How Effective Are Modern Air Defenses ?

Patriot Air-Defense

Introduction :

Air defense has come a long way from the famous large AAA-guns where literally, thousands of rounds could be fired without hitting anything to modern day missiles able to hit targets moving at hypersonic speeds.  
They have become some of the most famous military equipment even people not interested in the genre have heard of these systems like Patriot or the S-400 .

Each generation gets progressively better radars, better missiles, better electronics but despite this, most of these have never really been tested in combat. 
Testing seems to indicate that they are extremely capable but are they ?

Recent Failures :

If you include ballistic missile attacks we've seen several high profile failures of air defense systems to defend an area.  
The attack on the Saudi oil fields where dozens of drones and cruise missiles attacked.
The Syrian S-300 hasn't fired or defended against any Israeli airstrike since it's been operational.
Again in Saudi Arabia, the Patriot has failed several times defending against ballistic missiles from Yemen and the list goes on and on. 
Now granted some of these can be attributed to other factors than just the actual hardware itself maybe Patriot batteries weren't facing the proper direction in Saudi Arabia or maybe the Syrians have decided or been told by Russia not to use the S-300 but nonetheless, an area which was supposed to have been defended was not defended so i think that all has to be factored in when considering the effectiveness of air defense not just hardware limitations affecting performance but human limitations that affect performance as well. 

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SAM

Factor affecting Air Defense :

1. RANGE :

Air defense is an inherently difficult thing.  

You have an aircraft or missile flying at several hundred even a thousand kilometres per hour so you can't just fire at the target.

You have to lead it figuring out where it will be once your missile gets there but they can also manoeuvre making it significantly more complicated now you have to adjust as well and calculate a new point of impact for each little turn the target makes and as you do this you lose energy unlike in some movies surface-to-air missile engines only burn for a short time the rest of the time it's just gliding and slowing down each and every little manoeuvre it has to make loses more energy and will eventually just fall out of the sky.

If you've ever played DCS this is something you are well aware of when a SAM site launches on you, you begin making a series of manoeuvres to bleed energy from that missile so a system like the Patriot might have a stated range of 150 kilometers but it has virtually zero chance of hitting anything at that distance against a highly manoeuvrable fighter jet. 

The real effective range can be less than half of that so this is one difficulty another is the physical limitations of the missiles themselves.  

How much can they manoeuvre ? 

What kind of stress can it handle ? 

Can the onboard guidance system see and track a large enough area ? 

How reliable are the electronics and so on ?

2. RADAR :

The way that the system actually sees the target,  most SAM systems have two types of radars: 1. an acquisition or search radar and 2. an engagement radar.

The search radar does just that broadly searching the sky for any threat.  

If it finds something it passes that information over to the engagement radar. 

Engagement radar is more like binoculars zooming in and focusing on a small area of interest.  

It focuses all its energy on one spot giving it a much higher detailed view of that threat the engagement radar then uses that information to actually guide a missile to the target.  

There are other forms of guidance other than radar such as infrared and optical but those are typically confined to the shorter-range systems.

Either way, there are inherent difficulties there as well if a radar or infrared tracker can't see the target it can't hit it, if it passes beyond a hill or below the horizon or sends false returns jamming it or other techniques such as notching can make it impossible to engage.  

There are also the limitations of the radar itself the original S-300 FLAP LID engagement radar can only see up to 50 degrees in elevation.  

So if you can loft a missile into the air and have it come straight down on it it would not be able to defend against it. 

Engagement radars can only track so many targets and guide so many missiles at one time the FLAP LID again can only engage six targets at a time and guide two missiles to each. 

So if you have a few dozen aircraft cruise missiles or even small drones attacking all at once you can defeat the system by overwhelming it. 

3. COMMAND:

Then you have issues such as crew proficiency and getting approval up the chain of command to launch. 

Even if you have the greatest SAM system ever created it can be useless without proper command and control. 

SAM 

Recent Development :

So there are many points of failure where these systems can fail in its job to defend an area they are far from the silver bullet which can defend any airspace perfectly which brings us to real-world events each progressive generation of air defense systems generally improves on each aspect of these issues. 

The missiles can sustain higher stresses while manoeuvring.  

The radar can track more targets. 

Systems are more automated to cut back on the required training of crews etc.  

And they have all shown to be extremely capable in testing. 

Issues :

But a lot of modern air defenses have never been actually tested in combat.  
The S-300 family, for example, has been around for 40 years yet never once used in combat.
Testing is one thing it's controlled sometimes even delayed if the weather is bad.  
The operators know it's about to happen and the targets used are obviously never manned so they don't react and attempt to manoeuvre the same way they would in a real situation.  
There are some things you just can't learn from tests that require real combat experience to sort out.  
We saw this with the Patriot that despite it being talked about how good it was at defending against tactical ballistic missiles once it actually had operational use in the gulf war it performed pretty poorly.  
There were issues such as with the internal clocks used which were running for days on end and became just a fraction of a second off resulting in a failure of the system. 
In exercises this isn't a problem you probably notice as everything is set up and recalibrated for that test.  
There was a report that the S-300 in Syria was completely failing to engage Israeli aircraft and missiles hence why it has not been used yet if true this could reveal some pretty major problems with Russian air defense systems of which modern ones have yet to be tested in combat like the S-300 and S-400 or and probably more likely is that Russia has given Syria orders not to use a system for these attacks as doing so can only hurt the image of the S-300 if it fires on Israeli aircraft Israel would likely bomb it. 
As mentioned before even the best systems can be overwhelmed destroying an S-300 site will be a major propaganda victory for Israel and the west and really hurt the sales of Russian air defence systems and that is true with many military weapons the F-117, for example, it enjoyed a great reputation said to be invisible to radar and impossible to shoot down especially after the successes in the gulf war then one day that reputation was suddenly shattered forever when it was shot down by an older air defense system over Serbia in 1999.
So sometimes it might be better just to keep their reputation intact and a system can be effective in defending an area with fear alone regardless of its actual capability but without actual combat use, it's hard to know just how effective they are.  
I think it's reasonable to assume that each generation is an improvement over the last previous systems.

Conclusion :

So how truly effective the latest systems are is still up in the air the newest ones often have incredibly high reputations which might not be true however air defense is simply a tool one of many to defend an area from the attack they are not perfect but undoubtedly getting better every year.