Thanks. I have updated the OP with my latest rejections.
There's definitely a process of learning and development in that I made some rather hasty/slapdash applications last year, and I can go back to these now and see improvement.
I've also applied to a lot of firms, and I'm quite passionate about statistics: my profile is atypical, and I've found that it might or might not fit with firms' requirements, but evidently some candidates are more desirable than others, and might stand a high chance of making it through the first stage of the top firms, whereas I have a smaller but non-zero chance. I doubt my Milbank application was as compelling as my Slaughters application, say, but Milbank had a new person reviewing applications this year and this random event got me to the AC. OTOH, if I apply to less prestigious firms, my success rate is higher: it's less competitive, fewer applicants with less compelling applications, and statistically if I apply enough then I'm likely to make it through.
On the other hand, the pure "if you apply to 100 firms you'll become a lawyer because it's a 1-in-100 chance" approach is definitely wrong. It's a combination of randomness and application. If I'd spent 40 hours practising recording VI questions a few months ago, then I'd probably have made it through one of my second-round VIs, as opposed to failing all eight.
I've gone through my written applications and can identify where answers are not quite top-class: awkward wording, long sentences, illogical structure, failing to properly tailor my copy-paste answer to a generic question (e.g., "tell us about your hobbies") to the specific question being answered, but for VIs that's more difficult as a VI is a one-off performance rather than something that can be written, checked, edited, and restructured to attain a higher standard.
