Let see what we know.The comparison is between the S-300 Ukraine fields (max range 90km) and the Patriot variants they received (PAC-2 GME (max range 160km) and PAC-3). The former is 80s vintage technology, while the latter are 21st century upgrades.
As Ukrainie itself explained, their S-300 was unable to intercept the Kinzhal air launched ballistic missile, whereas their Patriot were. Therefore, there shouldn’t be any doubt as to which system is more advanced.
1. There is a most likelly valid video from atrafic or similar camera, that showing fast launch of 32 missiles from a Patriot battery.
2. Ukraine claim that they shoot down 6 Kinzal
3. Ukraine claim the Patriot battery damaged.
If we simply accept these claims on face value (that acutally would means we accept the Ukrainan claims about killing each Russian soldiers twice and destroy all russian tank made in past and future ) then the probability of interception considering 10 % chance for kill on each launches :
32 patriot missile launch, 10 % chance to interception, chances for 0/1/2/3/4/5/6/7/8/9 Kinzal kill.
Just clarification, it means that IN SELF DEFENSE with 10% chance of kill it has 5% to see one occasion when the battery defended itself successfully agains 6 incoming kinzal.
Means from 20 attack, one will be defeated, and the remaining times 1-6 missile going throught.
If we say the chance of interception is 20% , then we can get the next :
Now, the Patriot battery apporx. half of time can defend itself against ALL 6 incoming kinzal.
So, we can assume that the Patriot chance of defeat agaisnt single Kinzal in the most favorable, self defense mode most likelly bellow 20%, and in non self defence mode it is in the single digit percentage range.
Now, I have to say that it is in practice meaning and useless, I make two case study why.
The patriot system performance as good or inferrior compared to the next cases:
1. 20 pcs of Phalanx cis in a 500 m circle, against incoming Kinzals, having way better chance for SELF defence.
2. 2 meter diameter tungsten carbide sphere has way better self defense capability, it requrie 100-1000 kinzal to be defeated. Maybe the sphere could called as PAtriot Advanced Capability - 4 - Limitless Self Defence -> PAC-4-LSD