Further to that, I woke in a sweat thinking of another angle - what about all the promoted teams in their first season? How many survived and how much did they need to spend etc?
It's interesting to note that 9 of the last 15 promoted sides stayed up the following season, including all of last season's newcomers.
3 promoted clubs spent nothing in January with 1 surviving (Newcastle last season, unless Soccerbase is wrong).
Of the 6 highest spending in January promoted clubs, 3 went down, with 2 of those being outside the relegation places at Christmas. Of the other 3, Watford spent the most in 2015/16 (estimates of around £26.5m). They were 7th at Christmas and surely safe in any case though their post-Christmas form plummetted. Bournemouth's form, the same season, remained similar after shelling out something like £17m, as did Burnley's a year later having spent a similar amount.
Brighton, Huddersfield (last season) and Hull in 2013/14 were healthily placed and spent just over £10m each. Palace and Leicester were bottom in 2013/14 and 2014/15 respectively, spent around £10 and hauled themselves to safety. We spent modestly on a few Norwegians and went down.
My last bit of analysis was to think about how has transfer money affected the points a team has won and there is little correlation between the two. 3 of the top 4 spenders saw their points average decrease, as did 3 of the bottom 4 spenders. Only 5 promoted sides saw their points average increase after Christmas, including only one team that spent nothing. The rise of both Leicester and Palace was remarkable.
I think your suggestion of a couple of players around £10m, maybe more given that prices are further inflated with tv money, is statistically most likely to make a positive difference, though this certainly isn't guaranteed at all!! It's all about getting the right players and hope we continue to grow in this division. I forget sometimes that we have a squad virtually bereft of top flight experience. They're learning on the job and hopefully that will help us as the season progresses.