How many possible phonological forms could be represented by a randomly chosen single character?

Question

In Chinese, every character is monosyllabic and Mandarin has a total of about ~1200 licit syllables including tone (about 400 if you don't count tone). This means that if I take any Chinese character and randomly choose a Chinese syllable, there is roughly a 1 in 1200 chance that that syllable will be the correct pronunciation.

Now let's say I do the same thing with Japanese. I take any random Kanji character and I randomly choose a full phonological form that can be represented by a single character. What's the probability that the pronunciation will be correct? This is a much more complicated question than in Mandarin since a whole multi-syllabic word can be represented by a single character, but like any language, there is a finite number of licit phonological forms in Japanese. Are there any accurate estimates of this number?

Edit: To illustrate:

If I pick the character 鏡 then the phonemic form can be kagami. If I select 鵜, the phonemic form can be u. For 八, hati. I'm not particularly concerned with the characters being used in a multi-character word, my primary concern is solely with individual characters.

So if I pick the character 鏡 and then I randomly select from all of the full phonological forms that can be represented by a single character, what is the probability that I will correctly select kagami?

In Mandarin, because there are only 1200 syllables and characters are always monosyllabic, if I pick a character with one possible pronunciation I have a 1 in 1200 chance of getting it correct. Some polyphonic syllables may have multiple possible pronunciations so I could have a 2 in 1200 or 3 in 1200 chance of picking it correctly.

In Japanese, a character can represent a sequence of multiple syllables, so what's the chance that out of the list of all possible phonological forms I'll pick the one that consists of the correct sequence of syllables?

Edit 2: Overly detailed reason for the question:

I'm researching cross-script differences in reading processes between English and Chinese; here's a highly simplified explanation.

In English, readers mostly compute the sound of a word based on the letters and use that computed phonological form to pick the semantic information behind the word. Visual information play a smaller role, but it helps with things like disambiguating homophones (e.g. "flower" and "flour"). A reader sees "flower", computes /ˈflɑʊ.ə˞/, and activates the meaning ❀, maybe with some help from visual information.

In Chinese, readers mostly retrieve semantic information directly from the visual form. Phonological information plays a role, but it doesn't seem to be the primary route of activation. A reader sees "花" and directly activates ❀.

Like I said, this is a super simplified explanation, but it covers the main gist.

I want to approach this difference as having to do with the "usefulness" of the different routes. In English, the visual information route isn't "useful" because English speakers don't make direct associations between visual forms and meaning.

In Chinese, one possibility is that the phonological route isn't "useful" because that information is very non-specific. A Chinese speaker can read "书" and know what it means with no context because the meaning is directly associated with the visual character. However, if there wasn't that direct association and the character simply activated "shū", it would be difficult to retrieve a specific meaning with no context because that phonological form can represent several dozen morphemes.

I'm trying to figure out if Japanese could be examined as a language kind of "in between" these two. Chinese cannot use a purely phonological route to get from any one of tens of thousands of characters to any one of hundreds of thousands of meanings, because you would have to connect them through a thousand or so phonological forms, forming a serious cognitive bottleneck. If Japanese can get from any one of tens of thousands of characters to any one of hundreds of thousands of meanings by going through several thousand possible phonological forms, Japanese could potentially have better success with the phonological route.

The question basically comes down to this: is the bottleneck from form to meaning through phonology in Japanese nearly as bad as it is in Chinese?

Answer 1

I am not aware of any such analysis that looks at the full breadth of Japanese character readings. Some background first.

Background detail

Kanji have been used very flexibly, both historically and currently, with examples such as the historical 木乃伊【みいら】, where the spelling comes from Chinese and the reading comes from Portuguese mirra or Dutch mirre ("myrrh"), or 猟虎【らっこ】, where the spelling is vaguely phonetic and the reading comes from Ainu; or the modern 騎士【ないと】, where the spelling comes from Chinese and the reading comes from English knight. This flexibility is a wonderful feature of the written language, and is a big part of why furigana exist. You will see numerous examples of this phenomenon (where the reading and spelling basically come from different words) in many (most?) manga series.

There are also numerous cases where a reading from one term is later applied to a completely different spelling. A couple firmly-established examples of this kind of reading/spelling shift include:

• 玉蜀黍【とうもろこし】, where the spelling was coined in Japan using Chinese characters based on their meaning, and the reading comes from older Japanese terms 唐【とう】 referring to foreign goods + 唐黍【もろこし】 referring to sorghum.
• 美人【かおよびと】, where the reading actually derives from 顔【かお】 + 良【よ】 + 人【ひと】.
• 月見里【やまなし】, where the spelling apparently came from the old name for a place, and the reading came from the new name.

As extreme examples, there are also cases where a given kanji compound spelling uses a reading where the phonemes cannot be cleanly apportioned to the individual kanji characters. Examples include 啄木鳥【けら】 "woodpecker" or 胡頽子【ぐみ】 "silverberry, oleaster". These are rare, but they exist. (FWIW, this phenomenon also exists in Chinese -- where a multi-character spelling might have a single-syllable reading.)

Looking just at single-character readings, there is still a huge range of possibilities. One factor is that okurigana (the kana after the kanji on the end of a native-Japanese word, used to show inflection) can optionally be left unwritten. 始 could represent the native-Japanese readings haji, hajime, hajima, or even hajimari, depending on the written context. Similarly, 志 might be kokoroza or kokorozashi.

Fluidity

Assuming that someone somewhere has done this kind of reading count for Japanese, it is important to note that any such number would not be a constant: new phonological forms, new readings, can be added to and used for kanji spellings, such as naito above. How "correct" these new readings are considered is a different question, and partly just a matter of how popular and longstanding any such additional reading might be.

I think your underlying assumption here is flawed:

... but like any language, there is a finite number of licit phonological forms in Japanese.

While Japanese does have a finite number of phones (i.e. sounds), kanji readings are not limited to this small number. Moreover, as illustrated some above, kanji readings are not as fixed as they are in Chinese, and they keep changing.

Conclusions

To reduce complexity, let us assume just the fixed set of readings listed in current dictionaries, and evaluate your core query:

I take any random Kanji character and I randomly choose a full phonological form that can be represented by a single character. What's the probability that the pronunciation will be correct?

As Blavius notes in his post, the range of on'yomi readings is reasonably small, increasing the probability of an accurate random guess.

However, your question seems to be asking about the full range of Japanese terms and readings. Including kun'yomi in the mix greatly expands the scope. The sheer number of "full phonological form[s] that can be represented by a single character" is huge, probably orders of magnitude larger than the corresponding set of "full phonological form[s]" for Chinese. This vastly reduces the likelihood of a random match between character and reading. I'm not sure what that probability would be, but it's a vanishingly small number.

Answer 2

According to this answer, there are 335 音読み in modern use. Assuming that statistic is true, the probability of randomly guessing and getting it right is 1/335.

But the odds improve based on other things about the kanji. There are certain phonetic components will suggest a certain reading. For example, you can bet a kanji with the component 寺 in it will be pronounced じ. Also, some readings are associated with more kanji than others--81 Jouyou kanji have the reading しょう, while only 2 have the reading じき.