Discussion
Missile Defense is NP-Complete
u_sama: Great nerd title, the maths made me nostalgic as I haven't seen a Sigma/Pi in a few years
jsw97: The author explains that this problem is actually adversarial, in the sense that the attacker gets to observe defenses and allocate warheads and decoys accordingly.Thinking of our current circumstances, this suggests another cost of war: our offensive capabilities, as well as our defensive capabilities become more observable. Our adversaries are studying our strengths and weaknesses in Iran, and they will have a much improved game plan for countering us in future conflicts.
dboreham: It's been known since the 1960s that effective anti ballistic missile defense is impossible.
trollbridge: A lot of things involving rockets and putting things in space have changed since the 1960s.
heyitsmedotjayb: Would be interesting to know how the probabilities change once all your X band radars are destroyed. And then again how they change when all your L band radars are destroyed...
delichon: Add multiple decoys and the missile math tends to become an argument for the importance of preemption. Han shot first for a good reason.
busterarm: Careful. Preemption takes many forms, some of them many would find unpalatable.
SegfaultSeagull: Or perhaps they will learn they are outmatched, lack the resources and technological capabilities to compete, and deterrence will have been established.
srean: Death preempts all disease.
testaccount28: there is a benefit as well, though, as it makes your threats credible.
ErroneousBosh: > And then again how they change when all your L band radars are destroyed...Connection reset by Yugoslavs with microwave ovens
owenmarshall: Two more sobering axes to introduce: cost and manufacturing capability.Numbers are hard to find for obvious security reasons, but using the numbers most optimistic to the defender[0] suggests an adversary using a Fatah type hypersonic is spending 1/3rd the cost of an Arrow interceptor, and is launching missiles that are produced at a much faster rate. Interception is deeply asymmetric in favor of the attacker.[0] https://www.jpost.com/israel-news/defense-news/article-82314...
skywhopper: Have they, really?* Small rockets can now land themselves.Anything else?
sumtechguy: Computer guidance? Better materials? Better telemetry?
vasco: If we really want to put a certain hat on we can also say those adversaries have an incentive to not prevent (or even incentivize) those wars for that same reason. Even if that's by helping along a guy that is easy to manipulate through a childlike ego become president.
maratc: That's a false comparison. You want to compare between the actual options you have, which are either (a) firing an interceptor (or several); or (b) repairing the damage caused by a non-intercepted missile.
femiagbabiaka: could use some investigation of the ukranians techniques -- the number of interceptors the U.S. used within the first four days of the war eclipsed the total amount Ukranians have had for the war
gos9: Unpalatable preemption is generally better than reentry vehicles coming down your chimney.
phkahler: The problem there is you can't prove anything would have come down the chimney if the preemption is successful, so people will still be unhappy.
myrmidon: This is absolutely true, but there is a strong counterpoint: You also learn the limits of your own systems and how to operate them most effectively yourself (and better than adversaries can, too).Just to pick a recent example: Russian air defense in the early stages of the Ukraine war was dismal (more specifically: defense against big, slow drones like Bayraktar), despite having sufficient AA capability "on paper"-- the war allowed them to visibly improve.I'd expect much more value from validating and improving your equipment and its handling than the actual "cost" of revealing its capabilities to adversaries in almost every conflict.
bluGill: There are too many potential attackers though, and not everyone is sane. So you don't really get a choice about it. The cost of the interceptors needs to be considered in relation to the cost of what it protects. If the interceptor means an attacker doesn't kill my kids then it was worth the cost. If the interceptor keeps a multi-million dollar building around then interceptor at a million dollars is still cheap, even if the missile it takes out was only $100.Yes you should use diplomacy to ensure war doesn't happen in the first place. However if it does: they will send cheap drones and missiles at you in large quantifies.
quotemstr: The sole mention of directed energy:> Directed energy has been proposed as a cost-effective alternative, but introduces its own scheduling constraints — dwell time, platform coverage, atmospheric degradation — with similar scaling issuesThe author is doing the thing where a writer tries to bamboozle the reader into a conclusion without having to prove it by overwhelming the reader with nouns. Life is too short for shitty gosh gallops.
jvanderbot: Ah yes, but then you also have to add GDP + targetting/defense radii.Great Britian alone has 10x the GDP of Iran. So an interceptor costing 10:1 is (at first approx) breakeven just for GB, who would have to intercept much less than the total manufacturing capability of Iran anyway.Then you have every rich nation surrounding Iran as well. Let alone the USA who cannot be reached but throws their weight behind interceptions.And finally "total manufacturing capability" is set to decline in any prolonged engagement with an Iran-like nation, but GB, western EU, USA, et al, are likely to only increase production if an engagement played out.The math looks catastrophic on paper at 10:1, but I sincerely doubt that's the right analysis. An interceptor is worth what you're protecting, not what the attacking asset costs, so long as you can keep producing them.
Thaxll: This is wrong, for example Iran have thousands of Shahed drones, they cost almost nothing to build, to intercept just one the ratio is way way higher that 1:10. A single patriot missile is in the multi millions $ range.
jvanderbot: No, what I said is not wrong just because there exists other things to intercept, that just changes the ratio. You still have to consider whether it's worth it to spend a patriot missile to intercept a drone, vs letting the drone hit, say, a billion dollar radar installation or a dozen troops.on the manufacturing side, nobody said that all drones are intercepted with patriots. You have to look at the avg cost to intercept vs the average cost to attack, and if the ratio of those avg costs (across all attack/interceptions) is, say 100:1, and the combined GDP of the defending nations vs Iran is 1000:1, then what is the problem?
ceejayoz: > If the interceptor keeps a multi-million dollar building around then interceptor at a million dollars is still cheap, even if the missile it takes out was only $100.Not if it means you can't intercept the next one hitting much a more valuable/critical building.
bluGill: That is a trade off that hopefully you never need to consider, but it is a valid concern that does come up in the real world.
biker142541: History would suggest otherwise; rarely is this ever the case.
marcosdumay: You seem to be implying that there is a long history of countries starting wars against the USA?
XorNot: That's true. And while I disagree with the parent comment, ICBM interception remains enormously problematic and likely will remain so until directed energy weapons get really cheap.Fundamentally the rocket equation and orbital dynamics really fight you on this.It's a lot less "can't be done" versus "would be financially untenable to build and maintain even when the objective is nuclear defense".
p00dles: who is our/us?
myrmidon: You are basically complaining that the article is not about a your preferred, different topic.Directed energy defense does not really compete with a system like GMD at all, because the range is extremely limited by comparison.The US might be able to justify throwing a few billion at a few dozens of ICBM interceptors stationed in a handful of sites, but protecting every potential target (city, military base) with some kind of laser array is obviously unrealistic.
varispeed: You miss the fact that many adversaries will not act rationally.
gzread: More like the USA starting wars against countries, and those countries not immediately surrendering, to which the USA is shocked.
energy123: Practise is good, but exhaustion is bad. Russia is getting exhausted, which is why their influence collapsed in Syria, Azerbaijan and Armenia, allowing the US to overtake those vacuums.The US in WW2 staged their 20th century by letting others (China, South East Asia and the British/Soviets) get exhausted first. This was more an accident of geography rather than US grand strategy, but it worked all the same.
dlisboa: There is an assumption here that the value in improving defenses is the same as improving offensive weapons. That is not the case in the assymetry that drones provide and Russia is the first example.Russia has not been able to improve AA capabilities to the point where it's "safe", for any definition of the word, neither has Israel. Israel and Gulf states often tout over 90% interception rate yet it's really at the mercy of Iran to not target their most vulnerable sites. If Iran was routinely targeting desalination plants and refineries it wouldn't matter if it was 99%: one hit is all it takes. Similarly Russia cannot keep Ukraine from targeting their oil infrastructure.Air defenses need to be 100% to prevent physical, economic and moral damage. That is an impossibility.
neutronicus: "Data moats" are a problem for military tech, too, I guess.
1234letshaveatw: That seems like an acceptable trade off to get some real world experience with what works and what doesn't with regards to massed drones and swarming. There is a lot we can learn in this conflict with relatively low stakes
lejalv: Stakes for whom?>100 kids got murdered the first day of this "low stakes" war
icegreentea2: Air defenses do not need to be 100% effective to be... effective.Russia cannot keep Ukraine from targeting their oil infrastructure, yet here Russia is, still fighting on. Ukraine cannot prevent Russia from targeting their energy infrastructure or apartment buildings, yet here they are, still fighting on.If we're talking about strategic/civil air defense, then you must figure out what's tolerable to your population (and how to increase and maintain that tolerance), and then figure out all the means to reduce the incoming attacks to below that tolerance. That must include the full spectrum of offensive, counter offensive, defensive, and informational options.
jmyeet: In strategic circles, this was a common thought in the 12 day war: Iran was essentially mapping and testing defenses.As evidence of this, the US was forced to hastily move THAAD ground station radar from South Korea because Iran destroyed a bunch of them in the Gulf [1]. Bear in mind there aren't many of these and they cost half a billion dollars each.Further evidence of this is how quickly it happened. Iran most likely had detailed contingencies and battle plans for this kind of event.As an aside, this is what militaries do. They plan for things. So whenever you see some conspiracy about how government X reacted to situation Y quickly and thus had foreknowledge, you can ignore it. Military planners are paid to make up fictional situations and figure out how to respond. That's what they do.Weapons are the ultimate export. You use them and blow them up and the customer has to come back and buy more.[1]: https://www.theguardian.com/world/2026/mar/11/redeployment-u...
nerfbatplz: The Iranians just hit an F35 with a proverbial box of scraps they put together in a cave. The Chinese military must have experienced collective euphoria when they saw that.
dlisboa: Very few countries lack the technological capabilities to produce these kinds of drones.What most countries don't have is, for lack of a better term, the resolve Iran has shown. Venezuela could have built drones and resisted just the same, but it's internally divided enough that it was possible to strike a deal with an inside faction and have a coup from within.
jmyeet: Pardon the pun but this is an arms race and the defenders are going to lose. There are broadly five classes of missiles (one isn't a missile per se):1. Ballistic. These are traditional rockets, basically. While rockets are designed to reach orbit or leave the Earth, a ballistic missile basically goes straight up and comes down. The higher it goes, the further away it can get because of the ballistic trajectory and the rotation of the Earth.Ballistic missiles are most vulnerable in the boost phase ie when they're just launched. Since you have little to no warning of that, that's not really helpful.But one weakness of ballistic missiles is you pretty much know the target within a fairly narrow range as soon as they launch. That's the point of early-warning radar: to determine if a launch is a threat so defenses can be prepared.Attackers can confuse or defeat defenses in multiple ways such as making small course corrections on approach, splitting into multiple warheads, using decoys for some of these warheads, deploying anti-radar or anti-heat seeking defenses at key points and breaking into many small munitions, sometimes called cluster munitions on the news but traditionally that's not what a cluster bomb is or was. In more sophisticated launch vehicles, the multiple warheads can be independently targeted. These are called MIRVs (multiple independently targetable reentry vehicles).Economicallky, depending on range and capability, a ballistic missile might cost anywhere from $100k+ to $10M+.2. Rockets. Militarily this is different to a rocket in a civilian context. It's not much different to a hobby rocket, actually. Often these are "dumb" but some have sensors and guidance capability or might be heat-seeking.These tend to be incredibly cheap to produce and not terribly accurate but that's not really the point. The point is they're cheap and easy to produce and the interceptors are much more expensive.3. Cruise missiles. Rather than a ballistic trajectory, these have more sophisticated guidance and travel much closer to the ground, usually to avoid radar. The Tomahawk missile is a prime example of this. These tend to be relatively expensive and much slower than ballistic missiles.4. Hypersonic missiles. This is a relatively new invention that's kind of like a cruise-ballistic hybrid. It flies in the atmosphere for part or all of the time and, unlike cruise missiles, will fly faster than the speed of sound, usually significantly so (eg Mach 4-10). Such high speed makes interception near-impossible currently.The big advantage of a hypersonic missile is that it has the speed of a ballistic missiles without the predictability of the target area. Plus it can be retargeted in-flight.5. Drones (honorable mention). Not technically a missile but they fit in this space regardless. This is basically a scaled up commercial drone with an explosive payload. These are significantly slower than cruise missiles or rockets but can be live-targeted, re-targeted and have a variety of types ranging from dropping hand grenades from a height (eg as has happened in Ukraine) to suicide-type drones that explode on impact.Drones are typically so slow that you could shoot them down with an shotgun in some cases. But they're incredibly cheap and easy to produce.
Noumenon72: Posting a grade school report about types of missiles doesn't do anything to support your claim that defenders are going to lose the arms race.
captainswirly: This is rocket defense, not missile defense.Pretty much nothing can stop those ICBMs - those aren't rockets.If you dig deeper than mainstream news - Iran is lighting Israel up with those ICBMs, but they don't use them too often.
DivingForGold: Did I miss this ? Missing from the discussion is that Iran's cluster munitions in each single missle have absolutely overwhelmed Israels defense and would likely do the same to US military as well. Also to consider, Iran's $20,000 drones versus our $1 million dollar interceptors.
wavefunction: You could counter multipayload missiles by hitting the missile earlier in its trajectory before the payloads deploy, that was the plan for MIRV nukes but it requires usually forward interceptors or perhaps energy weapons we don't yet have.
OrangePilled: "Lessons US and Gulf could learn from Ukraine’s air defence warriors"https://www.thetimes.com/world/russia-ukraine-war/article/us..."Ukraine’s low-cost Shahed killers draw US and Gulf interest, but a wartime ban blocks sales"https://apnews.com/article/iran-ukraine-shahed-russia-drone-..."Ukraine Helps U.S. Bases in the Mideast With Stopping Drones"https://www.nytimes.com/2026/03/09/world/middleeast/ukraine-..."Ukraine deploys units to five Middle East countries to intercept drones"https://www.reuters.com/world/europe/ukraine-deploys-units-i...
sgtsteaks: What are you gonna do when Iran destroys the missile defense system itself, oops already happened
btown: One very interesting instance of the "military data moat" is Ukraine's annotated database of drone footage, perhaps the first of its scale from live engagements [0]:> They can now draw on an enormous pool of real warfare information. Last year alone, Ukrainian drones recorded around 820,000 verified strikes against Russian targets... Meanwhile, the country’s Avengers AI platform detects upwards of 12,000 enemy targets every week. Developers can now access these sources and the data that they gather to train their systems on the movements of a real Russian turtle tank or a camouflaged Lancet launcher.> “Ukraine currently possesses a unique body of battlefield data unmatched anywhere in the world,” recently appointed Defence Minister Mykhailo Fedorov said in a statement. “This includes millions of annotated frames collected during tens of thousands of combat drone missions.”With the latency and offline constraints of battlefield technology, smaller models, trained with better data, may prove to have a significant edge. But it's still early days on how data like this might prove advantageous in other environments.[0] https://resiliencemedia.co/how-ukraine-is-transforming-its-b... (unconfirmed source, this is not an endorsement)
falcor84: I think that there's a more general issue here with the US and the West in general having a mindset built up on playing Risk and Civ, which considers the foreign country as a whole as their opponent, whereas in practice, the adversaries are a multitude of individuals, for almost none of whom a surrender is the rational choice, especially (as sibling comments pointed out) when part of their reasoning and authority is based on a divine mandate.
testaccount28: to be clear: your claim is that the us military is misinformed because key constituents have played too many board games?does hearing it back like that make it seem absurd to you as well?
maxglute: >Hence, for one warhead, a defender can launch 4 interceptors and have a 96% chance of successfully intercepting the incoming warhead. >Unfortunately, those numbers are optimistic.This part worth stressing, ceiling for more performant missiles, i.e. faster, terminal maneuvering, decoys are geometrically harder to intercept. Past mach ~10 terminal and functionally impossible because intercept kinematics will break interceptor airframes apart.AFAIK there hasn't been tests (i.e. FTM series) done on anything but staged/choreographed "icbm representative" targets. Iran arsenal charitably pretty shit, including high end. Hypothetical high end missile with 10%-20% single shot probability of kill requires 20-40 interceptors for 98% confidence, before decoys, i.e. 40x6=240 interceptors for 1 missile with 5 credible decoys.The math / economics breaks HARD with offensive missile improvements.
Voultapher: Lasers. No really, near-future laser systems with adaptive optics and good spotting - for example distributed SAR satellites - dramatically shift that balance [0].[0] https://toughsf.blogspot.com/2025/05/the-laser-revolution-pa...
keybored: “Iranian kids may die... but that’s a prize I’m willing to pay.”
1234letshaveatw: "I much prefer nuclear conflict"
keybored: Propose a nuclear free zone in the Middle East, propose a global nuclear free zone, propose to cooperate with other nuclear powers to disarm.But that’s apparently not the real concern at all.
pwndByDeath: Still short amount of time to make a decision based on very messy data
energy123: The best missile defense is offsense: degrading the launchers, stockpiles and defense industrial base, with cheap stand-in munitions after SEAD, leveraging air and intelligence superiority. Expensive interceptors are only a stop-gap that buys you time for the offensive degradation. Expensive stand-off munitions, likewise, are a short-term stopgap until SEAD is complete.
hedora: Offense doesn't work at scale.As the cost of drones goes to zero, the expected damage you take is roughly proportional to how much you have to lose. This means larger / richer economies cannot win these sorts of wars. To see what I mean, check out this desalination plant map:https://www.theguardian.com/world/2026/mar/23/iran-threat-to...It doesn't help if your commander in chief is incompetent and your invasion strategy involves treating desalination plants as legitimate military targets.Of course, blowing up desalination plants in the middle east don't hurt the US all that much, but blowing up industrial supply chains does. We're something like 4 days away from a global chip manufacturing industry shut down (barring some logistic miracle, since we recently sold off our strategic helium reserves).
energy123: It's heavily dependent on geography. Iran is geographically "lucky" it's positioned near the Strait of Hormuz and near the oil facilities of multiple Gulf states, allowing it to exert extreme asymmetric pressure through a small amount of drones etc. Most states can't replicate that luck. Good luck to South Africa if they ever decide to wage a similar war. Strategic depth also largely nullifies the role of one-way attack drones in combat, but it doesn't nullify the role of fighters and bombers who can exploit that range. I'm not discounting drones, they're highly important in many geographies, as Ukraine is showing, but I don't buy into this conventional wisdom online that they're the pinnacle in every situation.
simonsarris: On the other hand, the best way to improve your capabilities is to use them frequently.The Russian army assumed a state of readiness for the Ukraine invasion that turned out to be, well, less. Their special forces floundered, their logistics were (are still!?) unpalletized - using bespoke metal containers and wooden crates! Whereas the US military learned an awful lot from its (mis)adventures over the last decades.
energy123: In the Ukraine-Russia war, air defense is used to deny air superiority to the enemy. Just a few days ago, Ukraine blew up Russia's helicopters in the air with drones. It's not the successful hits that matter, it's the capabilities that you deny by posing that credible threat.
hedora: Currently, we're using $1M interceptors to take out $30K drones. This asymmetry is here to stay.The end game probably involves < $1000 autonomous drones that target IR or RF and drop something like hand grenades. On the defense side, there would similarly-priced interceptors with bolas, backed up with sharp-shooters for important targets.At that point, it turns into a logistics problem that's much easier for the attacker than the defender. Iran's already demonstrated that one successful drone can do $100B-1T in damages, so a hit rate of 0.1% means a 1:100K cost:damage ratio.
pc86: What Iranian drone did a trillion dollars in damages?I'm not saying the general thrust of your argument is wrong, quite the opposite. But that's a big number for one drone.
ozgung: As an alternative formulation of the same problem, maintaining peace has linear cost, completely solvable in linear time and rewards are unbounded for all parties.
OrangePilled: Bearing in mind the three constraints quoted, which of these do you think a country's deployed directed-energy weapons (e.g., US, Israel, Russia) would be useful against:https://missilethreat.csis.org/country/iran/
iso1631: It's America that's waging this war, having attacked Iran for no reason the world can seeIt's somewhat similar to Russia waging a war in Ukraine, although I can see some reasons for Russia to attack Ukraine (mainly territory)
