carpalx - keyboard layout optimizer - save your carpals

Carpalx optimizes keyboard layouts to create ones that require less effort and significantly reduced carpal strain!

Download keyboard layouts, or run the code yourself to explore new layouts.

X11 layouts are available! Patches to include Carpalx layouts in xkeyboard-config and kbd have been submitted by Perry Thompson. Meanwhile, many thanks to Sven Hallberg for providing X11 configuration for Carpalx layouts. Richard Gomes contributed an archive of these files for KDE/Gnome users.

Love your coworkers? Switch them to QWKRFY layout or a fully optimized QGMLWY layout.

Hate your coworkers? Switch them to TNWMLC layout. It's the only keyboard layout that has its own fashion line.

Have ideas? Tell me.

16/aug/16 — Ergonomic Keyboard Layout Designed for the Filipino Language at AHFE2016 derives layout for Filipino language using Carpalx

18/apr/16 — Carpalx layouts soon to appear in freedesktop (package xkeyboard-config) and kbd. Thanks to Perry Thompson.

9/sep/14 — A new layout—De Correspondent—for the Dutch language in collaboration with De Correspondent.

16/may/14 — Added evaluation of the Norman layout. This layout modifies 14/26 keys and has statistics similar to Colemak. Detailed statistics are available.

12/feb/14 — Added evaluation of the abKey layout. Its alphabetic layout makes no attempt at ergonomics. Detailed statistics are available.

Dutch Keyboard Optimization — De Correspondent Layouts

update

The 48% improvement mentioned in the De Correspondent article is based on the difference in typing effort of Dutch text using QWERTY and De Correspondent layout. I don't make the claim that the typing effort model is a linear representation of perceived effort—something that I feel would be extraordinarily difficult to assess for any model, given the subjective nature of the concept of "effort". To appreciate what the 48% difference means you have to compare it to the differences for Dutch between QWERTY and other layouts, such as Dvorak and Colemak. For example, Dvorak provides a 28% improvement and Colemak 38%. I provide the details here.

PKL De Correspondent layouts will be available for download soon.

Dutch Language Keyboard Optimization

This page describes my efforts to find an optimized keyboard layout for Dutch text. This work is in collaboration with Thalia Verkade at the De Correspondent, an online Dutch language magazine.

De Correspondent generously provided me with text from 10 months of content and comments for the corpus for the optimization. The corpus contained 6.26 million words (38.5 million characters). It is approximately 3 times the size of the English corpus I used for English language optimization.

Figure 1 | De Correspondent layout. Dutch typing, made easier.

This collaboration makes De Correspondent to be the first publication to have its own keyboard layout—De Correspondent layouts allow their reporters to spend more effort on the stories and less on typing.

Carpalx for non-English Text

Optimizing layouts for languages other than English is made more complicated when the text contains compound characters with diacritical marks (e.g. â, é, ñ, ö). These are usually generated on keyboards using the AltGr key.

I haven't applied Carpalx to non-English text because Carpalx doesn't yet support alternate shift states of characters. In other words, the software doesn't allow for independent relocation of a key and its shift states.

Dutch, however, has very limited use of diacriticals (e.g. ë is fairly rare), making it possible to apply Carpalx. The terrific corpus provided by De Correspondent is a great opportunity to see how English and Dutch layouts compare and just exactly how much better a Dutch-specific layout can be for the Dutch language.

De Correspondent Layouts

I have derived two De Correspondent layouts for the Dutch language, shown below.

Figure 2 | De Correspondent layout — 1. The effort for this layout is 1.608. The ; key remains in place.
Figure 3 | De Correspondent layout — 2. The effort for this layout is 1.555, a 3.3% improvement over the layout above. In this layout, the ; key is allowed to move, freeing up a home row key for J.

Many layouts have very similar typing efforts. Below are the top 10 layouts, shown superimposed, for the case of ; on the home row, and off.

Figure 4 | Top 10 layout De Correspondent candidates for each key scheme.

Some keys are unambiguously placed, like a e. Others alternate between two positions, like i o and t n. You can see the extent to which a key contributes to the effort by the number of possible letters in each position—the more letters, the less impactful the key.

Below these layouts are described in greater detail, together with typing statistics and a comparison of these layouts to QWERTY, Dvorak and Colemak for both English and Dutch.

English vs Dutch — Letter, Digram and Trigram Frequencies

ENGLISH rel cumul 0 e 0.12698 0.12698 1 t 0.08973 0.21671 2 a 0.08098 0.29769 3 o 0.07914 0.37682 4 n 0.07005 0.44687 5 i 0.06488 0.51176 6 h 0.06287 0.57463 7 s 0.06285 0.63748 8 r 0.05857 0.69604 9 d 0.04516 0.74120 10 l 0.04152 0.78273 11 u 0.02975 0.81247 12 m 0.02548 0.83795 13 c 0.02338 0.86133 14 w 0.02326 0.88460 15 f 0.02183 0.90643 16 y 0.02102 0.92744 17 g 0.02004 0.94749 18 p 0.01615 0.96364 19 b 0.01456 0.97820 20 v 0.00944 0.98765 21 k 0.00826 0.99591 22 x 0.00150 0.99742 23 q 0.00103 0.99844 24 j 0.00093 0.99937 25 z 0.00063 1.00000 DUTCH rel cumul e 0.18925 0.18925 n 0.09826 0.28752 a 0.07596 0.36348 i 0.07116 0.43464 t 0.06799 0.50264 r 0.06217 0.56481 o 0.06049 0.62530 d 0.05156 0.67686 s 0.04096 0.71782 l 0.04004 0.75786 g 0.02919 0.78705 k 0.02628 0.81333 m 0.02449 0.83782 v 0.02317 0.86099 h 0.02314 0.88413 u 0.01819 0.90232 j 0.01688 0.91920 w 0.01486 0.93406 b 0.01469 0.94875 p 0.01439 0.96313 c 0.01429 0.97743 z 0.01239 0.98982 f 0.00823 0.99805 y 0.00127 0.99933 x 0.00056 0.99988 q 0.00012 1.00000

Letter frequencies

You can download the English frequency table and Dutch frequency table for letters, digrams and trigrams.

It turns out that letter, digram (two-letter combination) and trigram (three-letter combinations) are very different in English than in Dutch. First, let's look at letter frequencies.

Figure 5 | Letter frequencies for English and Dutch. Relative frequencies are normalized to the frequency of the most common letter, e in both languages.

In both languages, e is the most common letter. In English, the next most common is t which appears at about 75% of the frequency of e. In fact, 8 letters have relative frequencies greater than about 50% of e— these are t a o n i h s r.

In Dutch, on the other hand, the next most frequent letter after e is n, which appears at 50% of e. Importantly, no letter has a relative frequency more than 50% that of e. Because of the high relative use of the most frequently appearing letters in Dutch, the placement of these keys will substantially affect the typing effort.

Up to about the first 10 letters, the cumulative frequency for Dutch is larger than English. For example, 50% of Dutch text is composed of the top 5 letters—e n a i t—whereas this number is only 44% for English—e t a o n. 10 is a fortuitous number because the home row of the standard keyboard contains 10 letters, if we use the key for ;.

ENGLISH rel cumul 0 he 0.03620 0.03620 1 th 0.03593 0.07213 2 in 0.02400 0.09613 3 er 0.02210 0.11823 4 an 0.02174 0.13997 5 re 0.01765 0.15762 6 nd 0.01669 0.17431 7 ou 0.01588 0.19018 8 ha 0.01456 0.20474 9 ed 0.01414 0.21888 10 on 0.01377 0.23265 11 at 0.01376 0.24641 12 en 0.01344 0.25985 13 to 0.01214 0.27199 14 ng 0.01202 0.28401 15 hi 0.01168 0.29569 16 or 0.01150 0.30720 17 is 0.01150 0.31869 18 it 0.01135 0.33005 19 as 0.01072 0.34076 20 te 0.01035 0.35111 21 ar 0.01027 0.36138 22 es 0.01008 0.37147 23 st 0.01001 0.38148 24 se 0.00931 0.39078 25 ve 0.00926 0.40005 DUTCH rel cumul en 0.05562 0.05562 er 0.03292 0.08854 de 0.02868 0.11723 an 0.02244 0.13966 ee 0.01927 0.15894 et 0.01854 0.17747 te 0.01845 0.19593 ie 0.01809 0.21402 aa 0.01801 0.23203 ge 0.01770 0.24973 el 0.01661 0.26634 in 0.01609 0.28243 ij 0.01571 0.29814 he 0.01322 0.31137 at 0.01254 0.32391 ar 0.01156 0.33547 or 0.01126 0.34673 oo 0.01123 0.35797 re 0.01095 0.36892 nd 0.01094 0.37986 ve 0.01090 0.39076 st 0.01079 0.40155 me 0.01026 0.41182 le 0.01008 0.42190 al 0.00962 0.43151 is 0.00944 0.44096

Digram frequencies

Digram frequencies of English and Dutch are similar in shape to letter frequencies. Again, we see top top digram in Dutch en to have a frequency of nearly double the next common digram er.

The frequency profile falls off much faster than for English, for which 4 digrams—th in er an—have frequencies of at least 50% that of the most frequent one, he.

Some of the top 50 Dutch digrams—de ee et aa ge ch be ti oe ke we ni nt rd ma vo ed ra—do not appear in the top 50 list for English. These digrams may be unoptimally placed in layouts tuned to English.

As we look down the digram frequency list, 90% of all digrams are composed of 158 distict digrams in Dutch and 162 in English. 99% of digrams appear as 325 distinct digrams in Dutch and 289 in English.

Figure 6 | Frequencies of 50 most common digrams (two-letter combination) for English and Dutch. Relative frequencies are normalized to the frequency of the most common digram, he in English and en in Dutch. The cumulative frequency is shown over the first 50 digrams.
ENGLISH rel cumul 0 the 0.03148 0.03148 1 and 0.01646 0.04794 2 ing 0.01361 0.06154 3 her 0.00894 0.07049 4 hat 0.00784 0.07832 5 you 0.00661 0.08494 6 his 0.00648 0.09142 7 tha 0.00644 0.09786 8 ere 0.00606 0.10392 9 for 0.00591 0.10983 10 was 0.00545 0.11528 11 ent 0.00518 0.12046 12 ver 0.00475 0.12521 13 ter 0.00470 0.12991 14 ith 0.00464 0.13455 15 all 0.00463 0.13918 16 wit 0.00429 0.14347 17 thi 0.00426 0.14773 18 not 0.00415 0.15188 19 ion 0.00404 0.15592 20 ave 0.00355 0.15947 21 ght 0.00353 0.16300 22 our 0.00340 0.16639 23 oul 0.00331 0.16971 24 ear 0.00331 0.17301 25 eve 0.00326 0.17628 DUTCH rel cumul een 0.01104 0.01104 aar 0.01053 0.02157 van 0.00940 0.03097 ver 0.00916 0.04013 het 0.00850 0.04863 oor 0.00837 0.05700 nde 0.00809 0.06510 der 0.00759 0.07268 gen 0.00745 0.08013 den 0.00692 0.08705 ing 0.00658 0.09362 dat 0.00645 0.10007 ten 0.00594 0.10602 ijk 0.00585 0.11187 lij 0.00551 0.11738 nie 0.00549 0.12288 iet 0.00540 0.12828 aan 0.00536 0.13364 sch 0.00523 0.13887 ere 0.00521 0.14408 and 0.00508 0.14915 eer 0.00501 0.15417 ijn 0.00499 0.15915 ste 0.00492 0.16408 cht 0.00474 0.16881 voo 0.00471 0.17352

Trigram frequencies

Trigrams are interesting to look at because the Carpalx typing effort model works using three-letter combinations.

The profile difference for trigrams between English and Dutch is the reverse to that of letters and digrams. English has one common trigram the, with the next one and being about 50% as common. Recall this was the behaviour seen for the Dutch top letter and digram.

The top English trigram the appears 3x as often (0.03148) as the top Dutch trigram (een, 0.01104). Any English layout cannot afford to uncomfortably place any of the top English trigrams because each has a relatively large contribution to text. For Dutch, this isn't the case.

In Dutch, the top trigram is een and the next one aar has a very similar relative frequency. In fact 21 (!) trigrams have a frequency that is more than 50% of een—these are aar van ver het oor nde der gen den ing dat ten ijk lij nie iet aan sch ere and eer. A Dutch layout has to strike a balance between more trigrams because each has a relatively smaller contribution to the text.

Figure 7 | De Correspondent layout.

English Layouts for Dutch

English Layouts for Dutch

Let's first look how well (or poorly) English language layouts perform when applied to Dutch. I'll use QWERTY, Dvorak, Colemak and the fully-optimized QGMLWB layout as examples.

Here are the effort statistics for the English corpus. To understand these tables, see the keyboard evaluation section.

Common English Layouts — English corpus
model keyboard total effortrel% effort contributionsrel%
base penalties path
mod_01 qwerty 3.000

1.00033.3
1.00033.3
R0.408
F0.408
1.00033.3

dvorak 2.098 (-30.1)

0.39718.9 (-60.3)
0.93744.7 (-6.3)
R0.171 (-58.1)
F0.638 (+56.4)
0.76536.5 (-23.5)

colemak 1.842 (-38.6)

0.34418.7 (-65.6)
0.76341.4 (-23.7)
R0.158 (-61.3)
F0.487 (+19.4)
0.73539.9 (-26.5)

qgmlwb 1.668 (-44.4)

0.38222.9 (-61.8)
0.57034.2 (-43.0)
R0.153 (-62.5)
F0.363 (-11.0)
0.71642.9 (-28.4)

When these layouts are applied to the Dutch De Correspondent corpus, with the exception of my QGMLWB layout, all of them have a higher effort in Dutch than in English. The effort values aren't very much higher, though. For example, QWERTY has only about 1% more effort for Dutch than English (3.037 vs 3.000).

Common English Layouts — Dutch corpus
model keyboard total effortrel% effort contributionsrel%
base penalties path
mod_01 qwerty 3.037

0.97432.1
1.01133.3
R0.452
F0.381
1.05134.6

dvorak 2.159 (-28.9)

0.40718.9 (-58.2)
1.00046.3 (-1.1)
R0.200 (-55.8)
F0.662 (+73.8)
0.75334.9 (-28.4)

colemak 1.879 (-38.1)

0.31316.7 (-67.9)
0.75340.1 (-25.5)
R0.170 (-62.4)
F0.470 (+23.4)
0.81343.3 (-22.6)

qgmlwb 1.649 (-45.7)

0.40324.4 (-58.6)
0.52331.7 (-48.3)
R0.160 (-64.6)
F0.313 (-17.8)
0.72443.9 (-31.1)

So if you're stuck with QWERTY and typing Dutch, you're not that much worse off than people typing English.

However, we can do better than QWERTY. Much better! Our aim will be to reduce the effort below 1.649, which is the optimized English layout effort using Dutch text.

De Correspondent Layouts—Details

The De Correspondent layouts reduce effort substantially. In fact, out of all the optimizations I've run they have much lower effort for Dutch than the best English layout for English. Although 1.608 and 1.555 may not seem much less than 1.649, this ~3% improvement is actually impossible to achieve for English text (this is an educated opinion, not a fact).

Below are the finger and hand use statistics for the De Correspondent layouts using Dutch.

carpalx effort optimization keyboard name statistics effort
rowh rowb hand asym finger freq cumulative run distribution mod_01
full De Correspondent 1
XKGLMPUVWY[]\
SDTNRIAEO;'
QBJHFZC,./
0.71 0.09 0.01 0.04 0.17 0.32 0.46
1 2 3 4 5 6 7 8 9
rhl 0.49 0.90 0.99 1 1 1 1 1 1
rhr 0.59 0.88 0.96 0.99 1 1 1 1 1
rh 0.54 0.89 0.97 0.99 1 1 1 1 1
rrt 0.84 0.98 1 1 1 1 1 1 1
rrh 0.30 0.53 0.67 0.78 0.86 0.90 0.93 0.96 0.97
rrb 0.87 1 1 1 1 1 1 1 1
rr 0.59 0.77 0.84 0.89 0.93 0.95 0.97 0.98 0.99
rf 0.87 0.99 1 1 1 1 1 1 1
rj 0.79 0.95 0.99 1 1 1 1 1 1
1.608
full De Correspondent 2
QFKLMWVUJY[]\
SDTNRIAEOG'
;ZBHXPC,./
0.74 0.08 -0.06 0.07 0.15 0.31 0.46
1 2 3 4 5 6 7 8 9
rhl 0.54 0.93 0.99 1 1 1 1 1 1
rhr 0.52 0.84 0.94 0.98 0.99 1 1 1 1
rh 0.53 0.89 0.97 0.99 1 1 1 1 1
rrt 0.83 0.98 1 1 1 1 1 1 1
rrh 0.27 0.48 0.61 0.72 0.80 0.86 0.90 0.93 0.95
rrb 0.86 1 1 1 1 1 1 1 1
rr 0.57 0.74 0.81 0.86 0.90 0.93 0.95 0.96 0.97
rf 0.88 0.99 1 1 1 1 1 1 1
rj 0.81 0.96 0.99 1 1 1 1 1 1
1.555

The second layout, which moves ; in favor of j has 74% home row use (vs 71%), although slightly greater hand asymmetry (-0.06 vs 0.01), favoring the right hand more. This is due to the transition of the ; key off home row—now the right hand has access to one more letter, g.

detailed effort and finger use statistics

The breakdown in effort difference between the two De Correpondent layouts is shown below.

Colemak is excellent, with a lower overall finger distance, but increased path and stroke penalties. These penalties limit the use of the pinky (e.g. Colemak uses pinky 16% of the time, De Correspondent no more than 7%), increase the use of the index finger (e.g. Colemak 41%, De Correspondent 46%), and encourage more comfortable strokes, like rolling strokes.

De Correspondent Layout 1
model keyboard total effortrel% effort contributionsrel%
base penalties path
mod_01 correspondent-1 1.608

0.41926.1
0.45528.3
R0.172
F0.239
0.73445.6

correspondent-2 1.555 (-3.3)

0.38124.5 (-9.1)
0.47430.5 (+4.2)
R0.154 (-10.5)
F0.277 (+15.9)
0.70145.1 (-4.5)

qwerty 3.037 (+88.9)

0.97432.1 (+132.5)
1.01133.3 (+122.2)
R0.452 (+162.8)
F0.381 (+59.4)
1.05134.6 (+43.2)

dvorak 2.159 (+34.3)

0.40718.9 (-2.9)
1.00046.3 (+119.8)
R0.200 (+16.3)
F0.662 (+177.0)
0.75334.9 (+2.6)

colemak 1.879 (+16.9)

0.31316.7 (-25.3)
0.75340.1 (+65.5)
R0.170 (-1.2)
F0.470 (+96.7)
0.81343.3 (+10.8)

carpalx effort optimization keyboard name statistics effort
rowh rowb hand asym finger freq cumulative run distribution mod_01
full De Correspondent 1
XKGLMPUVWY[]\
SDTNRIAEO;'
QBJHFZC,./
0.71 0.09 0.01 0.04 0.17 0.32 0.46
1 2 3 4 5 6 7 8 9
rhl 0.49 0.90 0.99 1 1 1 1 1 1
rhr 0.59 0.88 0.96 0.99 1 1 1 1 1
rh 0.54 0.89 0.97 0.99 1 1 1 1 1
rrt 0.84 0.98 1 1 1 1 1 1 1
rrh 0.30 0.53 0.67 0.78 0.86 0.90 0.93 0.96 0.97
rrb 0.87 1 1 1 1 1 1 1 1
rr 0.59 0.77 0.84 0.89 0.93 0.95 0.97 0.98 0.99
rf 0.87 0.99 1 1 1 1 1 1 1
rj 0.79 0.95 0.99 1 1 1 1 1 1
1.608
full De Correspondent 2
QFKLMWVUJY[]\
SDTNRIAEOG'
;ZBHXPC,./
0.74 0.08 -0.06 0.07 0.15 0.31 0.46
1 2 3 4 5 6 7 8 9
rhl 0.54 0.93 0.99 1 1 1 1 1 1
rhr 0.52 0.84 0.94 0.98 0.99 1 1 1 1
rh 0.53 0.89 0.97 0.99 1 1 1 1 1
rrt 0.83 0.98 1 1 1 1 1 1 1
rrh 0.27 0.48 0.61 0.72 0.80 0.86 0.90 0.93 0.95
rrb 0.86 1 1 1 1 1 1 1 1
rr 0.57 0.74 0.81 0.86 0.90 0.93 0.95 0.96 0.97
rf 0.88 0.99 1 1 1 1 1 1 1
rj 0.81 0.96 0.99 1 1 1 1 1 1
1.555
none QWERTY standard
QWERTYUIOP[]\
ASDFGHJKL;'
ZXCVBNM,./
0.34 0.15 0.15 0.10 0.21 0.27 0.42
1 2 3 4 5 6 7 8 9
rhl 0.42 0.69 0.83 0.91 0.95 0.97 0.99 0.99 1
rhr 0.61 0.83 0.94 0.98 0.99 1 1 1 1
rh 0.51 0.76 0.88 0.94 0.97 0.98 0.99 1 1
rrt 0.55 0.78 0.91 0.96 0.98 0.99 1 1 1
rrh 0.68 0.91 0.97 0.99 1 1 1 1 1
rrb 0.94 1 1 1 1 1 1 1 1
rr 0.68 0.88 0.95 0.98 0.99 1 1 1 1
rf 0.89 0.99 1 1 1 1 1 1 1
rj 0.68 0.83 0.94 0.96 0.99 0.99 1 1 1
3.037
none Dvorak standard
',.PYFGCRL/=\
AOEUIDHTNS-
;QJKXBMWVZ
0.71 0.09 -0.14 0.18 0.21 0.26 0.34
1 2 3 4 5 6 7 8 9
rhl 0.76 0.94 0.98 0.99 1 1 1 1 1
rhr 0.47 0.81 0.96 0.99 1 1 1 1 1
rh 0.62 0.88 0.97 0.99 1 1 1 1 1
rrt 0.80 0.97 1 1 1 1 1 1 1
rrh 0.33 0.54 0.67 0.77 0.85 0.90 0.93 0.95 0.97
rrb 0.96 1 1 1 1 1 1 1 1
rr 0.60 0.77 0.84 0.89 0.93 0.95 0.97 0.98 0.98
rf 0.93 1 1 1 1 1 1 1 1
rj 0.84 0.96 0.99 1 1 1 1 1 1
2.159
none Colemak
QWFPGJLUY;[]\
ARSTDHNEIO'
ZXCVBKM,./
0.74 0.09 -0.06 0.16 0.17 0.26 0.41
1 2 3 4 5 6 7 8 9
rhl 0.55 0.85 0.94 0.98 0.99 1 1 1 1
rhr 0.49 0.77 0.90 0.96 0.98 0.99 1 1 1
rh 0.52 0.81 0.92 0.97 0.99 0.99 1 1 1
rrt 0.79 0.97 0.99 1 1 1 1 1 1
rrh 0.26 0.46 0.60 0.71 0.79 0.85 0.89 0.92 0.94
rrb 0.95 1 1 1 1 1 1 1 1
rr 0.57 0.73 0.81 0.86 0.90 0.93 0.95 0.96 0.97
rf 0.93 1 1 1 1 1 1 1 1
rj 0.83 0.95 0.99 1 1 1 1 1 1
1.879

Hogendoorn Layout for Dutch

Since the De Correspondent article, I've been made aware of a layout by Pieter Hogendoorn. Below, I compare it to the De Correspondent layout.

Figure 8 | A Dutch language layout by Pieter Hogendoorn.
Figure 9 | De Correspondent layout — 2. The effort for this layout is 1.555, a 3.3% improvement over the layout above. In this layout, the ; key is allowed to move, freeing up a home row key for J.

The Hogendoorn layout relocates , . / from the right to the left hand. It does a very good job in minimizing the finger travel distance. Carpalx evalutes its stroke penalties as also very low, only about 1.6% higher than the Correspondent—2 layout.

Dutch Layouts — Dutch corpus
model keyboard total effortrel% effort contributionsrel%
base penalties path
mod_01 correspondent-1 1.608

0.41926.1
0.45528.3
R0.172
F0.239
0.73445.6

correspondent-2 1.555 (-3.3)

0.38124.5 (-9.1)
0.47430.5 (+4.2)
R0.154 (-10.5)
F0.277 (+15.9)
0.70145.1 (-4.5)

hogendoorn 1.901 (+18.2)

0.32216.9 (-23.2)
0.83343.8 (+83.1)
R0.189 (+9.9)
F0.540 (+125.9)
0.74639.2 (+1.6)

The typing effort for Hogendoorn is significantly higher (1.901 vs 1.555) due to the large row and finger penalty. The layout makes heavy use of the pinky (15% vs 7%). The most used finger is the middle finger, which is unusual. However, it's as much as a choice by the layout designer as my own choice to minimize the use of the pinky and ring finger. Row penalties are applied because 70% of strokes are on the home row, lower than the 74% of Correspondent layout. The bottom row is used 11% of the time, which is heavily penalized in the effort model.

The hand asymmetry in the Hogendoorn layout is large (15%), favoring the left hand. This is quite a large value, equal to that of QWERTY for English.

Which layout is better? Well, it depends on what you're after. The Carpalx model favours hand symmetry, low use of pinky and index fingers but gives equal weight to finger distance as it does to finger/row penalties and to stroke path penalties.

carpalx effort optimization keyboard name statistics effort
rowh rowb hand asym finger freq cumulative run distribution mod_01
full De Correspondent 1
XKGLMPUVWY[]\
SDTNRIAEO;'
QBJHFZC,./
0.71 0.09 0.01 0.04 0.17 0.32 0.46
1 2 3 4 5 6 7 8 9
rhl 0.49 0.90 0.99 1 1 1 1 1 1
rhr 0.59 0.88 0.96 0.99 1 1 1 1 1
rh 0.54 0.89 0.97 0.99 1 1 1 1 1
rrt 0.84 0.98 1 1 1 1 1 1 1
rrh 0.30 0.53 0.67 0.78 0.86 0.90 0.93 0.96 0.97
rrb 0.87 1 1 1 1 1 1 1 1
rr 0.59 0.77 0.84 0.89 0.93 0.95 0.97 0.98 0.99
rf 0.87 0.99 1 1 1 1 1 1 1
rj 0.79 0.95 0.99 1 1 1 1 1 1
1.608
full De Correspondent 2
QFKLMWVUJY[]\
SDTNRIAEOG'
;ZBHXPC,./
0.74 0.08 -0.06 0.07 0.15 0.31 0.46
1 2 3 4 5 6 7 8 9
rhl 0.54 0.93 0.99 1 1 1 1 1 1
rhr 0.52 0.84 0.94 0.98 0.99 1 1 1 1
rh 0.53 0.89 0.97 0.99 1 1 1 1 1
rrt 0.83 0.98 1 1 1 1 1 1 1
rrh 0.27 0.48 0.61 0.72 0.80 0.86 0.90 0.93 0.95
rrb 0.86 1 1 1 1 1 1 1 1
rr 0.57 0.74 0.81 0.86 0.90 0.93 0.95 0.96 0.97
rf 0.88 0.99 1 1 1 1 1 1 1
rj 0.81 0.96 0.99 1 1 1 1 1 1
1.555
manual Hogendoorn
.UOPYXCLBV[]\
AIENHMDRTS'
:,?KQFGWJZ
0.70 0.11 0.15 0.15 0.19 0.36 0.30
1 2 3 4 5 6 7 8 9
rhl 0.48 0.79 0.89 0.95 0.97 0.99 0.99 1 1
rhr 0.63 0.94 0.99 1 1 1 1 1 1
rh 0.56 0.86 0.94 0.97 0.99 0.99 1 1 1
rrt 0.73 0.93 0.99 1 1 1 1 1 1
rrh 0.30 0.50 0.63 0.75 0.82 0.87 0.91 0.94 0.95
rrb 0.89 0.99 1 1 1 1 1 1 1
rr 0.57 0.74 0.83 0.88 0.92 0.94 0.96 0.97 0.98
rf 0.90 1 1 1 1 1 1 1 1
rj 0.86 0.96 0.99 1 1 1 1 1 1
1.901

hand, row and finger runs

Let's look at the hand, row and finger runs. These are given in the table above under the "cumulative run distribution" column. For a given category (e.g. rhl, which is the left hand) the number (e.g. 0.89) for a given column (e.g. 3) gives the fraction of successive strokes by the left hand which is 3 characters or shorter. This statistic measures the extent to which a row, hand, or finger is repeatedly used. In some cases, like home row, we want as many long runs as possible, because the home row is a low-effort location. On the other hand, for high-effort locations, like the bottom row, we want as short a run as possible. The meaning of the row codes is given in the keyboard evaluation section

The hand runs for Correspondent layout are fairly even with 99% of left hand runs being ≤3 and 94% of right hand runs being ≤3. Runs on the right hand are slightly longer than the left. Hogendoorn, because it favours the left hand, has numbers that are opposite. 89% for the left hand and 99% for the right. Hogendoorn uses the right hand for a single stroke 63% of the time (vs Correspondent's 52%), which again is a reflection of its favouring the left hand. Its left hand runs are also quite long—3% of them are ≥5 characters.

For row runs, the differences vary. Top row rrt runs are longer in Hogendoorn (73% of strokes on top row are singles) than in Correspondent (83%). Smaller differences are seen for home row runs are within 2-3% and bottom row runs. If we don't distinguish between the rows, then row runs rr are nearly identical in distribution.

Row jumps rj is the sum of adjacent row differences within a hand run. 86% of row jumps are ≤1 for Hogendoorn and 81% for Correspondent, with the other lengths having equal frequency. This is a difficult statistic to interpret because it doesn't distinguish between fingers. In future versions, I should probably track the row jumps by the same finger.