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eBA Encyclopedia Statistics Terminology: Unusual Event
In statistics, an unusual event is an event that has a low probability of occurring. ( Typically, but not always, it has a probability less than 5%. )
"...in terms of statistics, as we are discussing in the eBA Statistics Permanent Clinic, which of two events is the more unusual ? How we would decide, by example, which of the following two basketball events is the more unusual:
a. A 90 points scored game from Los Anageles Lakers.
b. A 100 points scored game from San Antonio Spurs. ..."
One would examine previous results records and note the relative frequency of 90+ point games for Los Angeles Lakers, and 100+ points games for San Antonio Spurs. Thus, relative frequencies are one method of estimating the probability of each event.
The first column shows the typical activity in each scene and the placement of the monitors. The other columns show examples of detected unusual events. We mark the median position of alerting monitors. In these scenes, the detected events gave rise to flows in an unlikely direction.
Please click here to see the enlarged image, opening a new Tab.
Note that the smallest frequency is the more unusual event. The more comprehensive explanation and relation with basketball themes are exposed at the eBA Basketball Basketball Statistics System.
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eBA Encyclopedia Statistics Terminology: About the Concept... 'histogram'
"... What is a histogram? ..."
A histogram is a way of summarising data that are measured on an interval scale (either discrete or continuous).
It is often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient form.
It divides up the range of possible values in a data set into classes or groups.
Graphic: eBA Basketball Encyclopedia
For each group, a rectangle is constructed with a base length equal to the range of values in that specific group, and an area proportional to the number of observations falling into that group.
This means that the rectangles might be drawn of nonuniform height.
All the terms in this answer are explained widely at The Global Basketball Encyclopedia and in eBA ONLINE.
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Basketball Statistics Terminology: The Standard deviation
In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma). It is defined as the square root of the variance.
To understand standard deviation, keep in mind that variance is the average of the squared differences between data points and the mean. Variance is tabulated in units squared. Standard deviation, being the square root of that quantity, therefore measures the spread of data about the mean, measured in the same units as the data.
Said more formally, the standard deviation is the root mean square (RMS) deviation of values from their arithmetic mean.
For example, in the population {4, 8}, the mean is 6 and the deviations from mean are {−2, 2}. Those deviations squared are {4, 4} the average of which (the variance) is 4. Therefore, the standard deviation is 2. In this case 100% of the values in the population are at one standard deviation of the mean.
The standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large. If all the data values are equal, then the standard deviation is zero.
For a population, the standard deviation can be estimated by a modified standard deviation (s) of a sample.
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eBA Encyclopedia Statistics Terminology: The Statistics Heritability Concept
Heritability is basically a statistical concept.
The chart to the center is the famous one used by Francis Galton to show the relationship between the height of parents and the height of offspring.
Heritability is the slope of the line of best fit for the data.
If there is a perfect fit, then heritability is ~ 1.
If there is no relationship then heritability is ~ 0.
Heritability tells you your expectation of the offspring trait value if you know the value of the parents.
Graphic: eBA Basketball Encyclopedia
Now, if you have a trait where there is no variation then obviously heritability is an incoherent concept.
If all the parents have value X and all the offspring have value X, and the whole population is of value X, then the chart to the left would simply display a point in space.
That point wouldn’t yield up any regression line. That does not mean that the trait is not genetic, rather, there is simply no phenotypic variation which is useful for statistical analysis.
With Data from our eBA Encyclopedia
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eBA Encyclopedia Statistics Terminology: The Statistics Heuristic Method Concept
Heuristic ( /hjʉˈrɪstɨk/; or heuristics; Greek: "Εὑρίσκω", "find" or "discover") refers to experiencebased techniques for problem solving, learning, and discovery.
Where an exhaustive search is impractical, heuristic methods are used to speed up the process of finding a satisfactory solution. Examples of this method include using a "rule of thumb", an educated guess, an intuitive judgment, or common sense.
In more precise terms, heuristics are strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.
Graphic: eBA Basketball Encyclopedia
A heuristic is a particular technique of directing one's attention in learning, discovery, or problemsolving.
The popularization of the concept is due to the mathematician George Polya, in his book How to Solve It: A New Aspect of Mathematical Method.
It is originally derived from the Greek "heurisko" (ευρίσκω, the verb from which Archimedes's famous exclamation of "eureka" was derived), which roughly means "I found". The term was introduced in the 4th century AD by Pappus of Alexandria.
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eBA Encyclopedia Statistics Terminology: Statistical Classification
In machine learning, statistical classification is the problem of identifying the subpopulation to which new observations belong, where the identity of the subpopulation is unknown, on the basis of a training set of data containing observations whose subpopulation is known.
Therefore these classifications will show a variable behaviour which can be studied by statistics.
Thus the requirement is that new individual items are placed into groups based on quantitative information on one or more measurements, traits or characteristics, etc. and based on the training set in which previously decided groupings are already established.
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eBA Encyclopedia Statistics Terminology: Pie Chart or Circle Graph Statistics
A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents.
When angles are measured with 1 turn as unit then a number of percent is identified with the same number of centiturns. Together, the sectors create a full disk. It is named for its resemblance to a pie which has been sliced. The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801.
The pie chart is perhaps the most ubiquitous statistical chart in the basketball statistics analysis. However, it has been criticized, and some recommend avoiding it, pointing out in particular that it is difficult to compare different sections of a given pie chart, or to compare data across different pie charts.
Pie charts can be an effective way of displaying information in some cases, in particular if the intent is to compare the size of a slice with the whole pie, rather than comparing the slices among them.
Pie charts work particularly well when the slices represent 25 to 50% of the data, but in general, other plots such as the bar chart or the dot plot, or nongraphical methods such as tables, may be more adapted for representing certain information. It also shows the frequency within certain groups of information.
A pie chart displays data as a percentage of the whole. Each pie section should have a label and percentage. A total data number should be included.
Advantages
• Visually appealing
• Shows percent of total for each category
Disadvantages
• No exact numerical data
• Hard to compare 2 data sets
• "Other" category can be a problem
• Total unknown unless specified
• Best for 3 to 7 categories
• Use only with discrete data
With data from our eBA Encyclopedia
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Sunday's Reflexions on Basketball Statistics:
ATS Definition in Sports Statistics and Betting
ATS stands for 'Against The Spread' and is not used in statistics analysis but is a betting term:
there are two manners of betting sides: the moneyline and against the spread. To bet against the spread is to make a wager that will be decided by adding points to one team or the other after the game is played.
Basically the spread allows you to bet on a fair contest where the underdogs are given a theoretical points advantage.
The ATS stats refer to the wins, loses and ties corresponding to the spread results, ATS stats are consequently more a means of judging overperforming / underperforming teams rather than successful / unsuccessful ones which a classic league table exposes.
Example: John bet against the spread that the Lakers (7) would beat the Bulls. That means the Lakers would have to win by more than 7 points for John to win his bet.
This topic is resumed in the eBA Basketball Statistics Analysis System
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eBA Encyclopedia Statistics Terminology: The Bell Curve Method Concept
When I was asked how to calculate the winning percentage to points scored and allowed, I brought to account the "Correlated Gaussian Method":
"... It is a method that relates winning percentage to points scored, points allowed, the standard deviations of points scored and allowed, and the correlation between points scored ( which can be replaced with offensive rating ) and points allowed ( which can be replaced with defensive rating ) ..."
Now, the Bell Curve Method, also related to points scored and allowed, is in a relative manner a more hypothetical and close approximation to associating points scored and allowed to a team's winning percentage, based on the premise that the arrangement of values for teams' points scored and allowed are normally spreaded and can be reduced from each other to create another randomly staged random variable, net points.
In statistics and probability theory, Gaussian functions appear as the density function of the normal distribution, which is a limiting probability distribution of complicated sums, according to the central limit theorem.
With data from our eBA Encyclopedia
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eBA Encyclopedia Statistics Terminology: Inferential Statistics
Inferential statistics refer to the use of current information regarding a sample of subjects in order to
(1) make assumptions about the population at large and/or
(2) make predictions about what might happen in the future. The basic statistical methods explained in the previous chapter are used a great deal in inferential statistics, but the data is taken a step further in order to generalize or predict.
We can easily determine the mean of a known sample of subjects by adding up all of their scores and dividing by the number of subjects.
The mean of a sample is therefore a known variable.
To determine the mean of the population that has not been testing or to predict the mean of a test that has not yet been taken requires the researcher to make assumptions because these variables are not known to us.
The goal of inferential statistics is to do just that  to take what is known and make assumptions or inferences about what is not known.
With data from our eBA Encyclopedia
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