Yesterday was a big test for Sling TV: How would the Web TV service do when lots of subscribers logged in at the same time, to watch some of the biggest sports events of the year?

Not that well, apparently. By Sling’s own admission, it couldn’t handle an influx of users who tuned in to watch Turner Networks’ broadcasts of the March Madness college basketball semi-finals, featuring Duke vs. Michigan State and Wisconsin vs. Kentucky. That led to streams that were choppy or nonexistent, according to frustrated Sling users.

“We’re sorry some basketball fans saw errors tonight due to extreme sign-ups and streaming. Engineers rebalanced load across network partners,” Sling’s @slinganswers Twitter account posted last night, around the middle of the evening’s second game.

https://twitter.com/slinganswers/status/584533011456139264

On conventional TV, Duke/Michigan State was one of the most popular Final Four games in a decade, while Wisconsin/Kentucky was even bigger: It attracted more viewers than any other Final Four game in the last 22 years. (On Wisconsin!)

Without any more detail from Sling or its parent company Dish Network (I’ve asked them for comment but am not holding my breath), it’s hard to diagnose what went wrong last night. But if you take Sling’s Twitter operator at face value, the company didn’t anticipate that one of the biggest nights in sports would be a big night for the service, which delivers a package of pay TV channels over the Web for $20 a month.

[UPDATE: Sling TV CEO Roger Lynch called back, and says his service was well aware that streams and sign-ups would be in high demand on Saturday. And while Lynch concedes that his service was overwhelmed, he says outages and quality issues only affected around 1,000 users — “a fraction” of Sling’s base. (And no, Lynch wouldn’t disclose his overall numbers). Lynch says new software he’s rolling out this week should help Sling deal with future spikes, which could come soon: Next weekend HBO launches a new season of “Game of Thrones” , and Sling will allow users to sign up for the pay TV channel for an extra $15 a month.]

On the one hand, that’s hard to believe. Watching live sports on the Web, via ESPN and Turner’s channels, is by far the most compelling reason to sign up for Sling, which attracted 100,000 sign-ups in its first month. So you’d think the Sling folks would have circled Saturday night on their calendars many months ago, and would have gone out of their way to make sure they could handle demand.

On the other hand, that excuse is uncomfortably familiar. Many big Web streaming events in the last few years seem to be accompanied by user complaints and operator apologies.

For instance: In February, some people who tuned into watch ABC’s streaming coverage of the Oscars saw old movies and game shows instead. Last year, ESPN cited “unprecedented demand” when it struggled to serve everyone who wanted to watch the U.S. play Germany in the World Cup. And HBO’s streaming service conked out a couple times when lots of people tried to watch some of its most popular shows.

(For what it’s worth, I streamed the second half of the Wisconsin game on my iPhone, via Turner’s “March Madness” app, and it worked just fine — except in the last couple of minutes, when it shut down twice, sending me into convulsions. Luckily it all worked out. (Nice job, Bronson.)

In the past, it was hard to get too worked up about Web TV streaming problems, since Web TV streaming was always presented as an alternate option for a relatively small group of people.

But now Web TV is supposed to be mainstream: Dish and Sony are presenting their online packages as full-blown replacements for cable TV subscriptions, and this month HBO will sell HBO Now, an online-only service targeted at an audience of more than 10 million potential subscribers. In the fall, the NFL will stream a game to a national audience. Apple wants to launch its own streaming service this year.

And bear in mind that there are many ways for a Web stream to break down before it gets to your laptop or Apple TV. Even when operators like Sling aren’t at fault, something else down the line — your local broadband provider, your router or your own operator error — can prevent you from watching what you want, when you want. It seems like it might be some time before regular humans can reliably depend on the Web to show them something that lots of other people want to watch at exactly the same time.