As climbers, we are constantly looking for ways to improve. We train strength, endurance, technique, but how do we know if what we do really works? How do we compare our progress or understand the results of a physical test? The answer lies in statistics, an essential tool that helps us interpret data and make informed decisions about our training.

In this post, we’ll demystify some key statistical concepts that will allow you to better understand the assessment of your physical qualities and how they are used to measure your performance and progress.

1. The Basics: Describing and Inferring

Statistics, although sometimes intimidating, is simply the science of data. It is divided into two main branches:

Descriptive Statistics: Its goal is to tell what is there. It uses tables, numbers, labels, and graphs to show how the values obtained from a measurement are distributed. For example, if we measure the heart rate of 50 young climbers and present that data in a table, we are doing descriptive statistics.
Inferential Statistics: This is the tool that allows us to go beyond the measured data and make hypotheses about a larger set (the population) from which the data originate, but which we have not measured completely. For example, if the average heart rate of our sample of 50 young climbers is 85 bpm, inferential statistics would allow us to estimate what the average would be for all young climbers in Spain, assuming a margin of error.

To understand this, two concepts are key:

Population: The total set of phenomena we want to study. For example, all climbers who onsight above 7a on rock.
Sample: A subset of that population that is accessible and measurable, and which we select to study. For example, 17 onsight 7a climbers participating in a study in Granada.

2. Types of Variables: What Are We Measuring?

Not all data behave the same. Variables are any information that can be measured:

Nominal or Categorical: Labels without numerical order or meaning. Only used for classification. Examples: sex, province of birth, yes/no.
Ordinal: Have an intrinsic order (we can say one value is “greater” than another), but we cannot perform mathematical operations with them or determine equal distances. Example: the order of arrival in a race without measuring times. Also used for training frequency (never, rarely, sometimes, etc.).
Numerical (or Interval): Allow mathematical operations (add, subtract, multiply, divide). An example is time. If Juan took 4 minutes and Pepe 1 minute, we can say Juan took 4 times longer. It’s important to remember that every numerical measurement carries a measurement error, so values represent an interval.

3. The Special Case in Climbing: French Grades to IRCRA

A very relevant example of “variable change” in climbing is the one proposed by the International Rock Climbing Research Association (IRCRA) in 2016. The traditional French grading scale (e.g., 6a, 6a+, 6b) was an ordinal variable: we could say 7a+ is harder than 7a, but not that the “distance” in difficulty between 7a and 7c+ was the same as between 7b and 8a+.

Switching to the IRCRA scale converts these labels into equivalent numerical values (e.g., 7a is 17, 7c+ is 22, 8a+ is 24). This transforms route difficulty into a numerical variable with which we can perform operations. Now, it’s correct to say that the difference in difficulty between a 7a (17) and a 7c+ (22) is 5 points, just like between a 7b (19) and an 8a+ (24).

4. Summarizing Data: Measures of Central Tendency and Dispersion

To understand a dataset, we use:

Measures of Central Tendency: Tell us around which value the data are organized.
- Mode: The most repeated value. Can be calculated for any type of variable.
- Median: The central value once the data are ordered, leaving the same number of data on each side. Useful for ordinal and numerical variables.
- Mean (or average): The sum of all values divided by their number. Only for numerical variables.
Example: If the hang times to failure are 22, 20, 25, 23, 22, 26, 30, 18, 25 seconds, the mode is 22 and 25 (bimodal), the median is 23, and the mean is 23.44 seconds.
Measures of Dispersion: Indicate how close or far apart the values are.
- Range: The difference between the maximum and minimum value. A “rough” measure dependent on the scale.
- Standard Deviation: The most common measure for numerical variables. Tells us how much the data deviate from the mean. A higher value indicates greater dispersion. It is the square root of the variance.
- There are also mean deviation and variance.
For the previous hang times, the range is 12 (30-18) and the standard deviation is 3.34 seconds.

5. Relating Variables: Dependence and Correlation

In an experiment, we often look for the relationship between two variables:

Independent Variable (x): The one whose values we can “choose” or “change.” It does not depend on the other.
Dependent Variable (y): The one we measure and whose values are the result of the experiment. It depends on the independent variable.

Example: If we want to know how the size of an edge affects hang duration, the edge size is the independent variable (we choose it) and the hang duration is the dependent variable (what we measure).

Covariation: Indicates if the increase or decrease of one variable is associated with that of another. If both increase or decrease together, they covary positively; if one increases and the other decreases, they covary negatively.
Correlation: A statistical measure that quantifies the strength and direction of the linear relationship between two variables. The correlation coefficient (r) ranges from -1 to 1:
- Positive (close to 1): Strong positive covariation.
- Negative (close to -1): Strong negative covariation.
- Close to 0: Little or no linear relationship.
- The coefficient of determination (R²) is the square of r (always between 0 and 1) and tells us what percentage of the variability of the dependent variable is explained by the independent variable.

Important! Correlation does not imply causation. That two variables are correlated does not mean that one causes the other. There must always be a causal mechanism that explains it. For example, the correlation between carrying an umbrella and wearing rain boots does not mean one causes the other; both are caused by rain.

6. The Regression Line: Predicting the Future (With Caution)

The regression line (or trend line) is the straight line that best fits the cloud of points of two correlated variables. It is mainly used to predict a value of the dependent variable (y) from a value of the independent variable (x) that we have not previously measured.

Practical climbing example: If we have data correlating an “F Indicator” (FI) with the Grade of Difficulty (GD) on the IRCRA scale, and we obtain the regression equation GD = 0.79 * FI + 13.13 with an excellent R² of 0.90. If a climber has an FI of 9.9, we can predict their expected GD is 20.95, approximately a 7c (21 on IRCRA).

Attention! If we want to predict the value of the independent variable (x) from the dependent (y), we must calculate a reverse regression line (x on y), not simply solve for x in the first equation.

7. Beyond Correlation: Intraclass Correlation Coefficient (ICC)

When we assess the reliability of a test (i.e., if it gives us consistent results in repeated measurements), we use the Intraclass Correlation Coefficient (ICC). The ICC measures the overall agreement between two or more measurements of quantitative variables. Its values range from 0 to 1:

< 0.40: Poor
0.40–0.59: Fair
0.60–0.74: Good
0.75–1: Excellent

Conclusion: Statistics as Your Ally on the Wall

Understanding these basic statistical concepts won’t make you an expert, but it will give you a solid foundation to better interpret physical tests, understand scientific studies, and ultimately make smarter, data-driven decisions about your training. So next time you do a test, think about the variables, the correlations, and how those numbers are telling you about your path to the top!

Understanding Statistics to Optimize Your Training