How efficient is Morse code?
Morse code was designed so that the most frequently used letters have the shortest codes. In general, code length increases as frequency decreases.
How efficient is Morse code? We'll compare letter frequencies based on Google's research with the length of each code, and make the standard assumption that a dash is three times as long as a dot.
|--------+------+--------+-----------|| Letter | Code | Length | Frequency ||--------+------+--------+-----------|| E | . | 1 | 12.49% || T | - | 3 | 9.28% || A | .- | 4 | 8.04% || O | --- | 9 | 7.64% || I | .. | 2 | 7.57% || N | -. | 4 | 7.23% || S | ... | 3 | 6.51% || R | .-. | 5 | 6.28% || H | .... | 4 | 5.05% || L | .-.. | 6 | 4.07% || D | -.. | 5 | 3.82% || C | -.-. | 8 | 3.34% || U | ..- | 5 | 2.73% || M | -- | 6 | 2.51% || F | ..-. | 6 | 2.40% || P | .--. | 8 | 2.14% || G | --. | 7 | 1.87% || W | .-- | 7 | 1.68% || Y | -.-- | 10 | 1.66% || B | -... | 6 | 1.48% || V | ...- | 6 | 1.05% || K | -.- | 7 | 0.54% || X | -..- | 8 | 0.23% || J | .--- | 10 | 0.16% || Q | --.- | 10 | 0.12% || Z | --.. | 8 | 0.09% ||--------+------+--------+-----------|
There's room for improvement. Assigning the letter O such a long code, for example, was clearly not optimal.
But how much difference does it make? If we were to rearrange the codes so that they corresponded to letter frequency, how much shorter would a typical text transmission be?
Multiplying the code lengths by their frequency, we find that an average letter, weighted by frequency, has code length 4.5268.
What if we rearranged the codes? Then we would get 4.1257 which would be about 9% more efficient. To put it another way, Morse code achieved 91% of the efficiency that it could have achieved with the same codes. This is relative to Google's English corpus. A different corpus would give slightly different results.
Toward the bottom of the table above, letter frequencies correspond poorly to code lengths, though this hardly matters for efficiency. But some of the choices near the top of the table are puzzling. The relative frequency of the first few letters has remained stable over time and was well known long before Google. (See ETAOIN SHRDLU.) Maybe there were factors other than efficiency that influenced how the most frequently used characters were encoded.
Update: Some sources I looked at said that a dash is three times as long as a dot, including the space between dots or dashes. Others said there is a pause as long as a dot between elements. If you use the latter timing, it takes an average time equal to 6.0054 dots to transmit an English letter, and this could be improved to 5.6616. By that measure Morse code is about 93.5% efficient. (I only added time for space inside the code for a letter because the space between letters is the same no matter how they are coded.)