SLM 275: Principles of Sport Analytics Lecture Flashcards

Comprehensive vocabulary flashcards covering principles of sport analytics, data types, descriptive statistics, hypothesis testing, visualization techniques, probability, expected goals (xG), and expected points added (EPA).

Sport Analytics

The practice of applying mathematical and statistical principles to sports and related peripheral activities.

Sport Business Analytics

The branch of sport analytics focused on business operations, such as ticketing, fan engagement, marketing, and revenue generation.

Sport Performance Analytics

The branch of sport analytics focused on on-field activities, including player evaluation, tactics, match performance, and athletic tracking.

Six Steps of the Data Analysis Process

The sequential six-stage framework for data projects: 1) Define the problem, 2) Collect Data, 3) Data Cleaning, 4) Analyzing the Data, 5) Data Visualization, and 6) Presenting the Data.

Data Management

The practice of collecting, organizing, protecting, and storing an organization's data so it can be analyzed for business decisions.

Delimiter

A character (such as a comma) used to separate individual data items, helping split raw unstructured text into defined columns in programs like Excel.

Qualitative Data

Unstructured or semi-structured data collected via methods such as interviews, field observations, or questionnaires that describes qualities, opinions, and characteristics rather than numerical quantities.

Quantitative Data

Factual information that is counted or measured in numerical values, organized systematically by variables and observational units.

Variable

A measurable characteristic of an observational unit (person, place, or thing) that can assume different values.

Constant

A known value or quantity within an analysis that remains fixed and does not change across observations.

Nominal Variable

A categorical scale of measurement where values merely assign a label or category name without inherent ordering, ranking, or quantitative meaning.

Dichotomous Variable

A specific type of nominal variable that has only two mutually exclusive values (also known as a binary variable), such as True/False or $1$/$0$.

Ordinal Variable

A categorical variable whose values can be ranked or ordered along a dimension to reflect greater or lesser amounts, though intervals between points are not equal.

Likert Scale

A survey rating scale commonly used to measure unobservable constructs (such as satisfaction or fan identity) where ordered values indicate degree of agreement, but numerical differences between scale points are not mathematically uniform.

Discrete Variable

A quantitative variable obtained by counting, characterized by gaps or interruptions such that the number of permitted values across any interval is finite and countable.

Continuous Variable

A quantitative variable obtained by measuring that can assume an infinite number of values within a specified continuous interval.

Descriptive Analytics

The branch of analytics focused on summarizing, organizing, and describing historical data to explain what happened.

Predictive Analytics

The branch of analytics that uses historical patterns and statistical models to forecast what will happen.

Prescriptive Analytics

The most advanced tier of analytics that focuses on optimization and decision recommendations to determine how to make a desired outcome happen.

Central Tendency

A statistical summary that identifies the central or typical representative value of a dataset, most commonly quantified by the mean or median.

Mean

The mathematical average and balance point of a distribution, calculated by dividing the sum of all observed values by the total count of values ($\bar{x} = \frac{\sum x}{n}$).

Outlier

An extreme observation located far away from the center of a distribution that can substantially distort the mean.

Median

The middle score of all observations arranged in order of magnitude, dividing a distribution into two equal halves while resisting outlier distortion.

Variance

A measure of variability calculated as the sum of squared distances between each individual data point and the distribution mean, divided by the total number of values.

Standard Deviation

The square root of the variance ($\sqrt{\text{variance}}$), measuring the typical distance data points deviate from the mean in the original unit of measurement.

Empirical Rule (68-95-99.7 Rule)

A statistical principle for normal distributions stating that approximately $68\%$ of data falls within $1$ standard deviation of the mean, $95\%$ within $2$ standard deviations, and $99.7\%$ within $3$ standard deviations.

Skewness

A measure of distribution asymmetry; positive skew features a long right tail with mean $>$ median, negative skew features a long left tail with mean $<$ median, and symmetrical distribution features mean $=$ median $=$ mode.

Database

An organized collection of structured information or data, typically stored electronically in a computer system for storage, retrieval, and updating.

Web Scraping

A programmatic extraction method used to harvest unstructured data directly from web pages.

API Scraping

A technique to retrieve structured datasets directly from a web service or platform using its Application Programming Interface.

Null Hypothesis ($H_0$)

The default statistical proposition asserting that there is no difference, change, or effect between the groups or variables being tested.

Alternative Hypothesis ($H_1$)

The statistical proposition stating the opposite of the null hypothesis, positing that a true difference, effect, or relationship exists.

P-value

The probability, assuming the null hypothesis ($H_0$) is true, of observing a sample outcome as extreme as or more deviant than the actual obtained result.

Significance Level ($\alpha$)

The pre-established probability threshold (conventionally set at $0.05$) against which the p-value is compared to decide whether to reject the null hypothesis.

Nondirectional t-Test (Two-Tail Test)

A hypothesis test evaluating whether two sample means differ significantly from one another ($\neq$) without postulating which mean is higher or lower.

Directional t-Test (One-Tail Test)

A hypothesis test evaluating whether one sample mean is specifically greater than ($>$) or less than ($<$) another mean in a designated direction.

Construct

An abstract, theoretical concept or idea for a study that cannot be directly measured and must be operationalized into concrete, measurable variables.

Baseball's Pythagorean Theorem

A formula created by Bill James estimating a baseball team's winning percentage based on runs: $\frac{(\text{Runs scored})^2}{(\text{Runs scored})^2 + (\text{Runs allowed})^2} = \text{Estimated Winning \%}$.

Bar Chart

A chart using separated rectangular bars to display and compare frequencies or metric summaries across categorical groups.

Histogram

A graphical representation of numerical data using contiguous bars without gaps to depict frequency distributions and data shapes across intervals.

Line Chart

A chart displaying a series of data points connected by straight line segments, designed primarily to show trends and changes across time.

Scatter Plot

A graph that plots individual data points on horizontal and vertical axes to display the relationship or correlation between two numerical variables.

Box Plot

A five-number summary visualization depicting data distribution through quartiles (Q1 at $25\%$, median at $50\%$, Q3 at $75\%$) and whiskers, specifically useful for identifying outliers.

Radar Chart

A two-dimensional chart displaying multivariate data across multiple axes originating from a central point, ideal for comparing multiple player stats sharing similar scales.

Probability

The proportion of times an event is expected to occur in an infinitely long series of identical sampling experiments, restricted to a range between $0$ and $1$.

Multiplication Rule (AND Rule)

A probability rule stating that the probability of the joint occurrence of independent events equals the product of their individual probabilities: $P(A \text{ and } B) = P(A) \times P(B)$.

Addition Rule (OR Rule)

A probability rule stating that the probability of either of two mutually exclusive events occurring equals the sum of their individual probabilities: $P(A \text{ or } B) = P(A) + P(B)$.

Conditional Probability

The likelihood of an event occurring given that a prior event has already occurred, calculated as $P(B|A) = \frac{P(A \text{ and } B)}{P(A)}$.

Hot Hand Fallacy

The cognitive bias and myth in sport holding that a player who makes a shot is more likely to hit subsequent shots, which early controlled empirical studies found no statistical evidence to support.

Expected Goals (xG)

A soccer metric calculating the probability (between $0$ and $1$) that a shot results in a goal, modeled using historical data and situational variables like distance, angle, shot type, and defender position.

Cumulative xG

The aggregate sum of individual expected goal values produced by a team or player over a game or entire season, measuring overall threat created.

Pearson Correlation Coefficient

A standardized measure of bivariate linear association between two continuous variables, ranging from $-1$ (perfect negative correlation) through $0$ (no linear relationship) to $+1$ (perfect positive correlation).

Game State (Football)

The specific contextual situation of a football play, defined by yard line, down, yards to go for a first down, score differential, and game clock time remaining.

Expected Value (EV)

A probability-weighted average of all possible numerical outcomes of a random variable: $EV = \sum [P(X) \times X]$.

Expected Points (EP)

An American football metric predicting the net scoring value of a given game state by calculating the expected value of the next points scored based on play probabilities ($\sum P(\text{score}) \times \text{points}$).

Expected Points Added (EPA)

The net change in expected points between consecutive game states ($\text{EPA} = \text{EP}_{\text{after}} - \text{EP}_{\text{before}}$), quantifying the individual value contributed by a play.

Completion Percentage Over Expected (CPOE)

An advanced quarterback metric that measures a passer's actual completion percentage relative to the statistical expectation based on contextual pass difficulty factors like throw depth and receiver separation.

Total Quarterback Rating (Total QBR)

An ESPN proprietary metric evaluating quarterback per-play efficiency based on an EPA framework that incorporates context, down, distance, pass difficulty, and credit division among teammates.