Statistics

Just as with layouts…

Isn't there one analyzer that is just better than all the others? 

No, there isn't.

Every Keyboard Layout Analyzer (KLA) is built around an important set of statistics and algorithms that reflect design priorities.  One analyzer may be designed to highlight the always important same-finger bigrams (SFBs), and another may be designed to help reduce the load on specific fingers (ie. pinkies), while still another might emphasize finger or hand alternation. These are often competing priorities. You can get fewer SFB by spreading letters out among all the fingers, but that runs the risk of making the pinkies or ring fingers do too much work. There are myriad issues involved, especially in the scoring algorithms that produce rankings. The rankings for any KLA must reflect those priorities, (with a given sample corpus). 

Then comes the decision you must make regarding those priorities and scores.  Does moving your ring finger from top to bottom row make you squirm as much as it does me? Some layouts put a heavy burden on the ring fingers, and so they may not be right for you, even if they have amazing overall scores. Some layouts put a much heavier burden on the index fingers than others, and might score really well on one analyzer, might score poorly on another, or have trouble integrating with other smart keyboard features (i.e. home row mods). Obviously, simply scoring well on one analyzer doesn't necessarily mean it's the absolute best layout for you. That it is why it is so critical to know what those priorities are (and the corpus) in order to interpret the scoring of any KLA. 

Here's a list of analyzers I've used (or at least consulted their algorithms), in no particular order:

• • SteveP99's Colemak-DH analyzer

  • Patrick Gillespie's (PatorJ) KLA

    • SteveP's [SP] fork of Patrick's KLA

    • Ian Douglas' fork of Patrick's KLA at kla.keyboard-design.com

    • Den's fork new version (Den4)

  • Semilin's Genkey (used to produce Semimak)

  • Clemenpine's A200 analyzer

  • O-X-E-Y's Layout Playground

  • O-X-E-Y's OXEYLYZER

  • Dario Goetz' Layout Optimizer 

There are a number of analyzers based on Patrick Gillespie's (PatorJ) KLA that produce a linear ranking of several layouts.  PatorJ) KLA puts equal weight on individual finger movement, use of particular fingers, and hand alternation. Ian Douglas' KLA at kla.keyboard-design.com is based on the Den1 fork, with similar priorities to tho PatorJ original but with a different ranking scheme that favors layouts with hand alternation or those that shy away from heavy burden on any one finger—BEAKL, Dvorak, & MTGAP like layouts that favor hand alternation preform better there (i.e. Hands Down). SteveP [SP] fork scoring reflects greater sensitivity to SFB and less to the burden placed on any given finger (or hand alternation), meaning that layouts that may demand more of any one finger (esp. index) will perform well provided the SFBs are low—Colemak like layouts perform better there. It appears that the  (Den 1,2,3) KLA has resurfaced in a new version (Den4)  that addresses more variables, including (inward) rolls and hand balance.  The scoring with Den4 weighs use of specific fingers to penalize layouts that abuse pinkies (or any other finger). You'll find that BEAKL layouts perform exceptionally well there. Ian Douglas' KLA newer KLANext has perhaps the most accurate measurements of the PatorJ derivatives, with appropriate measures for finger distance and same finger use, the two most important metrics. The scoring also seems to me to more accurately reflect an actual typing experience, (if that is even possible!).

While all these KLAs share a common heritage, they have different scoring priorities, and some measure things a bit differently. Currently, all the PatorJ derived KLAs will incorrectly score (inflate the score) of any layout that is missing letter/characters found in the sample corpus, so I have included all the standard characters, and then some, to try to be as accurate as possible. (Drop me a note if you find any errors by clicking on the info icon at the bottom of the page.) I've tried to ensure that other layouts used for comparison also have all the glyphs, and are on similar boards, to reduce the variables involved and not handicap anything.

Other analyzers/optimizers are more complicated to set up (Carpalx, MTGAP, etc. use python, C++, Rust, etc.), but can provide deeper insights. Some can iterate on a set of weightings (simulated annealing) to produce optimized layouts. I'll write more about my experience with some of these later. In the mean time, you may want to check out the Alt Keyboard Layouts (AKL) Discord for a lot of really interesting work being done on layouts and analyzers.

I really do not think any one analyzer is better than all the rest. 

There are many other layout analyzers that don't use JSON templates like these, and each has differing methodologies. The slick Colemak Mod-DH analyzer, for example, is fast, somewhat configurable, and focuses on the very important same-finger bigram problem; but its weighting of SFBs is fixed, and it doesn't handle some scenarios (like letters on thumbs, different corpora). You can easily copy a Hands Down layout from the top of each section and paste it into the analyzer to see its take on SFBs, especially. I think it is important to look at any layout from many points of view, with many sample texts, to see how it might perform under different real-world conditions. 

A menu of same-finger bigrams

I've evaluated Hands Down with many different analyzers, and where possible with a huge variety of sample texts. It consistently ranks in the top 5 layouts by some metric or another: frequently #1, sometimes at 4 or 5, but usually in the top #2 or #3 (by layout family).  But stats are not the whole story. For the reasons stated above in the design goals for this project, I think that Hands Down has some merit. Here are some detailed stats from the  Colemak-DH(mods) analyzer, that is great for quickly discovering potential problems with same-finger bigrams.

Poisson distributions: ratios of good vs bad bigrams

All Hands Down variations deliberately try to distribute finger burden roughly aiming to slightly favor the index and middle fingers while producing a functional balance between the critical same-finger bigrams (SFB), neighbor-finger bigrams, and individual finger usage frequency.  A layout with the lowest SFBs may over burden some fingers, or cause awkward row jumps, or other undesirable traits in practice. Any single metric alone cannot represent the best layout design.

Balanced Hand and Finger Diet

finger 0 6.31% finger 9 8.08%

finger 1 11.56% finger 8 10.06%

finger 2 15.62% finger 7 20.65%

finger 3 16.73% finger 6 10.99%

total L 49.77% total R 50.23%

Although this near perfect balance is exceptional, I feel that anything under about 3~4% feels balanced in practice...Any more than that and I can definitely feel the imbalance after a typing session. Swapping E<->A results in 16.98% for finger 7, and 13.07% for finger 9. See below for Pink E, Roll E, and Thumb E variations that all reduce the burden on finger 7, albeit with somewhat lower overall statistical scores.

Same-Finger Lickin' Good Bigram Frequency

finger 0 0.009% finger 9 0.003%

finger 1 0.319% finger 8 0.021%

finger 2 0.193% finger 7 0.360%

finger 3 0.116% finger 6 0.179%

total 1.309%

Hands Down primary design goal was to reduce same-finger bigrams, especially on the pinkies. It has among the lowest same-finger bigram burden and total bigram penalties in this critical metric. This is the measure that you feel really quickly when typing, perhaps more than any other. I feel that anything over 0.3% on any one finger is noticeable, and annoying with anything over 1%, or anything at all on the pinkies.  But a warning, too: some layouts with really good bigram stats suffer with awkward sequences that are so uncomfortable that a slightly higher bigram number may be worth it.  Hands Down is no exception. There will be awkward sequences. 

Fat Free Same-Finger Bigrams

finger 1 NC 0.295%
finger 7 E. 0.245%
finger 6 FU 0.095%
finger 2 HR 0.079%
finger 2 RL 0.075%

Hands Down has  among the lowest frequency same-finger and neighbor-finger bigrams, yet does not over-burden the awkward ring and pinky fingers. The added burden is taken up primarily by the strong middle finger. Phonetic analysis helped to isolate bigrams and balance finger usage to avoid co-occurrent phonemes placed on the same finger columns where possible, (QSX, CRM, HNL, and all 6 letters on each index finger). U attracts the fewest bigrams of any vowel so it is exposed to the most letters, and OE is the least frequently occurring vowel bigram, though they are the first and fourth most frequently occurring letters.

Low Carb Neighbour-Finger Bigrams

finger 8–7 BE 0.644%

finger 1–2 CH 0.518%

finger 9-8 AI 0.483%

finger 7-8 E, 0.406%

finger 8-7 IO 0.328%

Exceptionally low frequency neighbour-finger bigrams, similar to the other top ranking layouts. Trigram analysis is much harder to measure, and very sensitive to physiological sensations, and linguistic (word/meaning) influences because we're getting closer to spelling/sounding words out. I couldn't find an analyzer to help. The theory is that if the bigram numbers are low, then the trigrams will require a shift away from a finger or two, and it'll sort itself out. This is true in practice, but some awkward sequences still occur. The C-vowel-M tri-gram sequence is the most annoying to me on Hands Down.

Avocados are good for you

Some of the better performing layouts encourage "good bigrams and trigrams" as a part of a healthy typing diet, rather than avoiding same-hand bigrams altogether. Depending on the pattern, I agree with this. On the consonant hand, the most common consonant bigrams are deliberately placed for comfortable same-hand rolls or rakes, such as TH, and the most common N-bigram group of NG, NT, ND, and WH, LD, and the GH+T bi-gram is very easy one-hand sweep "the blighted ghost is happy." On the vowel hand, the least common vowel bigram, OE, is on the powerful middle finger. So, while finger 7 is heavily used, it is almost never used in quick succession on a different key. The result is that all of the vowel bigrams are easy rolls. OU IO EA EI AE IE. Bonus: LS isn't bad, a common Dvorak complaint. The L-R hand inversion of Dvorak is intentional, as it leaves more keys on the hand they were on QWERTY, which has made the layout easier for me to learn, and may help when necessity arises that you must resort to QWERTY.

Haute Qui-scene

Check out this layout evaluator that compares many layouts using weighted bigram lists from multiple languages. It shows many interesting things, including the reality that there are many good layout options that perform statistically similar to each other, along the lines of what I've discussed and recommended here. It somewhat confirms a key design goal: Hands Down performs very well in English without penalizing use of other languages. Sure, other optimizations will be better in a given language or a given corpus, and different analyzers will argue one layout is marginally better than another based on the stats or weighting schema they use, but in practice I can only use one layout at a time...

A layout is also a matter of taste. 

Artichokes to Ziti: I'm not trying to sell you on Hands Down, or make claims about the other layouts. I'm just excited that it works for me, and wanted to share it. You decide if it works for you, or doesn't. Sometimes significant variation occurs with different statistical weighting or sample corpus being analyzed. While a good number of layouts are close to Hands Down statistically, they all arrive at those similar-ish results in different ways, which means that typing on statistically similar layouts will likely feel very different—and that feel is very important. As much pun as I have had here with the name, there is, simply, no way to claim that any layout is, Hands Down, the beets, nor would that necessarily mean you should like borscht. Variations are GOOD FOR YOU—change it to suit your needs. Some keystroke patterns will freak someone out, and be no problem for someone else. That's why it's called the Hands Down Reference layout. I expect you to season it to suit your taste.

So always take stats with a dash of salt, knowing that what matters most in any Human Computer Interface is always the particular human. The important thing is that it works for the user, across a variety of texts they are likely to encounter (including languages). All this analytic stuff is just to help develop the layout, then communicate it to those who might want to use it—like a menu. It may look and sound delicious, but all that matters in the end is whether it is delicious to you.

It is very important to compare layouts on like keyboards. The keyboard itself has a profound influence on the typing efficiency and comfort. These tests all use layouts on a standard ansi keyboard.

You can download the JSON files (above) to see just how good Hands Down is on a run of the mill row staggered keyboard. Or you can download the OS Layout bundles (below) and install Hands Down now to use on the keyboard you already have. Hands Down Reference, Alt, and Extreme work very well on a typical row staggered keyboard. So do Hands On and Notarise. All of these are included in the native OS layout bundle installer.