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As far as this latest batch of period so-called epics, the Hollywood trend is due to two things, neither of them Braveheart: Gladiator and advances in technology.
Braveheart was released domestically in May 1995, and while it did respectible numbers at the boxoffice, the U.S. take was "only" around $75-million...about equal to its pre-marketing budget. And some of that total came from it's Oscar rerelease. It did win big at the Academy Awards, including Best Picture and Director, and while the total gross when accounting for the entire world brought it up to around $200-million, that's still not the kind of return on an investment that makes the suits salivate and greenlight similar pics - even with the Oscars. The evidence to this fact is no other studios mounted any projects of similar scale in the year or two following Braveheart.
By 2000 when Gladiator was released, advances in CGI made it much more cost-effective to create gigantic period sets and ended the need for thousands of extras, as was the costly tradtion dating back to the great Silent epics like Ben-Hur (1925), all the way through the boom of the '50s and '60s with the likes of Spartacus (1960), The Ten Commandments (1956), Ben-Hur (1959) and Cleopatra(1963), and even all the way up to Gibson's Braveheart. CGI made it much, much easier to mount such a flick.
That relative cost-effectiveness then coupled with Gladiator's $180-million or so U.S. boxoffice and its bag full of Oscars (including Best Picture), THAT is what made the "epic" an attractive proposition in Hollywierd again. If Gladiator had to be made the way Spartacus was, the Oscar potential would never have entered into it, as the production cost would have been so high it never would have been made in the first place.
So while the producers who took the chance and made Gladiator may well have had Braveheart's success to bolster their own hopes, it was CGI that really fueled this current crop. After these start losing money again and no longer justify their cost, they'll fall away for a while.
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"Film is a disease. When it infects your bloodstream it takes over as the number one hormone. It bosses the enzymes, directs the pineal gland, plays Iago to your psyche. As with heroin, the antidote to Film is more Film." - Frank Capra