This article provides an indepth explanation of why XDG played the final Baron in their game against Dignitas on February 9th (week 4) the way they did. Their goal was to stall out the baron for as long as possible against the massive steal threat out of the Dignitas composition while still holding Baron at a low enough health so that if Dignitas left completely, XDG could burst it down. Due to a misstep in leaving a ward alive, they were unable to gain full vision control of the pit, but they nonetheless achieved their goal of stalling, forcing Dignitas into a lose-lose situation, and taking the baron.
The entire fight can be found here. When watching, pay attention to where Xmithie focuses his damage and to the health bars of XDG's tanks Leona, Mundo, and Olaf, while they soak damage from Baron.
Let's first look briefly at the events leading up to the baron.
With Cruzer still dead for another 37 seconds, XDG have plenty of time in the 5v4 to take the Baron---however, if they play it at all incorrectly, there is a huge chance for Dignitas to either steal the baron or kill them all. Look at Dignitas's ult cooldowns here. While Annie's ult is actually down at the moment (Tibbers is still alive), Gragas's ult could actually be up before Baron is taken down all the way if Dignitas stalls for long enough. On top of that, Lee Sin is one of the best smite-stealers in the game--and Crumbzz is one of the best smite-stealers in NA.
Last time XDG took Baron, we saw Mancloud hop the wall to chase off Crumbzz and the objective was easily taken by XDG. But in that case, Lee was alone; in this case, he has a lot of friends. And while Riven does have a GA, overall there isn't that much defense for her to work with, and both Gragas and Lucian are doing a ton of damage.
In short, XDG look insane for starting Baron here, especially considering that the way they got back into the game in the first place was off a failed Dignitas Baron attempt.
Note here that Baron is at about 1/3 HP. There is zero chance of a smite steal at this exact health. XDG still has a bit of time to kill the green ward. They do have to stop DPSing Baron in order to focus the ward or Lee might have a steal opportunity right as the ward is dying, but they do have time to kill it.
Three seconds have passed, and XDG has done virtually no further damage to Baron, so smite-stealing is still impossible at this moment. Crucially, though, the ward is still in the pit, and XDG have no more true sight. That ward's survival is the reason it's so difficult for XDG to finish the baron, but on the other hand it gives them the opportunity to showcase exactly how to play a situation like this! You can see from the timers that there was a bit of a miscommunication---Benny and Zuna used their sweepers at exactly the same time instead of staggering.
Notice how Mancloud is mirroring Crumbzz's movement on the other side of the wall. He's Riven and he's threatening to jump the wall---even if he can't kill Crumbzz, at least he can CC him for the duration of the smite-steal window.
Mancloud has chased Crumbzz completely away from the Baron, and Mundo is tanking Lucian's Culling. At this point, Dignitas are so far away from Baron that XDG would be safe to burst it down, but what you can't see in this screenshot is that XDG's delay has allowed Baron to regen quite a bit. It would still take them a while to burst it down, and XDG don't want to risk that when Scarra's ult comes back up in a couple moments, he's able to burst down Mancloud to his GA and open the way back for Crumbzz to come in for a steal.
Notice BloodWater's positioning at the back of the pit. He has flash; he can flash over the wall either down or right to join the fight, and he's placing himself where he would be able to get a free Zenith Blade onto Crumbzz if Lee came near the pit. Solar Flare is also back up, and he wants to be able to provide the CC to back up Riven.
Cumbzz tries to follow up onto the Q on Zuna...
Xmithie gets the kill onto Lee, but Scarra still has Explosive Cask (it just came back up! XDG either know this for sure or know that there's a strong possibility of it). So, with BloodWater still extremely tanky and decently healthy, XDG delay killing Baron for just slightly longer while Sivir peels to push Lucian away. XDG has to wait for one of two things to happen here: Either Scarra needs to use ult or Mancloud needs to come back up from GA. Either one of those will result in Scarra no longer being able to steal because either his ult will be down or Riven will be able to CC/zone.