The post Sports Analytics Methods – Deductive and Inductive Reasoning appeared first on Agile Sports Analytics.

]]>Coaches often use this method to reach a particular conclusion—inductive reasoning is used to reach a generalized conclusion from a specific instance while deductive reasoning is used to reach a specific conclusion from a generalized instance about a player or the team.

For deductive and inductive reasoning in sports analytics, concepts and variables of interest are first identified and hypothetical situations are then developed between the variables. One example is the study of O’Donoghue and Ingram in 2001 regarding tennis strategy at Grand Slam tournaments. This is research, they formed three concepts around gender, court surface and strategy. It was around these three concepts that hypothesis were developed using the links and associations between the concepts.

The various methods that are used in such situations include intuition, experience, authoritative sources, and reasoning. But here, we focus on reasoning. Reasoning can either be deductive or inductive and coaches and sport analysts employ this reasoning technique to determine the potential links between the concepts they have formed. Let’s look at how the above concepts work.

**Gender**

Looking at the concepts formed in the study of O’Donoghue and Ingram, it can be said that if there were differences between style of tennis played by males and females, the revelation of this knowledge can be used by a coach to enhance the style of a new player to suit the style of their gender.

**Court Surface**

It has been noticed that in grand slam tournaments, some players performed relatively better on certain court surfaces and performed less successfully on other surfaces. This validated the consideration of court surface as a good concept, which reasoning techniques can be applied in tennis analytics.

**Strategy**

Another concept that was formed through this study was based on the strategy players adopted during their tennis matches. Typically, strategies are planned out before the match or even before the tournament. So for a coach to increase the performance of his or her player during a tournament, they might be able to leverage deductive or inductive reasoning to ascertain the best strategy that will help their player win the game.

Having come up with various concepts such as explained above, coaches, sport analysts and even commentators can rely on their reasoning technique to foretell the chances of one player winning against another.

**Deductive Reasoning**

In performance analysis, after various concepts have been formed, then different variables can be generated, which can be used around each of these concepts through deductive reasoning. So deductive reasoning is where a hypothesis is formed and tested through a systematic observation from the concepts and variables.

What is peculiar about deductive reasoning is that speculations are formed about general variables observed about a concept and these speculations become the hypothesis which are tested in order to arrive at a specific conclusion.

For example, the concept of gender in a tennis match mentioned above can generate variables such as: male tennis players are physically stronger than the female players. This is a generalized theory, which can result into a specific conclusion that it is most likely that a male tennis player will perform better on ground strokes than a female player due to strength. Or at least the stronger female players will perform better on ground strokes than weaker female players.

**Inductive Reasoning**

In inductive reasoning, however, observations derived from real life events are used to generate a general hypothesis, which is further tested. For instance, a tennis analyst who has observed particular matches in tournament finals over a period of time can use inductive reasoning to provide a case study about how a particular concept, such as gender or strategy can determine who will win another final.

In conclusion, deductive and inductive reasoning is a simple logical technique used in sport analytics to come up with either a specific or generalized conclusion about a player. This helps coaches better assess the players, according to their abilities.

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]]>The post Sports Analytics Methods – Simulation Applied in Professional Sports appeared first on Agile Sports Analytics.

]]>Coaches, managers, and sports analysts employ simulation methods to predict the outcome of events or performances of particular players or teams. This allows the managers to predict the chances of their team against opponents in order to enhance performance through training or player formations.

More often for sports analysts who enjoy predicting the chances of a particular team winning a match perhaps for the purpose of giving hints for a bet, simulation allows them to recreate the sport events through statistical models and to foretell the likelihood of the success of a team over a period of time.

This method starts with **observation **of team performance over a particular period of time. This observation allows analysts to develop a model for assessing win-loss predictions, the progression of matches (such as changes in lineups during a season, ball movements as the match progresses pass by pass, defensive and attacking strategies, etc), and the margin of error during simulation.

**CASE STUDY OF HOW SIMULATION METHOD IS APPLIED IN SPORTS**

Let’s take a look at a basketball match and see how coaches or analysts make use of simulation to predict various possibilities during the match, using Russell Westbrook of the Oklahoma City Thunder as a case study.

First, we consider a game or season as an “experiment”. Then the actual results observed of a player or team over the course of a season will reﬂect the natural randomness of that player or team which forms the “data set” of the experiment.

For our case study, observing the performance of Oklahoma City Thunder over the period of six seasons, it is possible to build a statistical model which shows the position of the team in each of the six seasons, number of titles won in each of the six seasons, and the strength of the players across the six seasons. By building the model, sport analysts can recreate basketball events through the models built. This model is then simulated for simulation matches which help them predict what will happen in real life matches over the next one or two seasons subsequently, after the six seasons which the team’s success is modeled upon.

Let’s a deeper look at how simulation helps make predictions based on the match progression of a team. It is very common to see changes during a match—like formation lineup, change of players during the match, or attack-defense strategy. These type of changes are critical, because they play a key role in the success of a team. So coaches are caught in the habit of making models and simulation to help them determine the performance of their teams against opponents during a match by changing the pattern of the team.

For instance, the manager of Oklahoma City Thunder might discover that taking out Russell Westbrook during a match would put the team out of possession, or switching the ball movements when the team is under-performing in a match can change the dynamism of the team and spur the team performance which will eventually increase the team’s chances of winning.

With the progression of a basketball match using a probabilistic graphical model, a coach can predict the best strategy that will produce wins.

**CONCLUSION**

Simulation as a method of sports analytics is widely used by various professionals. This is because it helps coaches and sport managers adopt the best tactics which will yield the most positive results. Also, in the area of sports betting, simulation helps developers build a virtual sport game based on the real-world performance of the team and players.

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]]>The post Sports Analytics Methods – Statistical Mean or Average? appeared first on Agile Sports Analytics.

]]>Let’s start considering that the average baseball match has only about 18 minutes or real play, of action, so to say.

Sports broadcasters have learned all too well that if they provide us with interesting data about the game, if they give us things to keeps us engaged while the real action is at a standstill, this helps them keeping us. The audience, glued to the tv-screens… despite the fact that the only thing we’re looking at is maybe a guy in a striped shirt pulling up and adjusting the rim of his socks… Not too exciting, right? And this in turns buys sportscasters a better share of the audience and this helps skyrocketing the price of the advertising slots they can sell on the media market-But wait a second… Without even really putting our mind to it we’re already knee-deep into statistics aren’t we…?

Didn’t we mention a second ago: “the average baseball match”..?

Yes that’s right, you’re spot-on. Statistics is much more of a “normal feat” for us than we can really think of it.

And as you may discover, following us in this series of videos. Statistics, the base of all sports-analytics, is easy. In facts, much easier than you may suspect. And when you apply statistics to sports magical things can happen! Yes. Even better things than preventing people from switching channel on the TV-set, as Billy Beane and Paul DePodesta discovered during their 2002 Oakland Athletics season when they were the first to systematically apply sport-analytics to their managerial and coaching decisions and in this way managed to secure a 20 games winning streak for their team As we will see in the coming episodes many more team coaches and managers have learned to leverage the same tools, over the past quarter of a century.

But let’s proceed in order. We’ll look at how these tools are applied more in depth in the coming episodes.

We’ve been so bold as to say “statistics, the discipline mother of all sports-analytics is easy”, right? Mmmh, don’t know why, but I suspect you’re not fully bought into this statement yet. Are you?

With all those mathematics and funny symbols and Greek letters involved… How can Statistics ever be “easy”…?

Well, maybe I’ve exaggerated a bit… Maybe not everything we’ll talk about is really just plain “easy”. But I can promise you that if not “fourth-grade easy”, we can make statistics and the concepts involved, at least, “readily understandable” for you…

And all this becomes possible when we realize one important thing: Statistics is not an esoteric science, available only to a handful of initiated priest… No sir, it’s not. Statistics is nothing more than another way we have devised to look at the world around us and maybe describe in a useful way what’s going on with it… Statistics is just another useful tool that we, clever human beings, the animals than more than any other one has learned to observe the world and speculate about it, have readied to describe and better understand certain facts that catch our attention.

Okay, here’s the catch. The key to unlock the mysteries of Statistics is to realize that we’re talking about nothing more than another language, a language different from the verbal one we’re so accustomed to, a language better fit to describe certain notable facts about the world around us and its phenomena. And by shifting just only a bit our attention, and concentrating on the real thing, the world and its phenomena, and understand what really is that we are describing through statistics, then the language and its conventions, its intricacies, can become all the way much easier and manageable.

Not convinced yet? Let’s start untangle the knot together, then.

—- end intro —-

Let’s go back to our “average baseball match” that we stated is only roughly 18 minutes long, when we consider just the action bits.

As we will see better in the coming episodes the concept of “average”, or “mean” as it’s conventionally named in jargon, is one of central importance in Statistics. So it’s a clever place where to start our journey from, since it’s one of the pillars that holds all the house up. And as promised let’s start from the observation of the world and the things we want to describe and understand better:

Okay, let’s go. What is the “mean” or “average” in Statistics?

First, by watching match after match we realized that our beloved game has lengthy moments without actual ball-play. And we take note that this same fact holds true for each and every game played, so it’s something worth our attention, worth investigating. Okay, but for how long then, during a game, do the teams actually play the ball..? We ask…

We solve this problem in a clever way. Timing with a chronograph the time that teams are actually busy playing the ball and adding together all the measures we collected. We end up with a final figure of 16 minutes and 48 seconds. For that specific game we’re scrutinizing. Second we ask ourselves: okay but do all baseball games can when stripped down will equal to this very same 16 minutes and 48 seconds of actual ball-play…? Probably not, we realize… so we get really curious and we go about timing in the same way a few other games, in search of evidences. As expected we get different figures for each one of the other three games we measured. One game was about 20 minutes worth of game play, another one was about 15 minutes, and the last one we timed was about 23 minutes. We decide as well that for the first game we timed we can get away rounding those 16 minutes and 48 seconds to 17 whole minutes: after all we decide that an answer

Precise-to-the-minutes would satisfy well enough our curiosity… We just don’t care if we won’t be more precise than that, for our speculations.

So we’re left with four measures to make sense of: 17, 20, 15 and 23 minutes. When we ask ourselves again: “okay, enlightened by my newly acquired observations how long do teams play the ball for in a baseball game, then…” I can notice two facts using common sense: first, usually games don’t last for the same length of actual ball-play, it’s different for every game as expected: second, this length it’s about 20 minutes, more or less…

“It’s about 20 minutes…”, “…more or less…” Wow, did you notice what just happened? No…?

Let’s see together what we just went about, and how easily we can land from that to the concept we use in statistics of “mean” or “average”.

First, more or less consciously, we tried to “generalize” our answer. That is we tried and agree about a single figure that could somewhat represent with acceptable approximation each and every one of the four games we considered.

Second, we tried and mentally calculate a value that could be as much as possible “equally distant” from all the single measures we started with, and which could therefore represent well enough each one of the games we are considering.

So these characteristics of generalizing a set of different quantities, by providing a single figure that, when needed, can stand in place of each of the values we started with, and of equidistance, which means “still landing in the right ballpark, with a meaningful figure” no matter what starting observation I substitute my “general value” for, are exactly the defining characteristics of the Statistical concept of “mean”, which by the way, is routinely represented in written form by putting a little horizontal dash above the name of the items we are considering the average value of…

We can then ask ourselves: “Okay, but in order to do the best job possible, what is then the best, the most precise, way we can use in order to calculate the mean… this equidistant, general, value… instead of relying only on our common sense…?” We are clever enough not to go about re-inventing the wheel from scratch every time, and we decide to borrow a bit of knowledge from our cousin-languages mathematics and geometry. After all these two have already gone a long way describing cool methods to work with quantities in meaningful and correct ways… And we find out that the way to calculate a number that has as best as possible the same distance from each one of a bunch of other given numbers is to sum the values of all the starting quantities together and divide the total result we get by how many numbers we are starting our calculation with.

If you want to try and understand why this mathematics trick works you can try and simplify this method to the case where we’re considering only two linear distances. By looking at this method “visually” it should be easy enough to see why the procedure works…

Anyway, let me state out clearly the approach we’ll use in these vids, we’re interested more into understanding how certain Statistical tools and methods came into being, we’ll look in detail into what these tools really describe and what’s their actual meaning and usage, rather than laying out the detailed mathematics and the actual procedure to calculate them. We’ll look at these last two subjects only to the extent needed and useful to understand the meaning and utility of each tool that we’re going to cover.

So, for this post the two important takeaways for the concept of Statistical “mean” or “average” are the fact that when using the “mean” what we are really doing is that we are attempting to generalize a bunch of other values, observations, so we’re looking for a quick, synthetic way to represent them all… and that we are at the same time accepting to pay a little price for this usefulness. The price is that our “mean”, average, value won’t be exactly equal to anyone of the values It represents, expect very special cases, but it will only be good enough to approximate them all by being as much as possible equidistant from each one of these.

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Learn all about Sports Analytics here.mean

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]]>The post Sports Analytics Methods – Normality Tests appeared first on Agile Sports Analytics.

]]>Sport coaches, managers and analysts are often found to attribute the performance of players in a team to various factors such as speed, height, body weight, jump power, etc. This enables the analysts to ascribe a player’s performance to certain factors, and then look out for a trend to create a distribution. However, because the distribution may not be normally well-modeled to truly represent the factor responsible for the performance of the players, a test of normality is carried out to establish the acceptability or rejection of the hypothesis made about each of the players. This allows analysts to determine the particular factor or skill that is largely or lowly responsible for the performance of the players.

**VARIOUS TECHNIQUES USED TO TEST THE NORMALITY OF A DISTRIBUTION**

There are many techniques adopted for normality tests, which includes the Chi-square test, Kolmogorov—Smirnov, Lilliefors, Shapiro—Wilks, and the Anderson Darling test. However, in sport analytics, Kolmogorov-Smirnov and the Shapiro—Wilks tests are most often preferred.

The difference between the two tests is the number of values that are present in the overall samples. Shapiro-Wilks test works for values below 50, while Kolmogorov-Smirnov test is used for values greater than 50. For example, after a football game, if the performance of players in two different teams is to be statistically estimated based on certain factors, Shapiro—Wilks test is used because the totality of the players is 22.

**HOW NORMAL DISTRIBUTION IS ADOPTED FOR TEST OF PERFORMANCE IN SPORTS**

Normal distribution is often used to represent random variables whose distributions are not known. For instance, say a rating system has been established for players and by statistical sample, the rating shows that the performance of the bulk of the players in a team is average (50%), while smaller number of players have a rating of 70% or 30%. And even smaller percentage of players have a rating of 90% or 10%.

This statistical data creates a kind of symmetrical graph where half of the data falls to the right of the mean, and the other half to the left. Mind you, this rating system is based on factors such as speed, height, body weight, and jump power. Now, what is the evidence that the normal distribution of the players is true based on the factors mentioned above? This is why sport managers go for the test of normality to determine if the data set such as above has been modeled correctly by the normal distribution.

**HOW IS SHAPIRO—WILKS TEST USED IN SPORT ANALYTICS?**

Shapiro – Wilks test follows a concept of null hypothesis, which works based on two factors—alpha level and p-value. In sport analytics, an example of null hypothesis is: “the height of a player doesn’t determine how many goals the player scores in a match.” This hypothesis is subjected to acceptance or rejection. If perhaps the null hypothesis statement is rejected because it is found to be true, the probability of rejecting such hypothesis is called “significant level” which is set to be 5%. That is, it is acceptable to have a 5% probability of incorrectly rejecting the null hypothesis. This significant level is called “alpha level”.

The p-value is called the “probability value” and it is the probability that when null hypothesis is true, the statistical result (for instance the sample mean different between two teams) would be greater than or equal to the actual observed results. It is this p-value that is used to quantity the statistics of normality. If the p-value is less than the alpha level, then the null hypothesis is rejected.

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]]>The post Sports Analytics Methods – Computational Simulation appeared first on Agile Sports Analytics.

]]>More than 10 years ago, Honeywell’s aerospace engineer, Barry Bixler, thought of joining aerospace simulation with sports and used Fluid Dynamics in his spare time to analyze the flow pattern around the arms of swimmers.

**Swimmers**

The swimming teams perceived the potential of the Bixler’s studies and began to apply their recommendations to improve the performance of the athletes.

Since then, computational simulation has been gaining ground and is gradually applied in different ways in sports to improve athletes’ performance, ensure comfort and reduce the risk of injury. This happens because the simulation allows predicting the behavior of a device, an athlete or a system that involves the athlete, devices and sports equipment under certain conditions.

**Simulation in Sport**

To be able to predict the behavior of these models, the simulation technology solves fundamental equations, such as conservation of mass, conservation of energy, Newton’s second law or Hooke’s law of elasticity to calculate magnitudes as speed, pressure, tension, deformation etc. Even the simplest models can provide interesting information about a system made up of the athlete, the equipment and the environment that surrounds them.

Through computer-based modeling, it is possible to determine and understand how parameters can impact sports performance and minimize or amplify an injury. Analyzing and foreseeing the consequences of these modifications means that sports team designers can better select the set of parameters to optimize performance and reduce the risk of injury. In addition to this, manufacturers can quickly launch improved products to the market and with a lower development cost.

**The Value of Simulation Engineering in Sport**

To better understand what is the importance and impact of these tools in sport, the report, “Dramatic Changes in Sports: The Contribution of Engineering Simulation” indicates how three different specialists focus on contributions that computer simulation made and can do in what refers to the most varied sports, whether high performance or not.

In order to make these computational models more and more realistic, there is a tendency to create and test more complex models and predict their behavior. New capacities are also added to interpret the environment, increase the fidelity of the models and incorporate combinations based on a system composed of the athlete, the product and the environment.

The simulation is already applied – occasionally and sometimes systematically – in different sports and has brought significant achievements in either performance or comfort. It also allows analysis of isolated products as well as complex and complete systems, taking the simulation to a deeper and more detailed study. This is important in the case of cycling, where the two main performance parameters of the athlete are aerodynamics and weight.

The reduction of the weight of the bicycle can be achieved, without compromising aerodynamic resistance, by means of variations in the geometry of the different components and the use of new materials, such as composites. In addition, the position, the comfort of the athlete and the format of the components of the bicycle are decisive for a good performance. However, it is important to note that to improve overall performance, in addition to optimizing each subsystem, it is important to understand that the final result depends on the interaction of the entire system, therefore, the performance of the system as a whole is essential, instead of optimizing each component in isolation.

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]]>The post Sports Analytics Methods – Sentiment Analysis appeared first on Agile Sports Analytics.

]]>**What is sentiment analysis? **

When we talk about Sentiment Analysis (also called Mining of Opinions or Emotional Artificial Intelligence), we are referring to a series of applications of natural language processing techniques, computational linguistics and text mining, which aim to extract subjective information from generated content by users such as comments on blogs, social media, etc.

With this type of technology, we can extract a tangible and direct value, such as “positive”/”negative”, from a textual comment.

**Depth of analysis**

To speak of Mining of Opinions is to speak of an increasingly extensive field related to the analysis of the subjective components that are implicit in the contents generated by the users. Within this field, there are applications that perform a more or less profound analysis of the textual content, depending on the task or problem that you want to solve. In general, we find two types of tasks related to Mining Opinions:

- Polarity detection: This refers to being able to determine if an opinion is positive or negative. Beyond a basic polarity, you can also obtain a numerical value within a certain range, which in a certain way tries to obtain an objective rating associated with a certain opinion.
- Analysis of sentiment based on characteristics: This refers to determining the different characteristics of the product, personality or team treated in the opinion or review written by the user, and for each of those characteristics mentioned in the opinion, be able to extract a polarity. This type of approach is much more complex and much finer than the detection of polarity.

**Relaying it to sports**

Relating sentiment or emotional AI to sports, for example, we live in the era of the “experts” of football, of deep analysis and of special guests who are ex-technicians and ex-football players who manage and weave countless possibilities. This generation of wise men analyze corner shots, make sketches on blackboards and between questions and answers assemble alignments and predict results. It is the intellectual age of football that has caused a notable influence on managers, coaches and footballers. Nobody escapes excessive criticism.

**From the show to the commercialization **

For those who have the opportunity to see soccer players and national teams, such as Brazil and Germany, get an exciting match every tie.

In the past, journalistic specials were unavoidable without the topic of “Pelé” being touched upon.

After the Argentina World Cup 78, soccer as a show and as a business began to take commercial roots. From the quality and brilliance of the Brasileirao, we passed to the skill and “malice” of the Argentineans without stopping recognizing the birth of new stars such as Diego Armando Maradona that led to the second albiceleste title in Mexico 86. There began sentiments.

The soccer world relives the golden stage of a rivalry created at the beginning of sports analysis, between Argentines and Brazilians. To be more concrete, between Pelé and Maradona. Who’s the best? This first controversy flooded the South American soccer world of an absurd rivalry that was well-taken advantage of by the merchants of the best spectacle of the world. From there, fierce rivalry and sentiments took over the football world.

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]]>The post Sports Analytics Methods – Bootstrap Simulation appeared first on Agile Sports Analytics.

]]>There are two categories of golf competitions. In a stroke play competition the player with the fewest strokes wins the game. In match play, the player who wins the greatest number of holes wins the game. As each golfer is unique, having a unique set experience and expertise, a handicap system has been devised in order to put players at a more even level with each other, in order to create fairer competitions.

A handicap indicates how well a person plays compared to par when they are playing their best. At the end of a competition that uses handicaps, the players’ handicap is subtracted from their score and the person with the lowest score at that point wins the match. In a match play game the process is more complicated in that the strokes a player ‘gives’ their opponent depends not only upon their own handicap but also on the ranking of each hole.

This research looks at whether the current handicap system allows for a truly fair game or if another approach could be more effective at providing each player with the same probability of winning the match. Data was collected from four casual stroke play tournaments held at the Shaughnessy Golf and Country Club in Vancouver, Canada including the player’s handicap and their scores on each of the 18 holes.

The data was graphed which indicated that the players’ handicaps and performance were equivalent. The graph also indicates that the net score for those with middle to high handicaps were more varied than the net score for those with a low handicap.

In order to calculate the over-all win percentages a bootstrap simulation approach was used. The 73,512 matches were sampled with replacement a total of 10,000 times. Following this, the win percentage was determined at each handicap differential using the same method.

Theoretically, the current handicap system should give each player a 50% chance of winning. This simulation calculated that the better player actually won 53% of the time indicating a bias in the current system towards the player with the lower handicap.

Three possible changes to the system are proposed: create three new hole rankings, change the holes to which the handicap differential is applied, and vary the number of extra strokes given to the weaker player. Giving an additional 0.5 strokes to the weaker player created the fairest outcome of all the scenarios.

Information from bootstrap simulation provides analysts with an additional tool in determining likely outcomes of different matches, as the current system appears to favour the better player. Golf courses and tournaments could use this information to develop a handicap system that is fair to all players, allowing for an optimal level of competition.

**Analytics Used: Distribution Graph, Bootstrap Simulation**

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]]>The post Sports Analytics Methods – Three Dimensional Markov Model appeared first on Agile Sports Analytics.

]]>Curling enjoys great popularity in Canada and is on the rise in the United States. This study models curling as a Markov process to estimate win probabilities of different states during a curling match.

Score information was entered into the model from the matches played from 1998 to 2014 in the Canadian Men’s Curling Championships, including the year of the match, round of the tournament, match location, teams competing, score in each end, final score, time remaining for each team, and which team started with the hammer in the first end.

In order to use the Markov method all possible scenarios that can occur during a game must be defined. All possible state transitions and their associated probabilities must also be known. This data is used to create a three-dimensional Markov model using three states – the end being played, hammer state, and score differential. The purpose of the three-dimensional Markov model is to determine the expected win probability for any team based on the current state of the game and taking into account all possible future transition states and their associated probabilities.

Two models were created: 1) a homogeneous model that assumed that state transitions were strictly a function of hammer possession and independent of any other parameters and, 2) a heterogeneous model, which assumed state transitions were dependent on other parameters. The results from both models were very similar with the exception of increased accuracy of the heterogeneous model in predictions of state transition towards the end of the game, specially the tenth end. Strategy at that point of the game is typically different from that employed earlier in the game. A team that is down by two points will choose very different strategies from a team that is up one point.

Teams can use the information to determine when to score one point and give up the hammer or blank the end to maintain possession of the hammer. The Markov process takes into account not only the team’s probability of scoring a point but also the effects of lost opportunities. The model will also aide teams in deciding when they should concede a game. The analysis actually determines that teams should concede less often than they currently do. Current decisions appear to be at least partially based on psychological conditions rather than statistical analysis.

Analysts can use the Markov model to graph the expected win probabilities for each team over the course of a game. This provides the ability to relay information to viewers in a clearly understandable manner. It also gives them opportunities to more deeply delve into how effective a team’s choices are, or if alternative choices should be made in any given situation.

This Markov model provides the ability to analyze the game of curling at a deeper level than was previously possible.

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]]>The post Sports Analytics – Multivariate Statistical Analysis appeared first on Agile Sports Analytics.

]]>Many statistical methods can be performed using ordinary pocket calculators. But, this is not the case with multivariate statistical analysis. For its execution, a computer is needed and a statistical program, which are offered on the market. In such conditions, even untrained and inexperienced people can perform complex multivariate statistical procedures, which is a double-edged sword, because, although the result is relatively easy and fast, there is a great chance to make a mistake.

Multivariate statistical analysis has been present in the sciences for almost a century. However, its application in economic research began in the late 1950s. Eventually, applications of multivariate analysis have become more and more frequent since they were increasingly appreciated by both scientists and businesses.

Prior to multivariate statistical analysis, most researcher used analysis that treated at most two variables at the same time. As a product of such analysis, results were most commonly reported as central tendencies (arithmetic mean, modus, median …), variation measures (variance, standard deviations, quarters…), confidence intervals and tests based on a normal schedule, t-schedule and similarly. The longest range in the study of the relationship of two phenomena was the correlation coefficient.

Multivariate statistical analysis has provided much more powerful techniques that enabled researchers to detect patterns of behavior in the interrelation of a large number of variables, patterns that would otherwise be hidden or barely noticeable.

In sports, multivariate statistical analysis can be used to determine the development of functional abilities of a group of soccer oriented athletes. In the experimental group of soccer-oriented respondents, the “circular” form of exercise was implemented for the additional 33 hours of motor exercises. Determining the load level as part of modeling the program for functional abilities development was in accordance with the individual abilities and characteristics of the respondents. Particular care was taken to ensure that the dosage of the load has a gradual and progressive character in all its components (intensity and extensiveness). The selection of the methods of exercise applied in the “circular” form of exercise for the functional abilities development was in the function of achieving goals and tasks, raising the level of preparedness, respecting the age characteristics and conditions in which the experimental program was realized. The organizational form of the “circular” form of work was carried out within homogenized groups. Transformation of functional abilities in both sub units during experimental treatment was determined by analyzing variance at the multivariate level.

The other purpose of multivariate statistical analysis in sport is determining which team has chances of winning in a competition. This is achieved by using principal component and cluster analysis based on the previous results of every sport’s team. After determining the principal components, first and second were used as new data and cluster analysis was used to divide them into two groups. The multivariate statistical analysis made it possible to crystallize the more and less successful teams within the groups.

Multivariate statistical analysis in sports is most appropriate when a researcher wants to analyze the relationships between multiple variables (more than two), and simultaneously according to the appropriate model on which this technique is based.

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]]>Mathematics is pervasive; it is virtually everywhere – around us, in our day-to-day activities and, of course, in sports. In fact, they become increasingly important in this domain, be it in professional or amateur sport. For example, mathematics programming helps in the improvement of performance, new technologies, technical revolutions, etc. Mathematicians deal with the themes of sport and performance in different ways. Thus, let us discover together and more precisely, how the practice of mathematics has an effect on the sport.

From birth, children discover numbers and geometric shapes, and adults continue to use mathematics in their day to day activities.

Sports and managing high-level athletes is a big business, and thus rely on big business solutions to gain a competitive edge. This is where analytics come in. Mathematical equations are a scientific basis that have become essential in all high-level sports. They lay the foundation of work for athletes who do not stop refining their technique to obtain better results.

**Breaking records with mathematics**

Mathematics can be applied to sporting activities to break records. For instance, Javier Sotomayor has the record of high jump since 1993 and nobody has managed to beat his 2.45 meters until today.

Do you all remember the 2009 World Swimming Championship in Rome? The records were shattered one after another and journalists could not understand this phenomenon. In total, 43 records were broken and set during this period. You have to think that the performance of swimming is measured by the principle of submerged movement, well known in physics, and therefore involves mathematical calculations. Vertical and horizontal forces are exerted and the Archimedes principle also influences it. How is it possible for athletes to continue breaking records? Does the human body have a defined physical limit for performance?

Mathematics helps us with questions concerning how records can be broken and if there is a physical limit to the human body’s performance. A study of September 2012 has shown that the classifications are governed by a mathematical law: the law of power. This law relates two elements: the frequency of an event and its size.

**Technology at the service of sport**

The advancement of sports equipment is making a big impact on sports science. The combinations of some equipment improve the time spent by swimmers to cross a specific borderline. It’s the same thing that has happened in cycling: the technical improvement of bicycles plays a fundamental role in improving performance. Lighter and more aerodynamic materials help in penetrating the air with minimal resistance.

**Mathematics to improve the technical skills of athletes**

If mathematics can help you manage your money and calculate percentages in your math courses, then they can also help you with sports. For instance, mathematics allows you to determine the trajectory of the ball. Therefore, it should not surprise us that sport rely heavily on algebra, geometry, multiplication tables, arithmetic, whole numbers, proportions, etc. Athletes no longer go to competitions accompanied only by their coach, their physiotherapist or their nutritionist. As times have changed, now there are other types of professionals who accompany the team. For example, the Australian or the New Zealander team in the J.J.O.O. 2016, had real mathematicians on their team. Their function was to gather data and take into consideration the context to develop statistics to optimize athletic technique in all possible parameters. The goal is clear: to achieve perfection in the discipline and optimize training.

**Mathematics in preparing football tournaments**

Mathematical analysis is also taken into account in the selections of football teams, since the selectors use it when they have to make the list for a big sports event. The analysis of team performance and the development of mathematical models allow strategic choices based more on logic than on the “instinct of the coach”. It is true that it is something complex, but it can make the difference between a victory and a defeat.

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Find out how Sports Analytics Expert Victor Holman can give your team the competitive advantage.

How mature is your team’s analytics program? Take the Sports Analytics Maturity Assessment.

Learn about the Groundbreaking Sports Analytics Model coaches and sports analysts are talking about!

Learn all about Sports Analytics here.

The post Sports Analytics Methods – Mathematical Programming appeared first on Agile Sports Analytics.

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