This decidedly un-Russian pronunciation has been approved by an article from the BBC’s pronunciation unit:
Sochi, the venue for the Winter Olympics, is usually anglicised as SOTCH-i (-o as in not, -tch as in catch, -i as the “y” in happy) by English and Russian speakers alike – and this is the pronunciation we recommend to broadcasters. However, the Russian pronunciation of -o in Sochi is somewhere in-between the English “law” vowel and the English “lot” vowel (so somewhere between SAW-chi and SOTCH-i).
To say that Russian o is “somewhere in-between” BrE THOUGHT and LOT is a bit misleading. In both quality and quantity, it resembles BrE THOUGHT oː more than LOT ɔ. Here is Сочи uttered by several Russians:
In my experience, Russian speakers (and I’ve been teaching an increasing number) find it harder to approximate BrE LOT than THOUGHT. I not uncommonly mis-hear them as a result: for instance, I once perceived talking where topic was intended. I haven’t noticed mis-hearings the other way round.
Russian also lacks the contrastive vowel length which is such an important feature of English, particularly BrE. The stressed vowel of BrE blotchy is very short, particularly as it’s clipped by the following tʃ. But Russian tends to lengthen stressed vowels, making native Сочи still more like SAW-chi and still less like SOTCH-i.
Of course there are considerations other than phonetic accuracy. The BBC article continues:
When forming recommendations, our approach is to reflect the native pronunciation as closely as possible while bearing in mind practical considerations. Our pronunciation advice is anglicised for ease of pronunciation by English-speaking broadcasters and to ensure that names can be discerned by BBC audiences.
SAW-chi would “reflect the native pronunciation” more closely than SOTCH-i, but there is a non-phonetic factor which would make it psychologically harder for BrE broadcasters and audiences, namely the spelling. There’s a small number of English words in which the spelling och corresponds to ɔtʃ, with the short LOT vowel: Rochester and cochineal, for example. But I don’t know a single case where this spelling corresponds to oːtʃ, with the THOUGHT vowel. More generally, in fact, written o doesn’t correspond to BrE THOUGHT before any consonant letter except r. So the association of SAW-chi with written Sochi feels awkward.
However, it wouldn’t be unprecedented to place phonetic accuracy above English spelling conventions. Back in the days of South African apartheid, it was common for BrE news people to pronounce the surname Botha with RP’s CURE vowel: bʊətə. Here’s the BBC’s Michael Buerk referring to Pik Botha, nearly 30 years ago:
This pronunciation placed phonetic fidelity to the Afrikaans pronunciation over a flagrant clash with English spelling conventions. I can even recall conversations in which Brits (ignorant of Afrikaans) expressed bafflement at the TV-news pronunciation of this word. Today, less aged BrE reporters are more likely to rhyme Botha with quota; I suspect this is due less to ignorance of the native pronunciation than to the demise of the centring diphthong ʊə in standard BrE. Here are the BBC’s Andrew Harding and Nick Childs last year referring to South African police officer Hilton Botha:
(The BrE GOAT vowel heard there would be another option for Sochi, and is used in many familiar Russian words: Shostakovich, Nabokov, etc. But from a phonetic point of view it’s too central and diphthongal for Russian o. The more back and less diphthongal GOAT of AmE is better, and is the most common choice by Americans for primary-stressed orthographic o in words from Russian and other foreign languages: Sochi, Shostakovich, Prokofiev, etc.)
I’ll end with an aspect of Sochi not discussed by the BBC article, namely the final vowel. Russian final unstressed i is pronounced ɪ, resembling the English KIT vowel. Here again are the Russian pronunciations of Sochi:
This feature verɪ clearlɪ differentiates Russian-accented English from contemporary standard BrE, which uses the FLEECE vowel in this position. Here again are the British pronunciations:
The Russian final vowel is nicely demonstrated by Russian-born American actor Anton Yelchin, who lays on a thick Russian accent as Chekov in the recent Star Trek films; here he says “Yes Sir, happɪ to”:
Fortunately there’s an easy way to help Russians who want to reduce their accent, namely by encouraging them to use a vowel more like their final unstressed –ij ий, as in Rimsky-Korsakov Римский-Корсаков:
This distinction is completely obscured by the confusing and superfluous ‘schwee’ symbol i, used so widely in BrE dictionaries and text books, and in the BBC’s respelling system. Schwee pulls off a remarkable double whammy: it adds a non-existent extra member to the already huge English vowel system, and at the same time obscures a valuable distinction!
To sum up. If you’re a BrE speaker who wants to pronounce Sochi in the most Russian manner that BrE vowels allow, you should put THOUGHT in the first syllable and KIT in the second. If you’re a Russian speaker who wants to pronounce Sochi like a BBC-type speaker, you need to make the first vowel much shorter and more open than the Russian vowel, and pronounce the final vowel more like -ий than -и.