I'd like to see data on how successful these guys are at predicting the profitability of the pictures they recommend for funding.

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Two things,
First, considering the dregs topping the box office (Transformers, Battleship), and what passes as 'smart' (Prometheus, Star Trek), I'm afraid a good chunk of the business can be more-or-less predicted.
Second, they're not pretending to be oracles, they're just doing stats. They are probably only providing ballpark estimates, and as they've been around for decades, it looks like they're doing fine.

Large publishers, whether it is for books, music, or movies, all rely on the same strategy: for every 10 works produced, they expect 1 to be successful and pay for all the others. I'm guessing these people are in the business of providing estimates to budget the 9 others.

This was certainly true in the past, but how many true flops can you think of since Waterworld? Even it ended up breaking even after video sales. In the 70s and 80s there were any number of gloriously awful 'B' films, or 'A' films that took risks and then flopped, but these have just gone away... they just aren't made any more. As film budgets have climbed, the business has become more risk-averse and predictable and, many people would claim, more boring.

Flops are still there, but with a lesser impact. This company helps set a maximum budget per project, so that over the whole year the studio will break even, or at least persist (hence the ongoing trend of risk-averse "neatly categorized + predictable budget" movies).

But they still don't know in advance which movies will make it. So we have a watered down version of the 70s "production roulette": the majority of movies will still lose money, but the with an overall budget under control the company is still there the following year.

Case in point: in 2013 most big budget movies bombed badly, but (as opposed to the 70s) no major company went bust.

This article may interest you, it explains why there is less impact - http://www.bbc.co.uk/news/business-25409796

It also partly explains why no major company went bust, although I'm sure there is at least some degree of luck involved there

It's a shame their table from Box Office Mojo didn't include the film budget... and I'm just a little bit too lazy to go and look them up myself