Telephone line modems were important in home and business computing for decades. Like a lot of people, I started with a Hayes Smartmodem 300. The modem came out in 1981 but I got mine about 1990. By then it was considered so slow that a lot of bulletin boards wouldn't let me call in.
From when did installed 1200bps modems outnumber 300bps units?
Related: What technological factors drove the rise of “high-speed” modems in the early 1990s?
I don't think it is likely that there will be published numbers showing the relative usage of different modem connection speeds over any large population of users. The best we can provide is some historical perspective on the timeframe for transition from 300 baud to higher speeds.
In general, 1200 baud modems enjoyed a fairly brief popularity because they were superseded quickly by low-cost 2400 baud models. Roughly speaking, 300 baud models dominated consumer purchases in the early 1980s, and 2400 baud models dominated consumer purchases in the late 1980s. There were a couple of years in the mid-1980s when 1200 baud modems were significantly cheaper and more widely supported than 2400 baud modems. More info is provided in the related question.
Short answer: Never - as virtually every 1200 bps also speaks 300 bps :))
Beside that, it's highly vague to pick any point in time, as the use of modems differed extremely over use cases which itself carried vastly different user numbers, so using any total might be distorting.
For example, by 1990, when you got your 300 bps modem, I was already using a Trailblazer for 3-4 years. Depending on the connection switched, it's PEP protocol (*1) sustained data rates of 18 or 19 kbps, depending on the line switched (*2). And all my peers where equipped alike - and ofc, all BBSes we called.
From a development point, 300 bps are around since the 1962 (Bell 103A), the 1200 bps 212A was introduced in 1976. Hayes did introduce their 300 bps Bell 103 compatible Smartmodem in 1981 and a 212 compatible Smartmodem 1200 in 1982. Internationally these standards were, in conjunction with other, similar ones, laid down as ITU-V.21 and V.22.
So yes, even by only looking at the US, 1200 bps were around in consumer-grade devices almost 10 years before you got your modem.
Then again, worldwide (and in the US after 1985) 1200 didn't play a big role at all, as 2400 bps was standardized in 1984 as ITR V22bis (*3). Since Standards take some time to become official, manufacturers already offered V.22bis compatible modems operating at 300, 1200 or 2400 bps line speed. Hayes did so in early 1985. By 1987 the Smartmodem 2400 was the only one offered, and available at or even below 200 USD.
Bottom line, in 1990 acquiring a 1200 bps modem was only possible second hand, and even then it was like stone age equipment. Standard was 2400 bps or faster. Not many BBS operators accepted users who occupied the line 8 times longer than what was considered average.
*1 - A protocol originally developed for military use in less than ideal conditions, with an emphasis to get a connection no matter how disturbed the line is - effectively the base of today's ADSL, pumping several megabits over classic phone lines :)
*2 - History insert: When in 1989/90 the iron curtain fell, we did help new BBSes popping up in East Germany with Telebit modems, enabling them to transfer at speeds never below 10 kbps - which is darn good, considering that much of the eastern phone network was basically pre-war technology - and often even from before then.
*3 - The suffix bis denotes a second, extended edition with new features - likewise ter stands for a third one. Both taken from French, once the official language for telecommunication standards.
It is hard indeed to answer the question, but I can share my Canadian anecdotal experience and I think it will give a general sense of the timeline, plus or minus.
I acquired my first modem in 1984 - a Commodore VICmodem, which was the first sub-$100 modem on the marketplace. At that time, 1200 bps modems already existed but were pretty much exclusively used by businesses (and the odd bulletin board system). The vast majority of BBSes in my city ran at 300 bps.
By 1986 Commodore had come out with the 1670 modem, a 300/1200 bps Hayes-style smartmodem, and other companies also had fairly inexpensive 2400 bps modems. I would think that it was here or slightly after that 1200 bps started to outnumber 300 bps ones.
By 1987 when I got my first Amiga, I had migrated to 2400 bps modems, which had come down significantly in price thanks to companies like Practical Peripherals and Supra, and at this point, 1200 bps modems probably started becoming a minority.
Things really changed when high-speed modems came out, and the paradigm shifter there was the Rockwell chipset and modems like the SupraFAXModem v.32bis (14.4kbps), but this is outside the scope of your question.
My old s-100 ~1978-1985 could use the 50 (teletype) and "Kansas City Standard" at 300baud but was capable to 2400baud; so 1200 never was "the" baud rate of choice. Through the 1970's I worked on many ASCII terminals that used DEC, Wyse, and IBM protocols and could be set to communicate at least up to 9600 and some may have been capable up to ~32,000.
The 300, 1200, 2400, and eventually 9600baud were only limitations to the budget of home economics. From my own experience, much faster baud rates existed in the ($)commercial world at least 15-20 years earlier than 1980 - probably even sooner.
The telephone companies would support what ever modem rate you wanted - for a price. As I remember it, telephone companies charged between $1000-3000 per month (plus a usage fee) for a T1/T2 line in the 1980's.
Fast modems have been in existence since the stone age - just not affordable. In ~1991 the Govt hospital I worked for paid about $8000 (~$15k in today's money) for a T1 modem (available from ~1960). So, fast modems remained pricey and well above the average persons budget until the Internet.
