I must admit that I indeed didn't watch the video.
I trusted that despite their reputation for being pretty terrible when it comes to comparisons and technical explanations (they seriously argue that the Profoto B10 is as powerful as a Godox AD400 which anyone with a brain and access to both devices could convince themselves is a boatload of nonsense) that they would manage to regurgitate some facts about sensor sizes that they read somewhere.
Alas, Lee managed in his typical style in which confidence trumps knowledge to misinform his viewers.
If you keep everything constant (except sensor size, presumably) then you get two wildly different images which cannot be reasonably compared to each other.
At the 6:56 minute mark, Lee attempts to start the one experiment that makes sense:
- have both cameras at the same position (otherwise perspective would change and with it DOF).
- compensate for the larger sensor by using a longer focal length (otherwise the FOV would change and with it the light gathered, DOF upon cropping, etc.)
- keep the shutter speed the same.
His result is that the larger sensor produces an image with a shallower DOF.
This apparently contradicts the title of the video but he offers an explanation: The longer lens is responsible for creating the shallower DOF.
This explanation is wrong. While it is true that using a longer focal length reduces DOF when not changing the sensor size at the same time, the reason for that latter phenomenon is not the longer focal length as such, but keeping the f-stop constant.
You'll only see the reduction in DOF when going from a shorter to a longer focal length, if you keep the f-ratio constant, say, use f/2.8 for both a 50mm and 100mm lens.
You could achieve exactly the same DOF if you stopped down the 100mm to f/5.6. Why f/5.6 exactly? Well, DOF is determined by the aperture diameter. In the case of a 50mm lens at f/2.8, the aperture diameter is 50mm/2.8 = 17.86mm. Now if you only change the focal length from 50mm to 100mm but keep the f-stop at f/2.8 then you increase the aperture diameter to 100mm/2.8 = 35.71mm. This larger light-passing port is responsible for the shallower DOF, not the the increase in focal length as such. One can prove this by stopping down the 100mm lens to f/5.6, resulting in the same 17.86mm aperture diameter we had for the 50mm f/2.8 lens.
I hope you can agree so far.
Note that f-stoppers use some nice diagrams to show why distance, for instance, affects DOF.
Have you noticed they they don't show you any diagrams to illustrate why increasing focal length changes DOF?
The reason why they don't show you respective diagrams with light rays, etc., is because there is no causal relationship between focal length and DOF.
I suspect that the actual effect -- the increase of the aperture diameter when the f-stop is kept constant -- eludes them and that they don't understand that DOF is essentially the result of a parallax effect, i.e., the larger the aperture, the more angles/positions exist to view the same point in the subject space.
To summarise: Contrary to what f-stoppers purport, DOF is not affected by focal length but by changes to the aperture diameter.
F-stoppers were correct in claiming (mainly through the video title) that a larger sensor does not produce shallower DOF per se.
They were also correct in attributing the change in DOF to the lens.
They were wrong in attributing the change in DOF to focal length.
The reason why the second image shot with the larger sensor showed shallower DOF was not because he used a focal length that was twice as long, but because he used an aperture diameter that was twice as large. Had he used the equivalent f-stop of f/5.6 for the longer lens, he would have achieved exactly the same DOF.
The difference between "myths" and "facts" is that the former can be disproven by experiments while the latter are confirmed by experiments.
I hope you can agree that 100mm is the FF-equivalent focal length compared to 50mm on a 4/3 sensor.
It is not the same focal length (100 <> 50) but it is equivalent because the longer focal length exactly cancels out the wider FOV of the larger sensor.
For all practical intents and purposes, the combination of 50mm on 4/3 and 100mm on FF are indistinguishable. There are some real world practical implications that would allow you to experimentally determine which combination you are dealing with, but theoretically, you cannot distinguish one combination from the other.
I think you know that already. Where it gets slightly trickier is to understand that in order to keep combinations indistinguishable, one also has to change the f-stop. The reason is simple, though. We need to keep the aperture diameter the same, as the latter is responsible for determining the DOF. Hence, the f-stop on the 100mm lens must be twice as large as the one on the 50mm lens.
This tells us that the FF-equivalent f-stop for f/2.8 on 4/3 is f/5.6.
I hope you can see that this is exactly the same conversion we had to do for the focal length.
All photographers seem happy with the idea of equivalent focal lengths, i.e., the notion that you have to adapt the focal length when you change the sensor size.
Far fewer photographers understand the idea of an equivalent f-stop, i.e., the notion that you have to adapt the f-stop when you change the sensor size.
In the comparisons I make or assume, I never ever change the camera to subject distance.
With equivalent shooting parameters, you'll find that you cannot distinguish the FF image from the APS-C image.
You'll find that only one eye is in focus for the FF image, if you choose to use non-equivalent f-stops.
Choosing, say f/2.8, for both shots, make the f-stops look the same numerically, but we know that the equivalent (i.e., the one that achieves the same effect) f-stop for FF is ~f/4.
I hope this helps.