I thought you might be overestimating the force of a thrown baseball as compared to the steel ball bearing, so I tried to do some research and run numbers to compare.

Some googling says a baseball should weigh 5-5.25 ounces (about 1/3 of a pound).

Another page and some quick calculations that I might have screwed up[ (4*pi*.5*.5*.5)/3*.283 ] say that the ball bearing might weigh about .15 pounds -- a bit under half of the baseball.

On the other hand, the fastest pitch ever recorded in MLB (by Nolan Ryan) was 108.1 MPH or 158.5 feet per second. Harder to find data on "muzzle" velocity of a slingshot, but this page suggests that some people claim some slingshot projectiles can travel at 300 feet per second, but he argues that 180 to 200 fps is probably a more realistic high end for a .50 caliber lead ball (which would probably/possibly? be heavier than the 1" steel ball since lead is more dense). Anyway, there is at the very least a slight advantage to the slingshot here as compared to the fastest pitch ever recorded in MLB. Considering the draw length and pull strength of the slingshot in the video, I'd say it is probably actually much faster than the conservative 180-200 fps number from that page.

So then you've got @cosmovitelli 's formula (mass times velocity squared). The mass of the baseball is probably double that of the steel ball, but the velocity is probably 25-90% faster (or even more) and then squared. That probably overcomes the disadvantage in mass and then some.

Then again, this is all fairly academic as you suggested because the lethality of the bullets/projectiles is dependent on them being small enough to puncture, tear flesh, break/shatter bones, etc. Apply that kinetic energy to a very small impact site. However, in spite of its large size, I bet that steel ball could do a lot of damage given its kinetic energy -- which is what I would take away from their claims of it "hitting harder". I wouldn't want to stand in front of a Nolan Ryan fastball either, but given the choice between that and the slung steel ball... I'd take the plunk and have somebody take my base for me.

The slingshot does "hit harder" i.e. impart more momentum into the target and thus more likely to knock you down.
Intuitively this seems like it would therefore cause the most damage and for several 100 years this was the prevailing logic with muskets and cannonballs.

So much so in fact that when Charles Whitworth first introduced his rifle it was dismissed by the British army partly for having too small of a bullet. Whitworth used a smaller more stable round for its increased range and accuracy/stability (though there were also concerns about "muzzle fouling" and slower reload time).
It was believed at the time that the larger (slower) much less accurate bullets from the Enfield were more effective at actually injuring enemy soldiers, but history later demonstrated that speed and penetration can have just as much (if not more) effect on soft bodies than sheer mass and momentum.

Simply put, that large slingshot round would likely knock you to the floor in the same was as an MMA fighter landing a roundhouse square in your guts would. It might even penetrate the skin a bit and embed itself in you. What it won't do however is travel through your soft tissues at high velocity and create a large "temporary cavity" which is how most firearms do their real damage.

The 9mm etc. don't carry as much overall energy as the slingshot, but they do deliver it to a soft target much more effectively (that is to say lethally). A much more informative test would have been to fire them into ballistic clay, this would have highlighted the differences between speed, momentum and penetration much more clearly. The slingshot would leave a massive dint, the bullets would leave tunnels.

That said, the point they are making does stand to some extent. If you used that slingshot on someone that was trying to shoot you there is a good chance you'd knock them down (or at least stop them taking an aimed shot back for a few seconds). Hell you might even hospitalise them with a good shot!

It's not fair to say that the slingshot is a more "powerful" weapon but I think they did clearly demonstrate that it's a viable alternative under some circumstances. In fact for defending yourself in your own home etc. it might even be better!

Little/no risk of collateral damage (unless you miss really badly)
Very cheap
Would put most people on the floor with one good hit
No firearms licence or background checks needed
More difficult for a child to misuse (Most kids would lack the strength)
Enemy wouldn't expect it
Much less likely to kill
etc. etc.

Hell I'd get one myself if UK law wouldn't fk me over for using it.
It's illegal here to use a weapon specifically intended or kept for defense. i.e. if you grab a random object like a chair and beat up an intruder that's ok, if you have a baseball bat etc. by your bedside for expressly this purpose then it's not.
Handy then that one of my broken computer chairs happens to contain a loose 1ft long iron bar. Naturally I'd never even consider using such a thing violently, but who knows what might come to hand when faced with an intruder

(Seriously though, as broken furniture its a viable means of defence, if I kept it by my bedside as a "weapon" I'd be breaking the letter of the law by using it. Fucking stupid!)

Yeah that's basically what I meant, but these guys don't seem to get that. They seem to be impressing themselves through pseudo-science that their little slingshot "hits harder" than the guns, without understanding the fundamental principles.

Your video, Can a slingshot hit harder than handguns? The Shootout., has made it into the Top 15 New Videos listing. Congratulations on your achievement. For your contribution you have been awarded 1 Power Point.

Gonna have to *promote the use of slingshots.

*isdupe=http://videosift.com/video/That-Wasnt-So-Bad?fromdupe=dude-passes-out-twice-on-slingshot-ride

3 more comments have been lost in the ether at this killed duplicate.

*dupeof=http://videosift.com/video/That-Wasnt-So-Bad?fromdupe=dude-passes-out-twice-on-slingshot-ride

*related=http://videosift.com/video/Condom-Applicator-Slingshot-Gun-Bill-Gates-Challenge

Invocations (related=http://videosift.com/video/Condom-Applicator-Slingshot-Gun-Bill-Gates-Challenge) cannot be called by speechless because speechless is not privileged - sorry.

I thought this would be a sequel to the Condom Applicator Slingshot Gun video I just watched. Almost...

6 more comments have been lost in the ether at this killed duplicate.

how can this be live? well the vocals are live, but the rest is not. me thinks that kirt~no~brain was not digging the slingshot to stardom and that this tune that changed the format of rock~n~roll on the wireless. i still wish that they never hit the mainstream. do not get me wrong, they were a good band. just WAY TOO over exposed by the media. thank gawd for the real alternative(the intertubez).

People don't just collect them. They enjoy shooting them. I don't own any, yet I can see why firing some FMJs from a Bushmaster would be fun. Similarly, people like to get drunk (a much more common hobby). I can also see why that might be fun. As you might expect, that hobby results in many more fatalities than all gun related deaths, yet the prohibition of alcohol is not on the table.

This myth that guns only exist to kill things needs to go. Most guns never kill anything. They are fun to shoot, just like slingshots and boomerangs. I would never say the only purpose of a boomerang is killing. For all of the above the primary purpose is entertainment. I'm of the opinion that methods of entertainment should not be forcibly banned by the government unless they represent a significant problem. I won't be convinced that ARs have crossed that threshold until everyone is willing to kiss off their liquor as well.