It’s long been the case that “Game of Thrones,” the hit HBO show, was in danger of running out of book material. Now that the first episode of the sixth season has aired, that much is assured. But with the end of the TV run now in sight, HBO is also quickly running out of show material, posing problems for a network that is essentially sitting on a single massive hit. And HBO, which might at best have only two additional seasons of “Thrones” to come, is now where it was when “The Sopranos” began to come to a close, itching for a new hit.

Granted, “Game of Thrones” is but one of the highly regarded television series airing on the premium cable network at the moment: Both “Veep” and “Silicon Valley” had their season premieres in the wake of “Thrones” on Sunday. But neither is the cultural force of “Thrones.” The network is, for now, doing stupendous, all things considered, firing on all cylinders. This is arguably the best suite of programming the network has aired at a given time. Arguably.

What do you say we try to settle that argument?

Here’s the skinny: I grabbed the IMDb user rating for every television episode that the site has listed with HBO as the distributor, which takes us back to the mid-1970s. To understand where HBO came from and where it’s going, let’s take a more step-by-step tour through the brief history of one of the most dynamic enterprises in television.

HBO had little in the way of dramatic programming in its early years, from its birth in 1972 to about 1996, compared with what we’ve come to expect today. The network gradually started building up a repertoire of original content; based on our data, this began with a spooky anthology series, “The Hitchhiker,” in 1983. In 1989, the network launched “Tales from the Crypt.” But a year later, maybe because it was running out of ways to knock off “The Twilight Zone,” HBO moved to sitcoms, and the half-hour comedy “Dream On” launched. “The Larry Sanders Show” was added to the schedule in 1992; it and “Dream On” served as the scripted anchors for the network through 1996, a year of major change at HBO.

When Jeff Bewkes took over HBO in 1995, he raised the budget of the original programming division from $50 million to more than $300 million, and the effects soon began to speak for themselves.

In 1997, HBO aired the first season of “Oz,” a gritty prison drama that was the tip of the spear for the dramatic overhaul of HBO’s programming. To see the effect that “Oz” and the shows that followed had on the quality of HBO’s programs, here’s the one-year rolling average of the IMDb episode ratings for HBO programs from 1990 on, relative to HBO’s liftetime average episode rating:

The network’s scripted genre renaissance would change HBO — and television as a whole.

In 1998, the network aired the second season of “Oz,” as well as “From the Earth to the Moon,” a highly regarded miniseries from Tom Hanks and Ron Howard. On the comedy side, “Sex and the City” premiered, and cult hit “Mr. Show With Bob and David” entered its final laps. In 1999, HBO tapped “The Sopranos” as the scripted drama successor to “Oz,” and in 2000, “Curb Your Enthusiasm” joined the network’s comedy mix.

Looking at the average episode score for each year hammers home just how huge this transformation in quality was. First, raw score isn’t everything here, because IMDb user ratings skew high, so we really want to compare HBO to itself. The average episode rating is just under 8.0. The average yearly episode score through 1997 never topped 8. In 2001, that figure was 8.44 — the highest annual average of all the years I analyzed — because of a strong mix of shows that included “Band of Brothers,” “Curb Your Enthusiasm,” “Oz,” “Six Feet Under” and “The Sopranos.”

From that perspective, 2001 was HBO’s best year ever. The extremely highly rated “Band of Brothers” played a big part in this. Its 10 episodes accounted for about 14 percent of HBO’s total episode production that year — the miniseries’ episode average score of 9.2 is the second-highest of any multiepisode HBO season ever.

When has HBO had lean years? You can see a couple of spots when you zoom in on the data since 1997, when “Oz” debuted. Since we’re well beyond the middling quality of the early years, I adjusted the baseline so that it’s strictly the average from “Oz” on:

“The Wire” was launched in 2002, bolstering HBO’s offerings, but in 2003, there was a pretty heavy dip in the overall quality compared with the average. This appears to be because “The Sopranos” didn’t air any episodes that year (Season 4 was in 2002, and Season 5 in 2004), combined with a weak season for “Sex and the City” and poor ratings for the new show “Carnivale.”

By 2004, with the debut of “Deadwood” and strong seasons for “The Wire” and “The Sopranos,” the ratings go back to above-average. The level remained consistently above-average through 2008 — boosted by shows like the BBC-HBO co-production “Rome,” “Entourage” (before it went to shit), “Flight of the Conchords” and “In Treatment” — but came crashing to a thud in 2009.

“True Blood,” which came out in 2008 to fill the hole left by “The Sopranos,” managed to be a hit but was not enough of one to singlehandedly prop up the quality of the network in 2009. “The Pacific,” “Boardwalk Empire” and “Treme” managed to marginally help the network through 2010 and 2011, but IMDb users hated the first seasons of “Hung,” “How to Make It in America” and “Enlightened.” It wasn’t until “Game of Thrones” premiered in 2011 that HBO’s overall quality bounced back to the network average.

In 2012, “True Blood” started on a decline in quality, “Girls” was not receiving high user reviews, and even the combined might of “Game of Thrones,” “Boardwalk Empire” and “The Newsroom” was not enough to bring the network above its post-“Oz” average.

But in 2013, HBO got back up from underwater: “Veep” and “Enlightened” hit their stride in their second seasons, and in 2014, the network had its best year since 2004. “True Detective” was a smash hit, “Game of Thrones” had its best season, and “Boardwalk Empire” was ending strong, “Last Week Tonight with John Oliver” went on air to substantial acclaim, and newcomers “Silicon Valley” and “The Leftovers” got high marks. A rising tide lifts all ships, and in general, the network has had average to above-average years since 2014.

At this juncture, it’s worth considering just how far HBO came: Recall that when Bewkes took over in 1995, the original programming budget was $50 million per year. This year’s 10-episode season of “Game of Thrones” cost an average of more than $10 million per episode.

And that brings us back to HBO’s current situation. Over the next three years, HBO may beat its 2001 high-water mark. It’s within striking distance, and the network has a strong suite of shows. But looking beyond that, HBO is in a bit of a pickle.

“Game of Thrones” is going strong but has an expiration date. “Silicon Valley” and “Veep” remain outstanding, but neither is the smashing franchise that “Thrones” is. “Vinyl,” which the network probably wanted to be a hit given all the money it gave to Terence Winter (of “Boardwalk Empire” fame) and Martin Scorsese (of “You Should Probably Know Who Martin Scorsese Is” fame) had a tepid first season and has to be a disappointment.

Now that we’re hearing that the “Game of Thrones” producers think they have enough gas in the tank for 13 more episodes that would be divided between seasons seven and eight, HBO has a concrete timeline within which it needs to find that new franchise. Sometimes this hit can be unexpected. When “The Wire” and “The Sopranos” came to a close, “True Blood” stepped up out of nowhere to pick up some of the slack. Sometimes the hit can be deliberate: When “True Blood” began winding down, “Game of Thrones” was tapped as the Sunday night successor. But HBO needs that hit!

What’s cooking in the pot? After a disastrous second season of “True Detective,” it doesn’t seem like the heir apparent in drama. “The Deuce” may take the sexposition pioneered by “Thrones” to its logical conclusion considering that it is a David Simon-created drama about porn in the 1970s. The most promising offering on the radar might be “Westworld,” a sci-fi show that’s being produced by Jonathan Nolan and J.J. Abrams and is based on a story by Michael Crichton.

So they have options. But it’s hard to bottle lightning, and if anything, this is cause to kick back and appreciate what HBO has pulled off, at least for the moment. When precisely HBO was at its best is somewhat solved. The network’s best calendar year was 2001. Its best consecutive 365 days was from June 17, 2006, to June 17, 2007, when we saw the third seasons of “Deadwood” and “Entourage,” the fourth and final good season of “The Wire,” the second season of “Rome” and the final episodes of “The Sopranos.” That’s certainly a hard tear to match! But still, we’re getting the chance to check out offerings among HBO’s best since the renaissance began.

CORRECTION (April 28, 10:08 p.m.): A previous version of this article incorrectly described “Gods and Secrets,” a show in development by Adi Shankar. The show does not have a distributor yet; it is not scheduled to air on HBO.