Great stories definitely impacted the ratings. From ESPN:

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ESPN’s presentation of the 2014 NFL Draft (May 8-10) – including the first two nights in prime time – was the network’s highest-rated NFL Draft telecast since 1993, based on fast nationals, according to the Nielsen Company. The telecast also saw significant increases in both ratings and viewership over the 2013 event.

The 15-plus hours on ESPN and ESPN2 delivered a 2.7 US rating, a 31 percent gain from 2013 (2.1) and a 35 percent increase from 2012 (2.0). The average viewership of 4,121,000 viewers is a 36 percent gain over 2013 (3,035,000) and a 41 percent increase over 2012 (2,924,000). All key male and adult demos were also up double digits from the previous two years.

This weekend matches ESPN’s one-day telecast of the 1993 NFL Draft (Sunday only), which also averaged a 2.7 rating

The top-10 metered markets for ESPN’s three days of NFL Draft coverage were New Orleans (5.6 rating), Cleveland (5.6), Birmingham, Ala. (5.3), Buffalo (4.8), Greenville, S.C. (4.8), Houston (4.5), Dayton (4.2), Columbus, Ohio (4.1), Austin (4.1) and Cincinnati (4.0).

Rounds 4-7 / Day 3 (Saturday)

ESPN’s 7.5 hours of coverage (12-7:35 p.m. ET) on ESPN delivered a 1.5 US rating, a 36 percent increase over last year’s coverage (1.1 US), while viewership averaged 1,962,000, pacing 22 percent ahead of 2013 (1,610,000).

Rounds 2-3 / Day 2 (Friday)

ESPN’s one hour of coverage (7-7:59 p.m. ET) delivered a 2.2 US rating and 3,155,000 viewers, based on fast nationals, while ESPN2’s remaining 3.5 hours (7:59-11:25 p.m.) delivered a 1.8 US rating and 2,693,000 viewers. Together, the two networks averaged a 1.9 US rating and 2,796,000 viewers, equaling the 2013 rating and a three percent gain in viewership from last year’s second and third rounds on ESPN and ESPN2 (2,727,000 viewers).

Round 1 / Day 1 (Thursday)

ESPN’s first round coverage of the NFL Draft averaged 9,943,000 viewers with a 6.1 US rating based on fast nationals, making it the most-viewed NFL Draft telecast in ESPN’s 35 years of presenting the event. The Thursday telecast ranks as the sixth highest-rated event of 2014.

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Richard Deitsch of SI.com wrote about how ESPN covered the Michael Sam moment:

What happened at the crucial moment on Saturday night? Following Sam’s seventh-round selection by St. Louis and a 10-minute examination of how Sam would fit in with the Rams both as a football player and a media curiosity, ESPN host Trey Wingo informed viewers that they were about to see footage of the moment Sam learned he had been drafted. (As you’ll learn in my MMQB piece on Monday, neither Markman nor any of the on-air ESPN staffers had seen the tape of Sam learning of his selection prior to it airing for the audience.)

Wingo began to talk over the footage but abruptly pulled out and let the natural sound of Sam’s weeping take over. The Missouri defensive lineman held the phone close to his ear as he spoke with Rams coach Jeff Fisher. Viewers saw Sam’s boyfriend, Vito Cammisano, consoling him and then wiping his own tears. They heard Sam say “Yes, sir” twice and then “thank you.” That was followed by Sam kissing his boyfriend and both men embracing. Then another kiss, more hugs and the raw footage running out. It was unlike anything viewers had ever seen at an NFL draft and remarkable, honest television.

Wingo then led the audience to analyst Bill Polian, the former Bills and Colts general manager who hit on the perfect tone. “One of the great parts of being a GM and head coach in this league is making that call,” Polian said. “You get the player on the phone and you say here I am and I represent this team and we are about to draft you. You can hear the overwhelming joy and screams and tears because for the families and players their life-long dream has come true…It makes you feel so good to be part of it.”

The conversation continued with new images of Sam, breathing heavy, and giving his boyfriend another kiss. Later, Sam and his boyfriend smashed cake into each other’s faces and kissed again. “This is a draft unlike any other from what we just experienced,” Wingo said. “Maybe one of the more relevant picks we have had in recent history — Michael Sam crossing that barrier, becoming the first openly gay man drafted in the NFL.”

ESPN went 17 minutes on the Sam selection, and it led up to the draft’s final selection. Sensational work.