Oh - just to clarify, transitioning from Qwerty is exactly what I was talking about here. Trying to assess the difficulty in learning a layout from scratch (as a first layout) would be a completely different (but still interesting) kettle of fish.

I had wondered about the relative effort in relearning frequent vs infrequent keys. It may be true to some extent that more frequent keys can be learned quicker due to them being more commonly typed. But during that learning period there would involve many more errors and no doubt frustration too. Also, the adverse impact on typing ability will more severely affected for the transitional period. After all, it's not just the key itself, as muscle memory often seems stored as bigrams/trigrams. Just think of all the relearned bigrams and trigrams that have to relearned for E!

Taking everything into account, I think more common letters are harder overall to relearn for these reasons. But perhaps the relationship is not linear with frequency as my formula assumes, but rather some other more complicated relationship. Oh well, at least it gives a quick and easy way to get an overall measure of difference/learning difficulty though, which might be of some use.

A nice web app! About the idea of 'learnability of layouts' I do have some hestitations though:

1 - sometimes small differences can be more confusing than large differences

2 - IF small differences are easier to learn than large ones, you would be right for present "qwerty touch typists". A small step (minimak, colemak etc.) would be easier to them than a large step (dvorak, carpalx, mtgap, adnw). But....many people (including me) cannot touch type in Qwerty. Many know roughly where the keys are, but it's not proper touch type. This means learning a new layout involves learning touch type *from scratch*. In that case, why not choose an optimal layout while you're at it? Such an optimal layout could be aiming for "rolls", of for "alternation" or "best balance over fingers & hands"  etc. But "looking like qwerty" does not have to be a goal, however.

@Dreymar "I speak Norwegian and Swedish and even Danish quite decently with ease because they're so similar"  Wasn't Swedish sort of "Norwegian pronounced in a funny way"? Or was is the other way around ?  ;-) ;-)  Just joking...

I understand the analogy. But yet, on the other hand: suppose you play upright bass and piano. You would never confuse them. But, switch from the upright bass to a cello, and you will get confused: that cello looks like a smaller bass, but it tuned differently (in 5ths rather than 4ths), meaning that the fingering is completely different. This could mean that maintaining Qwerty knowledge is easier for a Dvorak typist that for a Colemak typist.

I am not sure how this works in practice: is "qwerty-like" more of an advantage (like your Norwegian-Swedish example) or more of a hindrance (like the bass-cello example) ? The best way to find out would be to compare the qwerty-typing of trained Colemak typists to that of a trained Dvorak typists, I guess ?

Have you actually tried swithing between contrabass and cello? I never had a problem between my viola and a bass, and it certainly didn't feel any more confusing than going between the flute and the piano. At all. Bad analogy, or is it that I'm just dabbling with one of them anyway? But interesting observations about jiu jitsu schools! I haven't tried any of that.

Language fluency doesn't quite enter this analogy as I see it? I can no more speak perfect Danish (which is hard!) than I can speak perfect Japanese or Greek – but I'd have a much much easier time and get a hell of a lot closer a hell of a lot faster trying it with Danish (believe me, I've tried!)! What's the point there? And no, absolutely no problem switching between my perfect Norwegian and my decent Swedish and my half-decent Danish on the fly as necessary. No confusion.

All languages are pronounced in a funny way. Naturally, this includes the Nordic ones. Actually, Dutch is "only weird German", right? ;-)

People have very different feelings about ease of learning. I've seen people actually trying to hold ease of learning against Colemak, as if if it's easier to learn something must be wrong with it mustn't it? To others, it seems that Tarmak is necessary to make them even bother to switch. Besides warming my heart, it shows that people have widely different opinions on this. I no longer experience the ease of learning personally, but still feel that similarity to QWERTY helps. Particularly the shortcuts, but keys in general too.

I see that there may be no general answer to how this works for everybody. Maybe it varies a lot between people? Maybe it's hard to imagine how this works. I don't know.

This is really great!

I would propose renaming "The Difficulty Index" to "QWERTY Switching Difficulty" (QSD), as QWERTY should never score "0.0" on a "difficulty" scale :)

Two things that I'd like to see tested:

- Difficulty of switching to the Same Finger and Same Row, but Different Hand.
- Same Finger, Different hand may be easier than Same Hand, Different Finger.

I'll be tying QSD into two upcoming keyboard layout projects of mine, so more soon...

Thinking of how to improve the learning difficulty model:

I would like to also take into account the fact that changes seem easier to learn when the character moves to an easier position on the keyboard. Certainly it seems to be the case from my experience, but it also makes sense to me that a change that makes things more comfortable will bed in more easily that a change that makes a character more difficult.

To reflect this in the model, I am thinking about including an additional factor which takes into account the difference in scores (as defined here) between the old an new location...

s = 1 + ( [key effort in new position] - [key effort in old position] ] / [key effort in old position] )

Thus, in the Mod-DH change for example, the G (which moves to an easier position) gets a factor of 0.85, whereas M (which moves to a harder position) gets a factor of 1.7.

Of course, there is still the question of letter frequency. I still think it should be involved in the calculation in some way, as taking the extreme case, moving J or Z must be less work overall than moving E or T. I am toying with the idea of making it a square root factor rather than linear. But I can't think of a logical justification for that other than just wanting to reduce its importance in the overall scheme.

More to come on the difficulty model soon...

I suppose I was thinking along the lines of: If you have Key-A which is 4 times more common than Key-B, then rather than weight it 4 times as much, you'd only be weighting it twice as much. In other words, it would be like saying that the fact that you learn Key-A faster by typing it more often would cancel out half the effect. The whole idea of comparing keyboard layouts is guesswork of course, but still, I do agree with you and I am not inclined to introduce an arbitrary power law unless there's a more reasonable basis for it.

In the meantime I have updated my Switching Difficulty page to also include the index if letter frequency is excluded (the "Keys Moved Index", Σ m), so those who think letter frequency is irrelevent can consider that instead. I also added MTGAP and Qwpr layouts for comparison as well.

I have recently been re-evaluating how to measure layout similarity / switching difficulty, and as a consequence, have developed a new model.

This area is obviously still highly subjective - probably even more so that layout design - so there is not going to be an entirely uncontroversial way to model layout switching difficulty. But I have tried anyway :p

Previously the frequency of each key being moved was assumed to have a linear relationship with switching difficulty: a key with a frequency of 4% was deemed twice as hard to learn as a 2% one. However in practise, as DreymaR in particular has argued, it is observed that this is mitigated by the fact that more frequent keys are practised more, and hence tend to have a faster learning rate. I then came across the idea of Experience Curves, which seem describe this idea rather well by the use of a power-law relationship.

So I have modified the model to include a power-law frequency-related cost, which I think is a little more satisfactory. In case anyone is interested in such geeky details, you can read about it on my updated Switching Difficulty page.

I can't really judge how accurate the results are, as I have never tried to learn any layouts other than Colemak. I was initially tempted by Norman, mainly on account of it being seemingly easier to learn. Norman does try to keep a lot of keys on the same finger, which would account for its score. Probably hardly anyone uses any of the layouts listed apart from Colemak, Dvorak, (and perhaps Workman?), but who knows!?

I just generated results for tarmak layouts:

layout  |   ∑m   |  d
------------------------
tarmak1 |  2.50  |   8.3
tarmak2 |  3.25  |  11.6
tarmak3 |  4.75  |  18.5
tarmak4 |  6.50  |  24.5

Yeah, the overall score vs learning difficultly might be interesting.

But then again, once you start going down the keyboard layout rabbit hole, you are always likely to end up unsatisfied if you picked a layout that's only half optimized, even if it did take a little shorter time to learn!

Okay, a few more requests:

Could you do the analysis of Tarmak-Curl(DH) too? Just out of curiosity. ;-) And I thought you also had the Effort scores for the Tarmak layouts but I didn't see them. But I can use the Layout Analyzer myself, sure.

On your colemakmods pages, I've noticed that the layout effort metric with three decimal places is just a little clunky. Those "lower is better" numbers aren't wrong, but they aren't very easy on the eye either? Maybe it's hard to envision exactly what they're telling us anyway, but I thought it'd be nice to have a Typing Effort or Typing Ease Index that relates the layouts to QWERTY like your Switching Difficulty Index does? The former would be a ratio from 100% (QWERTY) to 69% (Colemak-CurlDH), while the latter would go to 145% for our favourite layout. Sure, it's probably totally wrong to just throw out that Colemak-Curl(DH) is "45% better than QWERTY"; but it'd be fun! ^_^

Not sure whether that's the most fruitful way to look at it, but I'm also not sure what to do instead! So, hehe.

Meanwhile, have a look at my Tarmak Analysis & History topic, in which I've now added your above analysis and that of your pages, with some number gymnastics for good measure. Good, cheap fun! Not sure whether I'm on the ball or not with that table, but it does paint a pretty picture doesn't it? ;-)