## In sports science, analysing and visualising data effectively is crucial for making informed decisions that enhance athlete performance. Z-scores, T-scores, and STEN scores are essential statistical tools that help compare and interpret performance metrics.

## Understanding Z-Scores

A Z-score, or standardised score, measures how many standard deviations a data point is from the mean of a dataset. It is calculated using the formula:

𝑍 = ( 𝑋 − 𝜇 ) / 𝜎

where:

*X*is the data point.*μ*is the mean of the dataset.*σ*is the standard deviation of the dataset.

Z-scores are useful in sports science as they allow for the comparison of different performance metrics on a standardised scale. A Z-score indicates how an individual's performance on a specific test compares to the mean and standard deviation (SD) of a reference group.

Given a normally distributed dataset, a Z-score of zero corresponds to the mean score, a Z-score of 1.0 represents about one standard deviation above the mean, and a Z-score of 2.0 indicates approximately two standard deviations above the mean. On the other hand, negative Z-scores reflect performance rankings below the mean.

For more on how to calculate z-scores, including different ways to calculate them in Microsoft Excel, watch this video below from our __YouTube channel__:

For instance, if an athlete's score today is 9.4, the average score is 8.1, and the standard deviation is 1.2, the Z-score would be:

𝑍 = ( 9.4 − 8.1 ) / 1.2 = 1.1

This means the score is 1.1 standard deviations above the mean, indicating above-average performance but not necessarily statistically significant.

The z-score statistic is particularly useful to allow different tests or metrics, each with different scales, to be standardised alongside each other. These are frequently presented in bar charts or radar plots (see figure below).

Remember, in some measures a negative z-score represents a better score i.e. speed tests: a lower time is better. In these cases, you can multiple the z-score by -1 to reverse the direction, allowing you to plot alongside other tests results in which positive is better.

These can be used to compare a player to the squad, a player to themselves (e.g., today's wellness against their last 28 days), as well as multiple players to a team and/or position average as demonstrated in the figure above.

## Moving Beyond Z-Scores: T-Scores

T-scores convert Z-scores into a more interpretable scale ranging from 20 to 80, where 50 represents the mean. This transformation helps in normalising scores across various metrics, making it easier to communicate results to non-statistical audiences.

The formula for calculating a T-score is:

*T *= ( *Z * 10 ) *+ 50

For example, with a Z-score of 2.1, the T-score would be:

𝑇 = ( 1.1 * 10 ) + 50 = 61

For stakeholders who do not understand standard deviation, t-scores can be useful as they put the data on a more intuitive scale between 0 and 100 (although more commonly between 20 and 80).

In an __open-access editorial in Sensors__, Dr John McMahon and colleagues (2022) presented standardised t-scores from countermovement jump data in a professional men's rugby league team. These were used to create performance bands and a traffic light system (right).

Traffic light systems can be an intuitive may to visualise data. McMahon and colleagues also demonstrated how these t-scores could be visualised across different test results and position groups (right).

## Simplifying Interpretation with STEN Scores

STEN scores, or Standard Ten scores, convert Z-scores into a simpler 1-10 scale, with 5.5 as the mean. This transformation is particularly useful for quick assessments and visualisations.

The formula for calculating a STEN score is:

𝑆𝑇𝐸𝑁 = ( 𝑍 * 2 ) + 5.5

For example, a Z-score of 0.3 would convert to:

𝑆𝑇𝐸𝑁 = ( 1.1 * 2 ) + 5.5 = 7.7

## Frequently Asked Questions (FAQs) on Sports Science Statistics

### What is a Z-score?

A Z-score indicates how many standard deviations a value is from the mean. It helps compare scores from different distributions on a standard scale.

### How do you calculate a T-score?

A T-score is calculated using the formula 𝑇=10*𝑍+50, translating Z-scores into a 0-100 or 20-80 scale with 50 as the mean.

### What is a STEN score?

A STEN score converts Z-scores into a 1-10 scale, making interpretation easier. It is calculated using the formula 𝑆𝑇𝐸𝑁=2*𝑍+5.5.

### How do these statistics help sports scientists?

Using Z-scores, T-scores, and STEN scores, sports scientists can monitor and compare athletes' performances over time. These scores help set performance benchmarks and identify areas needing improvement.

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