I remember watching Patriot missiles shooting down Scuds on TV during the Gulf War and a couple years later the GAO said they didn’t actually hit anything. I didn’t believe that report either.
This turned out to be largely correct. You saw Patriots being fired and their warheads detonating somewhere near an incoming Scud, but most of the time the incoming Scud had broken up before interception, and the Patriot was intercepting the body of the missile, and the warheads fell to earth and exploded.
I was sort of suspicious during the war of shots of where "Scud debris" landed, and it was a big freaking crater.
Having a Patriot explode somewhere near an incoming Scud and having the Scud warhead hit the earth and explode isn't much of a successful intercept.
The Patriot PAC-3 (which is misnamed, it's essentially a completely new missile, designed to intercept incoming IRBs instead of aircraft) was introduced prior to Gulf War II, and it actually worked.
To amplify on the other replies you already have seen, the Patriot 1 was an anti AIRCRAFT missile retasked as a Scud killer. To destroy aircraft it merely had to explode in proximity and allow the flak to strike and disable the fragile aircraft.
Applied to Scuds this meant in most cases the flak striking the expended booster, a useless exercise as the warhead would continue to earth.
In a news report of an attack on an Israeli civilian neighborhood I noticed the “intercepted” Scud booster largely intact, laying on its side perforated as though somebody took a shotgun to it. I felt that was odd enough to note and remember but I didn’t think it through to realize the failure of the system.
The Patriot 3s used in the last war don’t use flak, but instead the warhead targets the incoming missile for a direct hit, the “bullet hitting a bullet” that SDI critics swore for a generation could never be accomplished.
From memory they intercepted and totally destroyed in flight 27 of 28 incoming Iraqi missiles. The only one that got through to civilian areas hit a beach near a Kuwaiti shopping mall spraying its entrance with fragments. Other Scuds tracking towards uninhabited areas were not fired upon.