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How to grade a route when cumulating grades for multiple sections? Is it based on the overall feeling of difficulty or is there some cumulative formula to apply which yields a more or less accurate grade?

In the following explanation, I'll use the french sport climbing grading system (see link for details).

This question is better explained by using an example:

The route "Chilam Balam" is a long route (80m) which is made of 3 sections. In https://www.youtube.com/watch?v=t-0uyFWeOoE (french), the climber says the first section is 8c+, then 8c, then it's not clear but let's say 8b.

This route was rated 9b+ during the original ascent, but then 9b by Adam Ondra and even 9a+ by other repeaters.

Is there a formula where 8c+ + 8c + 8b = 9b?

In bouldering too, I heard things like "it's an 8B that goes into an 8A+, so the overall grade is 8B+".

If there is no formula, what is the difference between a short 9a route and a long one? Like a long 9a is just an 8c that is really long?

I also heard that you could explain sport climbing routes using bouldering grades, for example a route that contains a 7A boulder problem is ~8a (that is, you add +1 to the boulder grade to get the sport climbing grade).

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    There's no formula. Grading is subjective. – Qudit Sep 30 '17 at 17:23
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    It's not the sum of sections, only the crux defines the overall classification. – Wills Oct 1 '17 at 8:57
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    @Wills: that is true for British technical grades, but absolutely not true for UIAA, French, or Yosemite Decimal grades. – Michael Borgwardt Oct 2 '17 at 10:15
  • @MichaelBorgwardt I thought this is for UIAA too. Do you have sources? – Wills Oct 2 '17 at 21:18
  • @Wills: I can't find a source that explicitly says so either way, but my experience is that sustained difficulty is factored in. – Michael Borgwardt Oct 3 '17 at 7:13
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The theory is that (sport) grades should reflect the technical skill, strength and stamina required to redpoint the route.

Therefore the definition of, say a 8a route is that "a climber that consistently climbs 8a routes will succeed while a 7a+ climber will struggle"

When climbers talk about grades on sections of routes, they actually mean "if this section was an isolated route, it would be graded 8c". Naturally, climbing a hard crux after a sustained section of hard moves is not the same as if the same crux comes after a good rest position.

One must remember that grading is complex and subjective, and that an individual climbers will "achieve" higher grades on routes that suits their style and strenghts and "underperform" on routes that targets their weaknesses.

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There are many aspects to a climbing route's difficulty, so it is fundamentally questionable to lump it all into one number, and is really only accepted because most climbers don't have a huge imbalance in the different aspects of climbing proficiency, i.e. a climber who has very good technique probably climbs often enough that their power and endurance are also good.

So yes, the lenght of a route influences its grade and you could definitely have cases where "9a is just an 8c that is really long", i.e. it has no single move that is harder what you'd typically find on an 8c, but the length makes it hard because you have to do 8c moves while already pumped.

However, there is no formula, becuase there are still many aspects. Where in the route are the hard moves? One hard move after many easy ones is harder than when it comes right at the start. And, very important for endurance considerations: are there rest positions? A good rest position removes much of the endurance-related difficulty at that point.

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