The easiest way to do this is to look at the performance of LBO funds. It's up and down, returns are pretty poor compared to the stock market, but still positive, so that means they're getting back more cash than they are putting in - which means more success than failure, especially as success means +20 to +40% whereas fail means -80 or -90%
How many LBOs happen each year in the US? I would guess somewhere around a hundred. So dozens of success stories per year might be really good, compared to similarly distressed companies that did not get the LBO.