I climb, so I wanted to know if finger endurance actually lines up with harder climbing grades.

I’m comparing critical force (CF) and W-prime (W’) for both sport climbing and bouldering.

• The dataset comes from Giles et al.’s climber testing research.
• It has 121 climbers, including 80 sport grades and 72 bouldering grades.
• Grades use the IRCRA scale, so they’re not directly V-grades or Yosemite grades.

CF: how much force a climber can keep producing as the finger muscles fatigue.

\[CF_{relative} = \frac{CF\ (kg)}{body\ mass\ (kg)}\times100\]

W’: the extra force-time impulse available above critical force during the test.

\[W'_{relative} = \frac{W'}{body\ mass}\]

Both measures are adjusted for body mass so climbers are easier to compare.

I used correlation to measure how strongly two things are related.

\[r = \frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum(x_i-\bar{x})^2\sum(y_i-\bar{y})^2}}\]

I also used a simple regression line:

\[\hat{y} = b_0 + b_1x\]

A bigger positive \(r\) means a stronger positive linear relationship. It doesn’t prove cause and effect.

cor(sport$cf, sport$sport)
cor(boulder$wp, boulder$boulder)

sport_fit <- lm(sport ~ cf, data=sport)
summary(sport_fit)

I used these to check the correlations and fit a line through the data.

There is a clear positive trend (r = 0.78). Higher CF generally goes with harder sport grades.

W’ also has a positive relationship with bouldering grade (r = 0.57).

CF has the stronger relationship with sport climbing. W’ has the stronger relationship with bouldering in this sample.

Hover over the points to compare each climber’s CF, W’, and sport grade. Color shows W’.

• Finger performance is related to climbing grade, but different measures matter more for different disciplines.
• Sport climbing: CF was the stronger measure in this dataset.
• Bouldering: W’ had a stronger correlation than CF.
• That’s a relationship, not proof that training one number will improve grades.

These are self-reported climbing grades from an observational dataset.

Technique, experience, body position, and training history also affect climbing. The graphs only look at one finger measurement at a time.

• Giles et al. (2021), An All-Out Test to Determine Finger Flexor Critical Force in Rock Climbers.
• Data from Critical-Force-Visualization.