Cadden’s Thoughts: The Mathematics of Improving Your Climbing

Recently Andrew Woods posed an interesting question to my Facebook page.  I intend to discuss this in a little more detail than I went into originally.  My reasons?  I have the free-time to do it, and it has come to my attention that the Freshers may benefit in some basic climbing theory.  To the older members of the club, much of this will seem intuitive, though I intend to explain at greater depth than just intuition provides.


The original question was about injecting Mercury into veins to increase vascularity, and thus one’s ability to climb.  Now at first glance, this seems like one of the most powerful shitpost in recent history, to be totally disregarded by intellectual parties.  However, for those with more liberal a mind, this poses an interesting question; “How do I improve my climbing?”.  Now, that is very vague, and I seek add some clarity to the situation through a more scientific approach.

As many of the scientifically minded club will agree, Maths is the language of science.  Now as a Biologist I can attest to the reluctance of many to agree with this, but when you get down to it, it’s all about statistics and models, as depressing and confusing as these things are.  This then leads to the grand title of The Mathematics of Improving Your Climbing.

Now, I understand that not all of us get maths, again, I did Biology.  Being more numerically inclined than my peers, I am well used to trying to make things simple when explaining numbers.  So, as much as Alex will tell me off for any minute error, I will explain the governing equation of climbing ability.

Climbing ability = ({vascularity + strength to weight ratio} x scream volume + scream frequency) + ape index in inches.

For you fact checking bastards, this equation is slightly different though correct, due to a typo in the Facebook comment.

Ok, so simple stuff: How do we affect the equation, to increase the resulting climbing ability?

Well, the short version is that if any of these numbers increase, so does your climbing ability.  But each of these factors will have a different level of effect.  For example, scream frequency is additive, and scream volume is multiplicative.  Now again, for the math illiterate I shall go step by step.


This is basically how many veins you can see on your arms when you are climbing.  The natural ways of increasing this are simple; Pump, Training and Revealing clothes.  That’s right folks.  As I said, vascularity = VISIBLE veins.  By getting pumped we end up with more blood in our arms than normal.  This swells the veins, making them more visible and increasing vascularity.  Training will also naturally increase the demand for blood to your arms, this will prompt the body to start increasing the number of blood vessels to the area in need, though this takes time.  Revealing clothes, as the name suggests, increases the area of skin VISIBLE to the eye.

Put as simple as possible: more skin showing, more veins showing, more vascularity, greater climbing ability.  Perhaps the strongest evidence for this is seen through “tops-off-for-power”.  While many believe the weight loss of extra layers to be the key factor, it is actually caused by the increased vascularity.  Those who simply remove layers without revealing more skin report up to 74% less power increase than those who do show more skin.

So this is an additive factor within a bracket that is multiplicative.  Simple version, a small change here is multiplied later on, but needs balance with the other factor in the bracket.  This leads us to;

Strength to Weight Ratio

This is as simple as it sounds, ratio between body weight and strength.  You want to have the least weight to carry, with the most strength possible.  This can be achieved simply by removing extra layers, or that one quickdraw that you totally need, but won’t admit it.  Now this becomes more difficult when we look at the human body.  The problem here is LOOSING USELESS WEIGHT and MAINTAINING USEFUL WEIGHT.

So how do we identify what is useless and useful?  Well that depends on the discipline of climbing you are most interested in.  On first thought, fat seems useless as it adds weight, but not power, where as muscle adds weight but provides power.  But looking at the different areas, we can see it is not so straight forward.

For winter climbing, mountaineering and trad climbing a basic layer of fat is a positive, due to the need for insulation against adverse conditions.  By contrast, sport climbing and bouldering focus of the lowest body fat percentage possible, as the warmer climates don’t require the same survivability.  Now this can be taken to extremes, for example many a boulderer has considered having their legs removed, as footholds tend to be non-existent on boulder problems, therefore reducing the usefulness of the limbs.

Scream Volume

This is by far the most effort-efficient factor to increase.  The volume is the raw decibel value of one’s powerscreams.  The greatest testament to the raw effect of powerscreams comes in two names; Chris Sharma and Adam Ondra.  These iconic, and quite honestly, legendary climbers are best known for two things: being fucking strong, and screaming loudly.  Even when we take averages across the disciplines, we find that the average boulderer screams louder than the average sportclimber, with a staggering 30-50db disparity.  This is due to the greater focus on powerful moves in succession.

Two theories as to the actual mechanism of screaming exist.  One is that the psychological effect of screaming makes you “feel stronger” and thus spurs you on.  The second theory, growing in support through consecutive studies, is that when one screams one compressed the air around the climber.  This increase in density of air make the climber less dense in comparison, and allows them to “float” through harder moves momentarily.  Think of is, if you will, as the difference in lifting your body in water vs. lifting it in air, though the effect is not as profound.

It is the strong effect of Scream Volume which prompts our next section;

Scream Frequency

This is the raw numbers output of screams overtime.  Confusion between FREQUENCY and VOLUME is a common one to be sure.  How many times have we seen that bloke at the wall, who screams through every move, in a vain hope to climb better.  As scream frequency is an additive factor, it’s effect is weak in comparison to a multiplicative factor such as volume.  By screaming more frequently we increase the number of “power pockets” in a route, therefore better climbing right?  Well it isn’t quite that simple sadly.

One’s intercostal muscles and diaphragm are muscles like any other, prone to fatigue.  This means that the more you scream, the weaker the effect of individual screams.  You can pick one of two strategies; a few good screams, or many less effective shouts.  Now this is route dependent.  For example a route with several moves just harder than your regular ability, and you can probably throw several sounds of exertion into the void.  However, for routes with perhaps only a couple of hard sections, way out of your reach, fewer more powerful screams are what the doctor ordered.

Ape Index

This is our final factor.  It is additive and perhaps the most controversial factor.  The Ape Index, is the difference between one’s arm-span and one’s height in inches.  For example, if you stand 6ft tall, and your arm-span is 6ft 2inches then your index is +2, if they are the same it is 0.  And most dreadfully of all, a span of 5ft 10inches, the index is -2.

Now members of the club range from a lofty +5 and a small bit (Myself) to a pitiful -3 (Michael Campbell).  Now some see the issue as simple; big-ape = good, small-ape = bad.  Now granted this is not far from the truth, but things are not as black and white as they seem.

First off, the ape index is fairly hard to alter without surgery, so I am afraid you are stuck with it.  That’s just how it is kids.  So first off, it is true that a negative ape index is bad.  Simply put, your arms are short and so is your reach for your height.  Now you CAN get stronger, but simply put, there are just some long moves that you can’t reach statically, but will also be too hard to land dynamically.  That, my abruptly armed amigos, is life.  Now for the longer armed members the fun bit.  There are fewer moves that will be out of your reach.  But this is not to say you are a master-race of people called “Mungo the Monkey” who can sail up climbs.

You will find, as I did, that the easier grades are easier for you than most, its just maths.  There are 20 holds on the wall, but you only need 10 to get up the wall.  At the higher grades, and bouldering especially, you are going to struggle a bit more.  Physics sees to level the playing field a bit, because of moments getting stronger is worth less.  Simple version: push a door open at the handle=easy, push at the middle=harder, push at the hinge=hardest.  When you have longer limbs you need more muscle to get the same force at the end, than shorter limbs.

To cut a very long story short; Lanks will find slabs and vertical walls easier, Shorts will find overhangs and roofs easier as these are more strength focused.


So I hear you say “Conor, that was all complete and utter shite.  What should I actually take away from this?”

Well a list is probably easier;

  1. Focus training on Strength and Endurance, and loosing weight through fat, but gaining weight through muscle is fine.
  2. Screaming is grand for getting past a hard move or two, just don’t do it THAT often, or risk looking like a tit.
  3. Being lanky lets you reach further, and will lull you into thinking you are good.
  4. Being short makes long moves harder, and will lull you into thinking you are bad.
  5. Being short makes it easier to be strong, but being strong will lull you into thinking you are good.

The real secret is to balance strength with technique, and to understand you have weaknesses to be worked on.

Remember, excuses as to why you “can’t” climb a route are just that, excuses.  To thoroughly ground yourself and get to training try repeating what I do to myself every time you “can’t” climb a route;

“Conor, have you ever considered that you are just shit?  Most likely.  I suppose the only thing to do then is get better.”

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