How wide is a grade? TCG and Factor speculation!

Climbing grades are subjective. How much harder one grade is something climbers have debated and suggested since the beginning of the grading scales. The bottom line is that it is the FAs that have added the upper grade to the scale, on different crags, who have decided how wide one grade is. On the other side, in many cases, the community have later said the FA was wrong, by upgrading or downgrading old routes.

From a practical mathematical point of view, it seems that a factor of six multiplying the number of routes and boulders for a lower grade, is one way of describing the width of a grade. Here are some rough estimations of how many climbs that exist of the highest five grades from 9c (routes) to 9A (boulders).

9c:1, 9b+:6, 9b:36, 9a+:130, 9a:700
9A:2, 8C+:10, 8C:60, 8B+:360, 8B:2000
(Note that these are just estimations. Grades vary and some climbs are just variations.)

Another way to analyse the width of a grade is to use Time Comparison Grading. The diagram suggests that if a climber could do an 8b on the 3rd go, the next climb that was done after two days of projecting could still be 8b. Basically, the TCG curve indicates how much more time and effort are needed to step up one grade no matter if we are talking a 7a or a 9c route. Obviously, the plotted curve is just a community theoretical average meaning that for most individuals it does not apply perfectly. In practice, there are many considerations like conditions, style and luck that play a major role in each ascent.

In any case, by comparing route and boulder scales, we can, in fact, assume that the width of the boulder grades are a bit more narrow up to 7C and then after 8B, they get wider again. Here is a recent article trying to explain this?

It should be underlined that I welcome suggestions on how to better describe how wide a grade is. The TCG and Factor analysis is basically just ideas on how to approach the subject.