So your NCAA bracket is busted. Should you have just chosen all the top seeds?

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Much like your bracket, the trendy upset pick Drake did not beat the odds. / Getty Images

There's a familiar pang of regret that comes for many NCAA basketball tournament fans every March.

You were filling out a bracket for March Madness, and you thought it would be fun to pick some underdogs. Then perhaps you got a little carried away — how could you not pick the Hilltoppers, whatever that is — and now, taking stock after the dust of the first round has settled, you wonder if maybe, just maybe, your bracket should have been a little more boring.

Many of this year's trendiest Cinderella picks — New Mexico, McNeese State, Samford, Nevada, Morehead State — all fell to their favored opponents in the men's Round of 64, which wrapped late Friday.

In all, six lower-seeded men's teams won their games on Thursday and Friday (not counting 9-seeds, which aren't really underdogs). And in the women's tournament, only one of 16 games so far have been an upset (congratulations, Middle Tennessee!).

After 16 games in the men's tournament on Thursday, more than 22 million were busted in ESPN's men's tournament bracket challenge, and only 1,825 perfect brackets remained.

By the end of the day Friday, all of them were out — including yours.

Yes, you probably should have chosen all of the 1- and 2-seeds to advance, especially in the women's tournament, where there tend to be fewer upsets than in the men's event.

As you go about licking your wounds and thinking about how to strategize for next year, here are some things to know:

Bad news: Choosing the higher seeds for every game will also not work

Unfortunately, there's no way of getting around it: There has never been a tournament where every higher seed won a game, and the odds of that ever happening are infinitesimally small. It's never even happened in the Round of 64! (Sorry, Kentucky.)

To put an even finer point on that idea — in the 39 men's tournaments since the bracket expanded to 64 teams in 1985, only once has the Final Four featured all four 1-seeds. Only once!

The chalkiest men's tournament ever was 2007: That year, double-digit seeds won only two games in the Round of 64 and none in the rest of the tournament. Only 12 games total were won by a lower seed, and in eight of those, the "underdog" was rated just one seed below the favorite.

Still, the seeds exist for a reason. In the men's tournament, the title game has been won by a 1-seed nearly two-thirds of the time, and top seeds have lost to a 16-seed only twice. The 2-seeds are nearly as good; they've lost to 15-seeds just 10 times in more than 150 games.

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The top seed South Carolina Gamecocks were favored by more than 55 points against 16-seed Presbyterian. Unfortunately, they won by only 52. / Getty Images

Picking higher seeds is a better bet in the women's tournament

Higher seeds fare better in the women's tournament for a couple reasons. Women's college basketball is a newer sport and has historically had less parity than the men's game. Another factor is that early rounds in the women's tournament are played at the higher seed's home court, giving them a small advantage.

The result is that there are fewer upsets in the women's tournaments, and the gap between the best teams and the worst teams is bigger than in the men's.

Here's one example: The biggest betting spread in the men's Round of 64 was the 26.5 points between 1-seed UConn and 16-seed Stetson. In the women's tournament, top seed South Carolina was favored by 55.5 points over 16-seed Presbyterian (the Gamecocks ended up winning Friday's game by a disappointing 52 points).

Since the women's tournament expanded to 64 teams in 1994, a 16-seed has defeated a 1-seed only once, and the 2-seeds and 3-seeds have never lost in the first round. Top seeds have won the title about 75% of the time, and the Final Four has been all 1-seeds on three occasions.

But upsets are getting more common, especially in the men's tournament

All this is to say: A successful bracket must choose some upsets — especially in recent years, as upsets and runs by lower-seeded teams have become more frequent.

In both the men's and women's game, the likeliest upsets are 9-seeds over 8-seeds (in the men's tournament, 9-seeds have actually won more often than the 8-seeds). It's also wise to pick at least one 10- and 11-seed, both of which have historically won their men's first-round matchups about 40% of the time and only slightly less often in the women's.

In the men's tournament, the 11-seeds, in particular, have gotten better in recent years; since 2010, they're 30-26 against 7-seeds, including this year.

For the men's game, at least one 1-seed has been knocked out before the Elite Eight in all but one of the last 14 years. And a team seeded 5 or lower has reached the Final Four in the past 10 years.

One last tip: You can always fill out more than one bracket

Nobody will stop you from only telling your friends about the best one.