a second, an hour, a year, or a century. In older periods of history, this uncertainty was mainly related to weather conditions important for agriculture and hunting but also, on a personal note, to fear of death. In the modern age, however, being successful in almost any activity business, politics, sports and even personal life decisions - dominantly depends on the level of success in forecasting.Forecasting the future is in the midst of constant battle between sceptical scientific enthusiasts and self-confident quacks. While scientists are looking for methodologically and statistically relevant proof, those on the other side of the wall - classified as false prophets - base their popularity on constant demand for their visions. The problem is that this demand, starting from beginning of this century, has been accelerated by enormous growth of available applications designed for computers and mobile phones. Hence, today even those who never cared for astrology, tarot, numerology, or interpretation of dreams, can easily download applications for supposed forecast of their behaviour and upcoming events by using these techniques. It is only a matter of time when (the already famous) Balkan prophetess using kitchen spoons for fortune telling will appear on the internet and offer a mobile application for her method. For that matter, it is not surprising to see the resurrection of some earlier theories which, even at the time of their greatest popularity, could not win over enough scientific affirmation. However, with the absence of documented research counter-arguments, they managed to get a new chance in the modern times.

One of these reanimated ideas, and now available in applicable form, is the Theory of Biorhythm.

I. HISTORY AND CONCEPT OF THE BIORHYTHM THEORY

I.1. It all began with the magic of numbersThe crossroad between the 19th and 20th century was marked by a couple of intriguing ideas brought about by three doctors from two European capitals (Vienna and Berlin). One of these ideas, much more familiar but also more often disputed, was introduced by Dr Sigmund Freud. The idea in question is, of course, that of psychoanalysis. The other idea that looked at specific periodicity of internal changes and manifested behaviour of a person was named biorhythm (Very often used in plural form: Biorhyhtms).Initial authorship for biorhythm is shared between two eminent European intellectuals at the end of nineteenth century: Dr Herman Swoboda, professor of psychology at Vienna University and Dr Wilhelm Flies, a Berlin-based academician who was a nose and throat specialist. Judging by more than 100 letters exchanged between Flies and Freud in the period from 1887 to 1902, the father of psychoanalysis was a very strong supporter of Fliess biorhythm activities and at the same time was almost failing to notice loud gossips in Vienna medical circles regarding Swoboda's work. Their friendship was surely one of the reasons for Freud preferring Flies, as well as the fact the father of psychoanalysis was actually one of Flies's patients. (Freud eventually died of one type of mouth cancer).

In this initial part of its history, biorhythm comprised of two separate cycles distinguishable by rhythmical shifts of physical/organic and psychological oscillations in the human body. One of them was Physical (Pc) and the other Emotional (Ec). The first lasts 23, and the latter 28 days. Some promoters have assigned gender attributes to these cycles, so the physical cycle was called masculine, while emotional was referred to as the feminine cycle. Flies himself was obsessively practicing the magic of numbers (especially multipliers of number 23!). He even believed his biorhythm formula could determine the gender of a conceived child.

At the beginning of last century, Swoboda published 4-5 books about his version of biorhythm, one of those with an impressive 600 pages. Flies was not less productive, publishing 4-5 books, one with 564 pages!

Despite such extensive literature, due to strong contempt from the academic guild community, primarily in Vienna and Berlin, the entire biorhythm concept was doomed to be forgotten (as was psychoanalysis too).Biorhythm found itself again in the focus of public interest immediately after World War I. An Austrian engineer Alfred Teltscher (teaching professor in Innsbruck) noted the existence of good and bad days for studying among his students. The fact that this result matched with Platon's concept of cyclical changes of favourable and unfavourable periods in human life, has made it particularly attractive. Teltscher left no books written on the topic, but nevertheless he did establish the third biorhythm cycle. He named it intellectual (I) whose sinusoidal cycle lasts 33 calendar days.

And so, the psychologist (Swoboda), doctor (Flies) and an engineer (Teltcher), independent of each other, completed the unique biorhythm theory, yet it took just a little over half a century for it to reach its golden age.

The story about biorhythm was revived in the USA after World War II. This idea was strongly spurred up in the mid seventies of the last century by the book of G.S. Thomen Is This Your Day? News stories and books regarding research of these cycles in regard to accidents at work, traffic incidents, days of death and results of sports events increased hope that it was possible to predict important personal and social events. It was also a kind of timid prelude for New Age. By uncritical affirmation of psychological and, even more, parapsychological approaches to everyday life, this movement was raising belief in the possibility of self-improvement, but also in managing internal and external factors of health and happiness.

Of course, the critics were also very active, providing statistically supported results in favour of senselessness of those expectations. Soon, this battle spread rapidly from America to other continents and resulted in multitude of research papers, scientific articles and books. In the closing two decades of the last century, biorhythm was again about to be forgotten, for it seemed advocates of strictly methodological provisions and relevant statistical parameters prevailed over users of the so called anecdote-based approach to researched phenomena. The bottom limit of tolerance from the first group, as it seems, was an approval for use of biorhythm as a pseudoscience.

Despite the constant and battle between the pros and cons, biorhythm entered the information age still standing on its feet.Software presentation of biorhythm replaced the previous complex pencil calculation. Easy access and even easier use of computer and mobile applications reignited the public interest for Swoboda-Flies-Teltscher theory. To put it simply, it was very in again to have a personal or team biorhythm.

In the environment of dominant neoliberal limitlessness, biorhythm becomes one of old-new possibilities of predicting behaviour and success. Nowadays, every computer and/or smartphone application worth mentioning enables the user to calculate more than ten biorhythm indicators. The possibility of calculating the so-called compatibility factors indicators of mutual (in)compatibility of two or however many persons, has brought an additional appeal.

Although he was not occupied with this topic at all, the author of former world's bestseller the book Stumbling on Happiness- briefly diagnoses the human need for predicting future events (so evident with both founders and followers of biorhythm):

The influence of feeling that we keep things under control is beneficial, whilst the belief that we create our own future makes us happy (LIT. 2, p. 42).

Although the return of biorhythm into the public sphere (in fact, into the market) was more visible in media than in scientific circles, this fact does not reduce the need to continue testing to what extent this theory really works.

Before we bring up the results of one thorough research of biorhythm influence on performance in one (team) sport, we will briefly introduce main elements and features of the theory itself.I.2. - Minus is (like every) minus, but C is even worse...The existing software solutions mainly thanks to imaginative graphics enable easy reading of cyclical values, enabling fast comprehension of the idea of biorhythm itself.

The concept is simple: each cycle is really a sinusoid with a plus (active) and minus (passive) phase. Besides, the points on central flat line, where cyclical sinusoids cross from one phase to another, are specially emphasized. They are time-synchronous with the first and middle day of each cycle period. In Pc-cycle (which lasts for 23 days) these are day 1 and day 12, in Ec-cycle day 1 and day 15, in I-cycle day 1 and day 17, and in the Intuitive-cycle (38 days) day 1 and day 20.

These points are called critical days (C-d) because they hide, according to this theory, the highest risk and the highest lack of energy, will, physical strength, optimism and patience. C days in the middle of each cycle are especially risky. In addition, by default, critical days belong to the minus (passive) phase, but with a much more emphasised dimension of dysfunction of all kinds. For that reason, each biorhythm story in every research pays special attention to C-days. vGraph 1. Biorhythm sinusoids of each cycle have a plus and minus phases, while C-days are identified on horizontal line with the number of days (1-38), located on the points of passover from plus to minus phase (and vice versa)

Regardless of their different duration periods (23, 28, 33 and 38 days), all biorhythm cycles, according to the theory, start together with the day of birth. In the first 11 days of life, all four cycles are in the plus phase. Afterwards, Physical cycle enters the minus phase first, while INT-cycle does so last.

The situation of all four cycles starting together (Graph 1.) repeats itself only at the age of 57. It is interesting to mention that in Japanese tradition there is a belief that human life starts anew exactly at the age of 57.

Due to their relatively low representation in total number of biorhythm days of each cycle (up to approx. 20%), and due to rigorous methodological constraints for groups with small number of frequencies, C-days are often statistically analysed combined with the minus phase data.

Plus and minus sinusoidal areas can be directly linked to surplus, or deficit of physical and mental energy of a human being. The central sinusoidal horizontal line symbolically represents the separator between growth and decline of these capacities. The tallest and the lowest sinusoidal points represent optimum and minimum of each cycle.

Roughly speaking, minus phase of each cycle means additional quantities of energy, will and concentration are needed for achieving given goals. However, if important tasks and goals fall into C-days, it is best to prolong them into upcoming calendar days. Biorhythm followers emphasise that C-days do not necessarily forecast catastrophes or personal disasters, but, according to them, failure or misfortune is by far more probable during those days than in any other day before or after. Favourite and often illustrated example of this rule is a practice in some Swiss and Japanese hospitals whereby surgeons do not conduct surgery during their C-days. Certain airline companies give their pilots free days, and some taxi companies in certain countries do the same.

I.3. - Duets (perhaps) say more than a single cycleSince its emergence, the idea of biorhythm seemed unfinished. This represented a great challenge for reformers and innovators. In the multitude of attempts, often linked to Far East philosophies and thinkers from ancient Greece, Mort Gale, an American, deserves special attention. In his book Biorhythm Compatibility (Warner Books, Inc, New York, 1978.) he introduces, a little known piece of information in biorhythm literature that he identified and named as the fourth biorhythmical entity in human behaviour Intuitive cycle (INTc).

It is interesting that in relation to this, Gale (just like Flies) referred to one psychoanalyst, Freud's competitor, Carl Gustav Jung. And so, with Gale joining, the already famous trio of biorhythm story creators: Swoboda Flies and Teltscher became a quartet. Most of current computer and mobile applications include all four cycles.

These four cycles are named primary cycles, while their binomial combinations (Pc+Ic, Pc+Ec and Ec+Ic) make the group of secondary biorhythms.

Combination of Pc and I-cycle is named Mastery Biorhythm (MsB). When both cycles are in plus phase, the person's physical and intellectual superiority boosts and promises above average success on those days.

For the context of this research, and for the sport as a whole, of special interest is the binomial combination of Pc and Ec-cycle (Passion Biorhythm, PsB) which is responsible for the control of physical endurance and enthusiasm (motivation). Since the first research of the application of biorhythm in sports, assertions arose that these two cycles are crucial for motivational and physical readiness of athletes. There are many studies that prove, with more or less argumentation, a higher frequency of injuries and unexpected bad results for athletes in periods of Pc-cycle minus phase. O the other hand, others have discovered a connection between athletes' Ec- cycle plus phase with their exceptional achievements.

The third biorhythm duo marked as Wisdom Biorhythm (WsB), brings the synergy between Ec and Ic- cycle. In short, when these cycles are in the plus phase together, the person is more creative in performing activities and behaves more wisely. Both characteristics are of reduced capacity in minus phases.

Two three-cycle packages are added to all the above, one based on ancient Chinese meditations (I-Ching), and the other on binomial correlation of the Intuitive cycle with the other three primary biorhythms (Extra biorhythms).

In any case, it appears logical if the biorhythm theory is (at all) sustainable that these or different combinations have much more influence on behaviour, and success of failure of biorhythm, than single biorhythms and their individual phases.

I.4. - Fast, fitter the most successful?Mass professionalism and blatant commercialization of many sports inevitably caused panic pursuit for training methods, and game tactic likewise, that would produce champions more quickly, or would ensure promoted leaders remain in the winning track as long possible.

In this unstoppable process the native Olympic motto: Faster, Higher, Stronger has over time been reformulated into an imperative of Fast, Fitter, Most successful, where (non)performance is closely intertwined with careers and destinies of sportsmen and trainers.

For the same reason and equally passionately, the demand for help from psychologists and sports medicine specialists is on the increase. The quest for a formula of (fast) success, i.e. for the more desirable formula of happiness in predicting sports results, does not stop on the boundaries of science, but dives into the turbid waters of quackery.

There are many coaches, athletes and sports betting players who strongly believe in astrological projections and in power of various talismans. Others follow numerology axioms, or keep in touch regularly with celebrity fortune-tellers of different orientations. The Internet fame of Paul the Octopus, from an aquarium in the German town of Oberhausen, could be placed in this context. He made several accurate predictions of results of the German national football team during of the 19th World soccer championship in the South African Republic (2010). Therefore, it is no wonder that biorhythm, with its already described attractive performances of personal behaviour predictability and efficiency, intrigued coaches and even athletes.

Nowadays computer and mobile applications exclude complex mathematical calculations and experts-intermediaries. Easily available computer programs enable retroactive, proactive and multidimensional achievements tracking of unlimited number of persons/athletes including, of course, all of their biorhythm parameters.

Prediction capacity of biorhythm in sports has been tested since the 70s. One thematic book, containing detailed list of examples of biorhythm application in sport, including research on the topic, had two editions within the same year (LIT. 3).

Lists of affirmative and disclaiming studies on the topic are equally long. Biorhythm followers benefited from research of individual sports, while their adversaries from team sports.

The most quoted example in literature favouring biorhythm certainly is the achievement of American swimmer Mark Spitz who during XX. Olympic Games in Germany (1972) won gold medals in seven disciplines in a row, in a period of just 13 days. Although Spitz`s period of unprecented individual achievement started and finished with a duet of critical C-days of Fc and Ec cycles, the secret of success was actually hiding between them. Namely, during these ten or so days in between, both cycles were in the plus phase (LIT 7. pp 99-100).Somehow at the same time (1972), based on the analysis of personal biorhythms of 1000 sports record-holders, G. Shonholzer, G. Schilling and H. Muller from the Swiss centre for the research of biorhythm, resolutely concluded that biorhythm theory has neither biological, nor mathematical foundation.

Applying biorhythm in collective-team sports is more complex and more questionable. Some even explicitly refuse such a possibility (LIT 6., pp 79-81). Forty years ago, a research duet, Michael R. Wallerstein and Nancy Lee Roberts became media celebrities in American newspapers and magazines by claiming to be able to predict not only individual, but also team results, by using their mathematical-graphical invention Bio-curve. They were pretty successful in predicting results in American football, and were also passionate advocates of using biorhythm in business spheres.

Subsequently, many research papers followed, spreading optimism for biorhythm utilisation in team sports. There were also those who used biorhythm in practice. The literature points out an example of a Swiss soccer coach Helmuth Benthaus who, from his personal experience, claimed biorhythm was an excellent tool in preparing-training of the players (LIT 3. p. 51, LIT 4., pp. 102-3).II. RESEARCH TOPIC AND METHODOLOGYII.1 - The dream sample FIFA World Cup in Brazil 2014From the methodological and research point of view, World championships and Olympic Games are the most worthwhile statistical units for testing research hypotheses in sport.

First, they are always a summit of best teams and individuals, champions and record-holders. These are dream research samples for determining factors of competitors` success or failure. Such events are characterized by high incidence of independent variables (as they are called in research practice) such as territorial (continental) representation of participants, their nationality, sex and age grouping, etc. The last, 20th FIFA World Cup in Brazil (held in June and July 2014) represents one such research challenge. Factographic competition profile confirms it all: 32 national teams from all 5 continents, 64 ultimately competitive games, 736 registered players, 171 goals scored, 13 penalty kicks in regular time including referee time and 36 after extra time.

The subject of this research is a review of biorhythm theory on this specific sport sample 20th FIFA World Cup in Brazil (2014). Research plan focused on five segments, and within those, five research hypotheses were defined:1. Primarily, we were interested in knowing if biorhythm parameters specify differences between winning and losing teams.

In this competition, in the first group phase of 48 matches, 39 matches ended with one of the national teams winning. Nine matches in this phase ended with a draw, and these matches were not covered by this research (but their players were included in all research records of individual achievements such as scored goals, penalty cards, etc.) In next, eliminatory phase with 16 matches, eight ended with a winning outcome by the end of regular time (90 mins.), while the winners of four matches were decided after extra time (30 min), or after the penalty shoot out.

Therefore, this research comprises 55 matches with winning outcomes (out of which 78% victories were achieved directly in regular time and 22% through eliminatory rules valid for the final stage).

2. Furthermore, we wanted to test whether better-ranked soccer players had superior biorhythm than their colleagues from the defeated team.

Statistical testing was performed on marks allocated by reporters of eminent American internet media company Bleacher Report (BR) that in our opinion - objectively and competently covered all 64 matches in Brazil.

Soccer players with marks 6.0 and above made the group of better-evaluated players (1092 players), and those with marks 5.9 and lower were classified in the group of lower evaluated (360 players).

We were also interested in:

3. Peculiarities of biorhythm parameters of goal scorers and their comparison with equivalent parameters of players who did not score goals in the Championship (in this group, of course, there were no goalkeepers).

4. Peculiarities of biorhythm parameters of soccer players with yellow and red cards and their comparison with equivalent parameters of players with no cards, and

5. Peculiarities of biorhythm parameters of coaches of winning and defeated national teams.

In accordance with research standards, we have formatted detailed and precise templates for keeping records of necessary data.

Pre-designed research plan also included criteria for representation in data as well as all other necessary methodological limitations in relation to dependent and independent variables.

In addition, we have determined in advance the relevant sources of necessary biographical data of soccer players (and coaches), and selected the appropriate computer software for calculation of biorhythm parameters.

Summarized, per each match we entered in appropriate templates approx. 600 various data (individual identification data, biorhythm values, types of performance in the field and other information for each soccer player and coach). In this way 40,000 pieces of data was processed for all 64 matches.

II.2 HypothesesAlthough the available data fundus allowed for higher number of hypotheses in standard research form of Null-hypothesis (Ho) authors of this work chose the following five:

1. There is no statistically significant difference in representation of plus, minus phases and C-days at the level of each of the four biorhythm cycles, between winning teams and defeated teams;

2. There is no statistically significant difference in the representation of plus, minus phases and C-days - at the level of each of the four biorhythm cycles - between players who got higher marks for their match performance (6.0 and higher) and those with lower marks (5.5 and lower);

3. There is no statistically significant difference in representation of plus, minus phases and C-days at the level of each of four biorhythm cycles - between goal scorers from one side, and soccer players who did not score goals in this Championship on the other side;

4. There is no statistically significant difference in representation of plus, minus phases and C-days at the level of each of four biorhythm cycles between soccer players with yellow and red cards and players without these types of referee`s punishment; and

5. There is no statistically significant difference in representation of plus, minus phases and C-days at the level of each of four biorhythm cycles between coaches of winning teams and coaches of the defeated ones.Alternative hypotheses (H), as well as alternative subhypotheses (pHo), in the context of this research defines the existence of relevant correlation between the same variables as well as in the Null-hypotheses from 1 to 5.

The test of significance of the differences for all hypotheses has been done by using standard statistical X-square test (chi-square test) with additional utilisation of its statistical infrastructure (Summed-up X-square, p-value, contingency tables, correction formulas, etc.)

For the purpose of this research work, 1460 individual biorhythm packages have been calculated. Each individual package includes four primary (Pc, Ec, Ic and INTc) and three secondary biorhythms (MsB, PsB and WsB). Individually, they belong to 528 soccer players. That is 69% out of total number of players participating teams submitted to FIFA. These players played 3 matches on average, and that is also the average number of biorhythm sets per each soccer player.

Results of statistical analysis, whose interpretation is about to be presented, can be expressed with a common sports headline: Null-hypotheses vs Biorhythm 5:0!

III. RESULTS

III.1. - Common debacle of Brazil - and BiorhythmThe first semi-final match of this championship was played on July 8th 2014 between the host country Brazil and Germany. Everybody expected great soccer and few goals. The only thing nobody expected was a debacle of either one of the confronting national teams. However, a real soccer miracle happened: Germans simply sank the host`s boat having won with Guinness-standard result of 7:1!

It was a catastrophic day even for the boldest of betters, if ever existed someone believing that Brazil, playing in front of its fans and so close to the final - could lose with a 3 or 4 goal difference. Among those unsuccessful forecasters, there was also biorhythm whose cycle parameters announced a mediocre match with miserable goal scorers and close to sleepy goalkeepers. The host even had fewer players with their minus phase in three out of four cycles, whilst Germans additionally had one soccer player with a critical C-day (in the Intuitive cycle).

To biorhythm's disadvantage, this player was Andre Schrle, who scored no less than two goals in this match. He scored those goals after only 32 minutes on the field (he entered the game in the 58th minute of the match). The fact the other three Schrle`s cycles were in minus phase almost equalize the failure of biorhythm theory with the Brazilian score debacle.

Biorhythm has shown weak validity of prediction in most of other 53 matches with nominated winners.

As it can be seen in Table 1a, calculated X values for Pe and INT cycle are far below borderline value for which is 0.05. At the same time, corresponding p values in both cases are higher than 0.05. This undoubtedly supports our first formulated Null-hypothesis (Ho).

Darker shaded X square for E-cycle is very close to the borderline value but remains in the acceptable zone of Ho. However, X for I-cycle (non-shaded field in the table) is higher than borderline value for 0.05, so the Alternative subhypothesis (pH), or better said - the possibility these differences are not coincidental - is accepted. But, are these differences in favour of the biorhythm theory?

In cases where Xi-square does not identify direction and the logic of real differences between examined groups, the occurrence and the logic sequence of the obtained results is determined by insight in the distribution of the obtained data itself. Table 1b (Annex page 24), with frequencies of number of soccer players in each of the three biorhythm phases (plus, minus, C-days), shows the winning teams having 50% of their soccer players with Ic- cycle in minus phase, and the defeated teams only 45%. Besides this, winning teams also had 4% of players with C-day, while the defeated teams had half of this number 2%. An almost identical inversion of data and significance can be seen in Ec- cycle whose X value is very close to the borderline value.

It is all contrary to key postulates of the classic biorhythm theory.

The aggregate Xi-square (X) for all four cycles sums up to 14.039, which is lower than borderline value for 95% reliability ( 0.05 =15.510).

For this reason, the first formulated Null-hypothesis, claiming that there is no statistically significant differences in representation of plus, minus phases and C-days in biorhythms of winning and defeated teams, can be accepted.

Table 1a also shows that (X) for the group of secondary biorhythms does not come even close to borderline value either and this, again, goes in favour of the formulated Null-hypothesis.

III.2. The one and only and missed!In Brazil, Lionel Messi (Argentina) has been proclaimed as the best player of the tournament. Many argued that there were better players, among other things, due to the fact Argentina lost in the finals, and that Messi was not the best goal scorer. However, Messi was the only player in the Championship given straight ten mark (10,0) by evaluators of the Bleacher Report for his play performance in a game. It happened in the Nigeria-Argentina match (2:3), when he scored two out of four goals he scored in total during this tournament.

And what was the predisposing biorhythm profile of this Argentinian on July 26th 2014 when this match was played?

In short: more worrying than optimistic. F, I and INT cycles were all in a minus, and Emotional cycle was the only one with a positive prefix. The state of combinations of secondary biorhythms was even worse. MB and PB were in minus and WB which, according to the theory, is directly responsible for success or failure of goal scorers and midfielders fell into a C-day on that day. It turned out, despite bad biorhythm profile Messi was in great form.

This convincing failure in predicting Messi`s performance during this match is an integral part of the more detailed statistical argumentation for acceptance of our second Null-hypothesis proving that existing differences in number of plus, minus phases and C-days between better and worse ranked soccer players in this competition do not have statistical relevance. More precisely speaking, this statement is related to three of four primary biorhythms (F, I and INT) whose X -scores - as it can be seen from Table 2a are lower than borderline values.

However, X -score of the fourth, emotional cycle, equals 8.328 and is therefore higher than marginal value (5.991), so in this case the alternative pH , that is different in number of plus, minus and C-days of better evaluated and worse evaluated players of the World Cup in Brazil 2014 are not coincidental, but statistically significant.

Relatively high X -score for the E-cycle has taken the aggregate X -score for all four primary biorhythm cycles almost to the borderline value, but not above it, so in regard to paired variables the third Null-hypothesis is also accepted. As such, the third Null-hypotheses is not contested by the obtained X -score for binomial combinations in the group of secondary biorhythms either. Namely, neither individual, nor the aggregate X -scores have exceeded corresponding borderline values (5.991 and 12.590).

III.3. Three goals with three (biorhythm) plusesThe only hat trick scored from the game in this championship was achieved by a member of the Swiss national team, Shaqiri Xherdan during the match against Honduras (3:0). On that day (June 25, 2014), the ball really was on his side. Perhaps also because biorhythm was on his side too. Three of his cycles were in plus phase (E, I and INT) with only the Physical cycle being in the passive phase. Besides, all three binomial combinations in secondary group had a positive prefix.

Even so, noted differences in the aggregate number of plus, minus and C-days between goal scorers and soccer players who did not score during the game in this championship appeared from the statistical point of view - irrelevant. The obtained X -scores for all four primary cycles were below corresponding borderline value (Table 3a) and therefore do not annul the Null-hypothesis.

III .4. - Identical biorhythms completely different performancesZokora Didier, an Ivory Coast defender, was given a yellow card in the 58th minute of the match against Japan (2:1). For his performance in this game, evaluators gave him just a comforting mark of 5.5. Biorhythm followers would probably say: it could have been even worse for him considering on the day of the match his E and INT- cycles were in C-days, while F and I- cycles were in minus (- C, -, C).

Ten days later (June 24, 2014.) Japan and Colombia played against each other (1:4). Japanese offensive player, Yoshito Okubo had exactly the same biorhythm combination as Didier (-C, -, C). Even so, in this match, it's not just that he did not get any yellow or red cards, but he also achieved the best mark of all players of his team that of 7! By the way, the only Japanese player to get a yellow card on that day was the defender, Y. Konno. Biorhythm followers would cheerfully say: completely justified, for he had all four cycles in the passive, minus phase!

These are typical anecdotal (individual) instances of cases for and against biorhythm. For larger samples at least in the scope of our research this balance is disturbed at the expense of the biorhythm approach. Statistically speaking, key differences in biorhythm parameters between players with red and yellow cards and those without being penalised by the referee in that way - are coincidental and irrelevant.

Values of X- scores in Table 4a illustrate this:

III.5. Coaches in the jaws of biorhythm tooStrategy and team game tactics are the primary responsibilities of any coach. Very often, other roles are assigned to the coach, from club leadership to the role of an alternative psychologist. In any case, the coach is held responsible for the results, and particularly for the failures. Moreover, a coach needs to be the leader into something improbable(LIT. 1. p 251). By actively using his intellect, knowledge and personality, the coach participates in club's achievements often to a critical degree. It is logical to assume then if biorhythm theory is functional that coach`s biorhythm should be some kind of an psychological additive which gives a taste of success or failure to club`s achievements.

The championship in Brazil was a good opportunity to test this assumption as well. There were 55 matches in total ending with a winner, and equally as many coaches in groups of winners and losers that were subject of our research.

Statistics remained unchanged towards biorhythm in the case of this part of research too. There were no biorhythm cycles with statistical indicators (X) having a reference level of significance (Table 5a). Hence, the Null-hypotheses no. 5 is also affirmed stating that there are no significant differences in the number of plus, minus and C days between the group of winning teams' coaches and group of coaches of defeated teams.

If we apply the so-called Anectodal method of comparison, that is, if we focus on individual cases, the situation is much more favourable towards biorhythm.

Result-wise very rare semi-final match between Brazil and Germany (1:7) has already been used as an illustration for explanation of the first Null-hypotheses in this piece of work. There we compared biorhythm of soccer players, and here we compare same indicators of two coaches.

Table 6: Biorhythm profiles of coaches on the day of BrazilGermany match (1:7)ManagersPRIMARY CYCLESes

PcEcIcINTcMsBPs

BWsB

Luiz F. Scolari BRA-C-+-+-

Joachim Lw GER+-+++++

The host team's coach had a very bad biorhythm combination with two biorhythms in the minus phase (Pc and I- cycle) and Emotional cycle with a C-day. On the other side, coach of the (dominant) winner had three cycles in plus phase and only E- cycle in the minus phase. The German coach also had all three secondary biorhythms in the plus phase, while the Brazilian coach had minus in two out of three cycles.

Coaches of teams playing the final match of this Championship also had very interesting - conditionally speaking "pro-biorhythmic" combinations of cycles. The Argentine coach was in an absolute minus, whilst the winning team's coach had two cycles in plus and two in minus phases, with all three secondary cycles in plus phases. Table 7: Biorhythm profiles of team coaches in the final match Germany vs Argentina (0:0, 1:0 after extra time): CoachesPRIMARY CYCLESes

PcEcIcINTcMsBPsBWsB

Joachim Lw - GER-+-++++

Alejandro Sabella - ARG----++-

Looking at the above table, it is evident that the German coach, who had pluses on the sinusoid of Emotional and Intellectual cycle, had an advantage over his Argentine colleague, who to say the least started this deciding match of the championship with much more calm and good mood. According to this theory, a better INT-biorhythm, along with plus-WsB in secondary groups, enabled him to show more tactical creativity that, at the end of the day, led him and his team to the throne.

******************************************IV. CONCLUSIONS AND DISCUSSIONA. Testing of statistical significance of differences in number of plus, minus and C days of four primary and three secondary biorhythm cycles - conducted in pairs of soccer players and coaches as selected by research plan - has confirmed all five initial Null-hypothesis (Ho). The aggregate Xi-squares (X), as earlier shown in aggregate tables (Tables from 1 to 5) do not - in any case - exceed the standard marginal values (at a level of 5% statistical error) to form a statistical basis for acceptance of any of the affirmative hypotheses (H).

Rightly so, there are examples of X values for individual cycles having higher than borderline values, but they are not numerous and do not correspond with generally accepted biorhythm postulates.

Taking into account all of these facts, formulated Null-hypotheses are accepted in their initial form, both for primary and secondary group of biorhythms:

1. There is no statistically significant difference in representation of plus, minus phases and C-days - at the level of each of four biorhythm cycles, between winning and defeated teams;

2. There is no statistically significant difference in representation of plus, minus phases and C-days at the level of each of four biorhythm cycles between better evaluated players and those who received weaker marks for their performance;

3. There is no statistically significant difference in representation of plus, minus phases and C-days - at the level of each of four biorhythm cycles between goal scorers from one side and the soccer players who did not score in this championship;

4. There is no statistically significant difference in representation of plus, minus phases and C-days - at the level of each of four biorhythm cycles between soccer players who received red and yellow cards and players without this kind of referee`s penalty and

5. There is no statistically significant difference in representation of plus, minus phases and C-days - at the level of each of four biorhythm cycles between coaches of winning teams and coaches of the defeated teams.

At the level of individual biorhythm cycles, based on which the Null-subhypotheses (pHo) were formulated, there are examples that support acceptance of alternative subhypotheses (pH) but, in the given form, they do not correspond with classic biorhythm postulates.B. On the other hand, in the data fundus available for this research, there are quite a lot of individual examples in which the actual performance of soccer players (including both value prefixes) can be directly correlated with particularities of individual biorhythm cycles and their binomial combinations. Some of these typical cases were described in previous pages. Although examples given do meet the requirements of the so called Anecdotal method, their sporadic nature and absence of statistical relevance do not allow them to be accepted as convincing proof of support for the biorhythm theory. Here it should be added that the majority of illustrative examples in favour of biorhythm are founded on the strength of individual cases (the days of athletes' great achievements and misachievements, deaths of famous people, bizarre events in the life of individuals and similar).

In any case, there are far fewer arguments founded on relevant samples and significant statistical indicators. There is extremely high shortage of biorhythm research at the collective level among working or ad-hoc sports teams, for in those situations little known and hardly measurable synergistic factors of psychosocial nature also have an influence.

C. Soccer is a typical team sport where detecting factors of competitive success or failure just by using team averages of any kind of available parameters is extremely hard. The result is also significantly affected by players` psycho-profile and achieved psychodynamics within the team at a certain moment. By their nature, both of these components greatly lessen the mathematical-statistical evening-up of the contribution of an individual to the team result.

There are at least 27 active individuals appearing on the soccer field (two teams each with at least 11 players, two coaches, and the main referee with 2 assistant referees) all with lesser or greater opportunity to influence the final result. Often, a great contribution to the final result, especially to the atmosphere, comes from people outside the court, those in the audience. Although the most important protagonists are, by all means, the players on both sides.The final result of the match is often marked with a specific performance of one or more individuals. The goal scorer in the mood for goals (with 2-3 scored goals) and the goalkeeper with a bad day (with a few scores in his net) are typical examples of personalization of the team result. However, these situations as research variables are not completely legitimate from the methodology point of view. Both at scoring and conceding goals, there is a significant share of joint ownership, starting with the creative assistance from co-players to gross mistakes of the opposing players. There is also a surprisingly high share of mere coincidence!

For all these reasons, when evaluating performance of a sports team, one should equally take into account factors deriving from an individual's character, in parallel with those acting as a consequence of playing in a team. In pursuit for the best talent composition, training, motivation and efficiency in the team sociogram, it is necessary to individualize the sequence of significance of these components.

In this package, the motivation of an individual to make optimal performance on the field is perhaps the biggest enigma, especially when the part related to financial satisfaction (premiums, transfers, additional bonuses) is put aside. One of procedures that are more successful is the persuasive technique, originating from counselling psychology. Its task is to inspire and encourage the individual. In sports, it practically means persuading the athlete he can do better, or even be the best at a given moment. Usually, in doing so, one may use the arguments identified in the person`s psychological profile such as his educational anamnesis or the series of worthy achievements from the past.

Despite controversies about the biorhythm theory (which, as we believe, became even more exposed with results of our research) we conclude that biorhythm, in the context of persuasive effect, can also increase motivational capacity of athletes.

The extent of this additional motivation does not need to be enormous, although in some cases it can even be decisive. Existing mobile and computer biorhythm applications use the precision of their numerical values (most frequently up to two decimals) and attractive graphic illustrations of cycle sinusoids to appear suggestive, especially towards persons with insufficient confidence. It is easy to interpret them motivationally, understand them visually and then accept them. Of course, here we talk of the cases with positive, stimulating values of biorhythm parameters. Keeping in mind insufficiently proven validity of biorhythm application in sport, team coaches should not use biorhythm down-parameters (days in minus phases and C-days) as deciding criteria for selecting players for particular matches, or in instances of criticism or sanctioning of players. We emphasise again the complexity of psychosocial surrounding in which an athlete performs during a competitive event. Besides, we point out our belief in great importance of positive motivation in sport.

Motivation is, by its energetic nature, cumulative. It means that every new stimulus directed to strengthening self-confidence and will, regardless of its individual dimension, even to its possible placebo background, gives a stimulating synergistic effect.

D. Betting and sports especially soccer have for long been enjoying an inseparable, symbiotic relationship. Bookmakers are aware that data on tradition, together with mathematical observations of the current shape of the opponent on the betting slip, are of little help in predicting surprises. Therefore, as a rule, they look for additional pieces of information. Many betters believe that such magic information can be found via parapsychological and pseudo-scientific techniques. Considering biorhythm belongs to this club, and is now easily accessible via PC and mobile applications, a good deal of bookmakers are devotedly using it. This research does not support a belief in predictive power of biorhythm at team level, at least not in the case of soccer. However, this research does leave space for use of individual biorhythm profiles of important players as useful additional information in evaluation of competitive impact of their team. E. We also want to point out the methodological and interpretative limitations of this research.This research refers only to determining the possible influence of biorhythm on the effectiveness of soccer players at team level. We have analysed only one out of many possible options of testing this possibility, that of establishing statistical relevance ( X-score) of number of plus, minus and C- days in biorhythms of soccer players from 32 national teams-participants of the 20th World soccer championship Brazil 2014.

Every transfer of these results, and especially their interpretation to other fields of life and other sports, need to be justified by relevant research documentation. Biorhythm parameters are calculated based on data and program procedures, described in footnotes 13 and 14. The data itself has been analysed using standard statistical procedures, including appropriate computer applications (Excel and other). We used all of these with full confidence, but we do not exclude the possibility that in different circumstances and with different procedures, results obtained could be different.IV. ANNEXED DOCUMENTS: Tables with data (frequencies) for calculation of X -score, according to defined research hypothesis

VI. LITERATURE AND OTHER SOURCES

1. Bierman, C. (2011), Die Fuball Matrix/Soccer matrix , translation to Serbian language: Milutin Stanisavac), Laguna, Belgrade, Serbia2. Gilbert, D. (2008), : Stumbling on Happiness/Spoticanje o sreu, (translation to Serbian language: Vesna Petrovi), Dereta, Belgrade, Serbia3. Gittelson, B. (II. ed. 1977), Biorhythm Sports Forecasting, Arco Publishing Company, New York, USA4. Gittelson, B. (VI ed. 1990), Biorhythm A Personal Science, Futura Book, London, Great Britain5. Matei, K. (1983), Biological Rhythms and Human Behavor /Bioloki ritmovi i ponaanje ovjeka , published only in Croatian/, Biblioteka popularne psihologije, Zagreb, Croatia6. Russell, G.W. (2001), Sport Science Secrets: from myth to facts, Trafford, Canada7. West, P. (1980), BIORHYTHMS Your Daily Guide to Achieving Peak Potential, Thorsons Publishers Limited, Wellinghborouh, Great Britain8. **** Short Biorhythms Encyclopaedia (Part of package with the purchased Biorhythm application), www.binarymark.comInternet sources:9. Duch J, Waitzman JS, Amaral LAN (2010), Quantifying the Performance of Individual Players in a Team Activity, PLoS ONE 5(6): e10937. doi:10.1371/journal.pone.001093710. Gale, M., A Brief History of Biorhythms11. Maura S. (2009.), Bio-periodicity and its Influence on the Football Results Obtained by the Student Teams During the University Spring Sport Competition, University of Pitesti, Romania

12. NASA Ames Research Center (1983) , Recap on Biorhythms Theory with Bibliography13. Rummel, R.M, (1977), Individual and Team Biorhythms and Perfomances in the 1975 AIAW National Basketball Championships, Harrisonburg, Virgina, USA14. Sharma, R., Singh, R. (2011), Critical Analysis of Biorhythms and their Effect in Industrial Accidents in Angra Casting Manufacturing Units, Dayalbagh Angra, India15. Vazifedest, H., Alizadeh, A., Dehghan, A. (2013), Study of Biorhythm Cycles that Influence on Decision Qualities of Investment Managers in Mutual Fund of the Iranian Capital Market Islamic Azad University, Teheran, Iran16. Wysotskyi, O.L (.....), The Characteristics of Biorhythms Days, Independent researcher, Kyiv, Ukraine17. ***The Sceptic's DictionaryABOUT AUTHORS:Drago Maric is long-time biorhythm enthusiast analyzing effects of biorhythm in sports, soccer particularly. His interest in biorhythm started in late 1980s when he published predictions based on biorhythm calculations for World Cup in Italy in 1990. These predictions were published in Yugoslav sports daily "Sportski zurnal" during the World Cup. He is also avid statistician of English Premier League and other top European leagues, following and analyzing statistics of teams, players, results and betting odds.

Boris Maric is a fan of soccer, English Premier League in particular. In his free time he analyzes soccer results and performance of different teams. He also runs a couple of websites not related to sports. In this research document he contributed with Excel expertise and data analysis.

Vladimir Mari is aspecialist for media analysis. He contributed this piece of work by translating, editing and proofreadingboth English and Croatian language versions.

Contact us through our website: http://biorhythminsoccer.blogspot.com/ Thanks to media and numerous users, the notion Biorhythm theory has been generally accepted, although it is certain that lack of affirmative research and multitude of denying documents greatly contributed to this concept being considered highly controversial and suspicious from the scientific point of view. It should be noted that pioneers of this concept would rather point out individual cycles and specifics instead of new theories.

Crown Publishing, New York, 1964, reprint 1973.

The US Army Research Laboratory, as part of NASA, in 1981 published a voluminous overview of then available titles from all parts of the world related to biological rhythms in human organism. One special chapter in this overview was dedicated to biorhythm. Bibliography comprises of a bit more than 2000 titles, out of which 212 are biorhythm related (mostly published in the period between 1965 and 1980).

Anecdotal method (Anecdotal evidence) consists of an all-round specialist processing of individual cases with the intention to confirm hypotheses about something new based on rich sample of determined particularities/uniquenesses. It is often used in medicine and psychology as Case report (atypical case), for example in cases when there is a suspicion of an unknown disease occurrence or psychic syndrome. However, taking into account it does not carry statistically representative quality in relation to assumed population, it is not considered relevant to be able to undermine valid, or promote new theories.

Pseudoscience, an activity trying to present itself as science by imitating scientific processes, yet failing to obtain standards practiced in the legitimate fields which it attempts to imitate. Pseudoscience does not appreciate debates and criticism and rarely shows intellectual toughness and true progress. Pseudoscientific theories do not usually get along with the well-founded accepted knowledge, and its own findings seldom, if ever, can stand critical review of competent critics (Wikipedia)

However, in the last about ten years, many interesting pieces of research have been published regarding possible application of biorhythm in different life spheres (see examples in LIT. titles no. 14 and 15)

LIT 12, Abstract 896 - pp 265-66.

LIT 3, p.31 (Case of boxer Joe Louis's match with Joe Walcott on June 25,1948)

Quoted from NASA Recap of biorhythms research from Lit 12, p. 440.

HYPERLINK "http://bleacherreport.com/"http://bleacherreport.com From the research point of view, it seemed especially valuable that this media house was evaluating the performance of each player separately for each half time and also for performance in extra time. For the purpose of this research work, for each soccer player we took the average of such segmented marks for his performance in one match.

Authors of this work followed live coverage of matches from Brazil, as the Bosnian-Herzegovinian national public radio and television broadcaster (Televizija BiH) bought exclusive rights to broadcast all matches. In that way, researchers had the opportunity to evaluate performances of soccer players independently and to re-evaluate BR`s ranking marks and marks of other media reporters.

The average individual mark in this championship, for entire course of the match is 6.3, with average mark for group of better evaluated players being 6.7, and for the group of lower evaluated being 5.0. It is easily noticeable that these relatively low average marks deviate from exceptionally high aggregate evaluation mark for the quality of soccer played in the Championship (9.25 out of 10.00), given by Sepp Blatter, the Chairman of FIFA, after completion of the tournament. It is interesting to point out that the Bleacher Report, throughout the entire competition, has given only one 10.0 mark (for Lionel Messi performance during the Nigeria-Argentina match). At the same time, BR evaluators gave eight 1.0 marks and all of them to Brazilian players for the match against Germany (1:7).

For example: The team set of all data used for statistical analysis (calculation of all average marks) by rule included 11 soccer players, with substitute players being included only if they spent 61 minutes or more in the field, the statistical calculation comprised the soccer player who played 61 minutes or more. However, if such a player played less than 60 minutes but significantly contributed to the performance of his team (e.g. by scoring goal, penalty kick due to his fault, or getting red card), his parameters were included in the team average. In this case, the team average was calculated for 12 players.

For this purpose, we used the official FIFA web site with the existing data on June 12, 2014 (day 1 of the Championship). Although, a priori, we accepted the official FIFA web site as the most relevant source, we also checked and compared birth dates of two soccer players from each national team with Wikipedia records and records from national team and soccer club web pages. This was done because the credibility of these data is of crucial importance. Namely, the calculation of each biorhythm parameter starts from the birth date, so an error, even by just one day, can cause enormous distortion of the final parameter. In this random - and certainly, small sample - we found no discrepancies.

HYPERLINK "http://www.binarymark.com/products/biorhythmcalculator/default.aspxhttp://www.binarymark.com"http://www.binarymark.com/products/biorhythmcalculator/default.aspx This program enables calculation of 15 biorhythm parameters in total (4 primary cycles, plus another 9 of their binomial combinations as well as two cumulative averages). In order to ensure complete reliability of these parameters, we performed a check on a random sample of 100 individual biorhythms using two other programs, and received same values.

Considering the innovated version of the biorhythm theory includes four separate cycles (physical, emotional, intellectual and intuitive), each of these hypothesis practically has four identically formulated Null-subhypotheses (pHo) defined by the significance of each individual cycle. Hence, besides individual chi-squares (which are, in fact, related to subhypotheses), aggregate chi-square (X) has also been calculated for each data group and was the base for interpretation of the relevance of main hypotheses (Ho). Although they have been statistically equally thoroughly analysed just like the proximate hypotheses, the subhypotheses were not qualitatively analysed, except in cases when their X values supported corresponding affirmative subhypotheses (pHo). The same procedure has been applied with secondary biorhythm groups (MsB, PsB, WsB).

Countries-participants of the Championship (32) could register 24 players. Therefore, in total, 768 soccer players were registered. However, not all of them took part: besides first team regulars with highest number of games played, there were players who took part as substitutes, as well as those who did not get a chance to play.

Although it sounds controversial in relation to the very concept of biorhythm theory, its leading supporters, the already mentioned American research duet M.R Walterstein and N. Lee-Roberts express their opinion in an interview for newspaper Tonawanda News Frontier (August 4, 1973), that in a sport team the players with weaker biorhythm (meaning those with more minus and C-days) give better performance than those with biorhythms in plus phases. The reason is, they explain, an assumption that biorhythm pluses drive individuals to show more individuality and selfishness (during the game). In line with this, individual biorhythms with dominating minus and C-days contribute to higher level of cohesion.

It is the case with I-cycle in the context of data for testing of Null-hypothesis no.1 where X = 6.347 - with df=2, and =0.05% - higher than borderline value (5.991). In this case, formulated Null-subhypothesis is rejected and we accept the possibility that the differences in number of plus, minus and C-days between players of the winning and defeated teams are not coincidental. However, any further interpretation of the noted differences, as already said, is contrary to basic postulate of the biorhythm theory.

Methodologically, it is very hard to define precisely the variable of players without goals scored. In modern football, not only exposed top scorers, but all players (except goal keeper) are obliged to score goals.

The author of the book Soccer Matrix C. Bierman presents one research about conditions for scoring nearly 650 goals in six European national leagues (2005) according to which as many as 38.9% instances were the result of pure coincidence. Researcher of this research (Martin Lames) discovered that 41.8% of goals scored in the World soccer championship in Germany in 2006 were also scored - by accident (LIT 1., p 245).

One possible procedure for testing is determining the significance of arithmetic mean differences of nominal daily values for each biorhythm cycle, and for each pair of confronted variables of Null-hypotheses. More complex procedures could include weighted averages of particular cycles, or possibly, weighted averages of biorhythms of key team players. Forty years ago, American research duo M.R Walterstein and N. Lee-Roberts, authored their very complex method for evaluation of team results with the help of biorhythm (LIT 4, p. 105).

Note: Apart from the sources listed above, in preparation of this work authors also took into account a greater number of biorhythm related newspaper articles published in world media and on the Internet.

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