Is sliding into first base faster than simply running through it? It's a question that's been kicked around baseball for years, with few satisfying answers. Of course, for most of those years, Statcast™ data weren't available to apply to situations like this. Let's use it now to dig into one of baseball's longest-running discussions, and hopefully we can prove at least part of it.
As the only non-home base that allows the runner to run through the bag rather than requiring him to stay on it, first base occupies a special place in the baserunning conversation. While everyone agrees a slide is fine if you're specifically trying to avoid a tag, there's never been 100 percent consensus about the best approach otherwise.
Those against sliding into first argue, reasonably, that when your feet stop pumping, you lose propulsion and then incur friction -- i.e., slow down -- upon the rest of your body scraping against the ground. Those in favor of the practice don't disagree with that, but they argue that the ability to get horizontal and reach out with your arms ahead of your center of mass make up for that fact. The correct answer is probably in between, in that diving or sliding may be as fast if you do it perfectly -- except it's rarely done perfectly. 
Since we'll be showing just a handful of examples here and not doing a full large-scale investigation, this won't end the discussion. But we are hopefully going to add to the conversation in a new way, with Yankees outfielder Brett Gardner as our test case. It's faster to run, of course. But is it better?

We chose Gardner because he's long been one of baseball's foremost examples of slides into first, to the point that he was featured in an article about the topic here more than six years ago.
"If somebody wants to argue with me about it," Gardner told MLB.com in 2011, "I'll sit them down in front of a computer for two minutes and show them that I do get there faster."
We don't wish to argue; after all, the article later noted that Gardner "has pored over the tape [and] has timed himself down the line," so he'd clearly put the work into it, and Gardner has been a successful regular for nearly a decade doing things his way. We do have the computers, though, in a way we didn't in 2011. Let's put Statcast™ to work.
Everything we're about to show you uses Sprint Speed, which measures runner speed in "feet per second," in a runner's fastest one-second window. The Major League average is 27 feet per second, and Gardner, averaging 28.7 feet per second on his max-effort runs, is well above average on the leaderboards. Each of the play diagrams shows the moment the runner hits first base.
Let's keep it simple to start, showing two Gardner runs to first where he ran hard the entire time and ran through the base.
Apr. 21, 2017 (No slide)
30.2 feet per second, 3.67 seconds home-to-first

Back in April, Gardner attempted to bunt his way on against the Pirates, and while he wasn't successful, he did come up with his fastest home-to-first time of the season, 3.67 seconds, which seems like a good place to start. As you can see in the speed chart of the second half of the play, he ran hard the entire time, topping out just above 30 feet per second, and getting faster as he neared the base.

Aug. 17, 2017 (No slide)
30.3 feet per second, 3.94 seconds home-to-first

We'll show a similar play against the Mets from mid-August, except this one wasn't a bunt. This 3.94 second time was Gardner's second-fastest non-bunt home-to-first time of the season (we're showing this rather than his fastest, since inefficient defense made that one less than competitive), and these two help us put a baseline to what a full-run play "looks like." Both times, he's at or near his peak speed as he gets to the base.

But what about when Gardner doesn't run all 90 feet?
Aug. 28, 2017 (Slide)
30.5 feet per second, 4.09 seconds home-to-first

In late August, Gardner attempted to beat out a grounder to the right side against Corey Kluber, and he was narrowly thrown out while sliding into first. Unlike the two full-run plays, there's now a noticable speed dip at the end of the play diagram, making it clear when the slide began. When he stopped running, he stopped maintaining his speed.
Instead, Gardner got slower. While his Sprint Speed of 30.5 feet per second in his fastest one-second window was similar to what he'd done in the first two examples, that peak window came earlier in the run -- and the overall time to first was higher. 

Aug. 2, 2017 (Slide)
30.6 feet per second, 4.09 seconds home-to-first

We can see the same thing in a play from early August. Gardner grounded out to first baseman Jose Cabrera, who flipped to Jordan Zimmermann to narrowly get a sliding Gardner, with the ball arriving just .18 seconds before Gardner did. Again, the speed decline is clear.

Sept 22, 2016 (Slide)
30.7 feet per second, 4.11 seconds home-to-first

One more example, this time from last September against the Rays. The speed decline upon diving is clear, and Gardner was out. While five plays isn't exactly a huge sample size, these are the three fastest home-to-first times on diving plays he's put up in the past year, so this isn't a case of choosing only favorable plays. We have two of Gardner's fastest overall times, and his three fastest sliding times.

Let's combine them all to show what these look like all at once. The speed Gardner shows for most of the play is nearly identical, and then at the end, there's a clear speed drop when he dives. It's hard to dispute.

Now if we just left it there, you might think we've proven that sliding into first is indisputably slower and no one could argue against that. If we're talking about simple running speed, that's basically true; it's difficult to accelerate without your feet. As you can see in the diagrams, Gardner's speed while sliding is dropping from slightly over 30 feet per second to more like 21 feet per second, and dropping rapidly as he gains friction. 
But as we said, the argument to the contrary is that if done properly, the ability to reach out with your hands can make up for that, and Gardner has been used as an example in other studies of someone good at doing just that.
So let's acknowledge that. So far, we've been focusing on Sprint Speed, which clearly drops when you dive, and we've talked about time, in seconds, of home-to-first. But really, the first 80 feet or so ought to be identical no matter whether you slide or not. Would we find a difference if we look at the final 10 feet for these selected plays? If sliding is faster, that's where it would present itself.

The answer is … inconclusive, perhaps. Looking at our five plays, Gardner got to the 80-feet mark in as little as 3.29 seconds and as high as 3.76 seconds. Over the last 10 feet, he got there in .34 and .35 seconds running, and .36, .36 and .37 seconds sliding.
If we repeat it using 85 feet rather than 80 feet, it's about the same. Over the last five feet, Gardner needed .18 and .18 running, and .18, .19 and .20 seconds sliding. It's not much of a difference. Or put another way, if he ran the final 10 feet at 30 feet per second, he'd need an estimated .33 seconds, which is what he showed in our pair of "running through" plays. If Gardner slid the final seven feet at 21 feet per second (seven, rather than 10, assuming he can reach out with his arms for the final three), that would be ... an identical .33 seconds.
So Gardner could at least make a reasonable argument that even though he's no longer maintaining his top speed, he's not losing as much speed as you'd think, gaining the ability to grab the bag, which may get him there a split second or so faster than we're giving him credit for. (Plus, it doesn't matter that after 90 feet, diving is indisputably slower.)
There's more to it, of course. This is just five plays, and five plays from a veteran who somewhat specializes in this sort of thing, at that. The injury risk that headfirst slides can cause -- and slides into first base are just about always headfirst -- is another part of the discussion entirely. (And let's not forget about the "lunge", when a player finds himself caught in between run and diving and tries to "leap" to first, which is awkward and can also result in injury.)
There's probably never going to be one concrete answer that applies to all players on all plays. As we said, this might just create arguments, more than end them.