#### skribs

##### Grandmaster

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On a slow day at work, I decided to make a formula for poomsae difficulty. I attempted to factor in a larger variety of techniques, greater variation, and mor detailed footwork/handwork as a more difficult form.

( (NUT * TPS) + (TNS * (1 + FC)) ) * Steps * Sets = Difficulty

NUT = Number of Unique Techniques

TPS = Techniques Per Step

TNS = Total Number of Stances

FC = Footwork Coefficient; Percentage of Steps with Stance Switches, Spins, or Rearward Motion

Steps = Number of Steps

Sets = Number of Repeated Parts

**Total Number of Techniques**is simply how many different blocks, punches, and/or kicks you have. For example, if you just have a bunch of low blocks and punches, then NUT would be 2.

**Techniques Per Step**is the number of techniques you do divided by the number of steps. If every time you step forward or turn you do one technique, then TPS will be 1. If you do a kick and a punch, or do multiple techniques without taking a step, then you add those in. Total up the total number of techniques and divide by the number of steps to get your answer.

**Total Number of Stances**is how many different stances techniques are used from. A basic Taeguk will probably use Front Stance and Walking Stance, which would be 2. A form that uses front, back, horse, and cat would have 4.

**Footwork Coefficient**is the method I use to factor in detailed footwork within a step. Any time you do anything besides step forward or turn (meaning step backward, change stance, spin, jump, etc) you add to the Footwork Coefficient. A basic form will have an FC of 0, while forms that have you do several techniques without moving might have a much higher FC.

**Steps**is simply the number of steps your feet take. Any time you move forward, backward, or turn on the axis, it counts as another step. Times when you face a different direction but either don't move your feet or barely move your feet, that is adding to the FC, but not the step count.

**Sets**: the number of repeated sets. A set is simply a combination along the lateral or longitudinal axes. For example, Kibon Il Jang repeats the lateral set of low block, punch, turn, low block, punch 3 times and the forward/backward set of low block, punch x3 twice. Because it repeats 2 different sets, it's Set value is 2. Taeguk Il Jang has 3 different lateral sets and a different set forward and back, so its Set value is 5. Any time you have a set that comprises of a single technique or two, or you have two sets that are similar except for one minor detail, that is only 0.5 extra sets.

Now, I plugged in the data for the forms we do at my school, at least the ones I already know well enough to plug the data in for. I'm not going to post it, because of a few reasons:

1) We use 5 kibon forms and 8 palgwe forms, while most people I think just do the Taeguks.

2) Our master has taken some creative liberties with the later palgwe forms that make them more technically difficult, but also completely different from what I see on Youtube. There are also minor differences in the earlier forms.

Because of this, I don't think my

**data**is useful to anyone outside my school (if it even is useful to someone inside my school). But, if you're a math nerd in addition to a TKD geek,the formula itself might be fun to plug in the forms you do at your school.

I will say that the results of my data are not surprising at all. Going up through all 5 kibons and the first 6 palgwes, the difficulty goes up every time, with only one peak (that I expected). Here's an example using Kibon Il Jang and Taeguk Il Jang:

Kibon Il Jang: 80

( (NUT * TPS) + (TNS * (1 + FC)) ) * Steps * Sets = Difficulty

There are 2 techniques used: low block and punch, so NUT = 2.

You do one block or punch per step, so TPS = 1.

You only use front stance or walking stance (depending on school), so TNS = 1.

There is no fancy footwork, so FC = 0.

There are 20 steps, so Steps = 20.

There are 2 sets repeated 3 and 2 times, so Sets = 2.

( (2 * 1) ) + (1 * (1 + 0) ) * 20 * 2 = 80.

Taeguk Il Jang: 660

( (NUT * TPS) + (TNS * (1 + FC)) ) * Steps * Sets = Difficulty

There are 5 techniques used: low block, punch, inside block, high block, and front kick, so NUT = 5

There are 20 blocks, punches, or kicks and 16 steps (added up below), so TPS = 1.25

There are 2 stances used: front stance and walking stance, so TNS = 2

There is no fancy footwork, so FC = 0

There are 16 steps taken, so Steps = 16.

There are 5 repeated sets (technically none are repeated and there are 5 sets), so Sets = 5

( (5 * 1.25) + (2 * (1 + 0) ) * 16 * 5 = 660.

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I think the one thing I should have done different is move Steps to the beginning because of the other bits that require you to divide by Sets, but that's a minor issue.

Anyway, I was bored enough to make this, so even if it's got no real-world value, it at least killed time for me!