10 ms·
Missile defense is NP-complete
- OrangePilled 6mo agoIf you're looking for a job and are still squeamish about working in the defense industry...I'm sorry to hear about that. Because, boy, do I think you'll be missing out.
- dgroshev 6mo agoNot sure where the crucial SSPK number came from, given that the referenced link https://missilethreat.csis.org/system/gmd/ https://missilethreat.csis.org/system/gmd/ does not have neither the number nor data to calculate it. Even more importantly, using the test history too far back is incorrect, since the system was debugged and refined. Also, a big omission in the post is NGI carrying multiple kill vehicles. Considering the relative cost of a launching system and a KKV, multiple KKVs flip the math quite significantly.
- dboreham 6mo agoIt's been known since the 1960s that effective anti ballistic missile defense is impossible.
- trollbridge 6mo agoA lot of things involving rockets and putting things in space have changed since the 1960s.
- skywhopper 6mo agoHave they, really? * Small rockets can now land themselves. Anything else?
- sumtechguy 6mo agoComputer guidance? Better materials? Better telemetry?
- pwndByDeath 6mo agoStill short amount of time to make a decision based on very messy data
- tliltocatl 6mo agoVastly cheaper and more powerful control and guidance systems (and cheaper, if only a bit cheaper, radars too).
- BoredPositron 6mo agoObservability has changed in most other ways we have regressed.
- XorNot 6mo agoThat'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".
- cpgxiii 6mo agoThere are several different levels of ballistic missiles. ICBMs, for which the GBI is intended, are the most challenging to defend against and show the least interceptor success. In contrast, we do have some pretty definitive evidence that theater and "lower" MRBM/IRMB ballistic missiles can be intercepted successfully. If you define "effective defense" as "most missiles that would cause damage are intercepted", then it is clearly possible with current technology. If you define "effective defense" as "all missiles are intercepted", then it remains beyond the current technology.
- hedora 6mo agoIf you define "effective" in terms of cost ratios: R = (cost of defense system + cost from failed intercepts) / (cost of attack system) then N < 100 is well beyond current technology, regardless of whether the defense system is perfect or non-existent. There's no magic Pareto-optimal point where investing the right amount in missile defense means that starting a war against a medium-sized country makes economic sense. Russia figured this out in Ukraine, and the US figured it out in Iran. Israel's genocide worked pretty well tactically, but is a long-term strategic disaster. If the US continues to be a democracy, polls say that it will cause us to withdraw support sometime this decade. Also, it only works if you have an incredibly asymmetric fight.
- zabzonk 6mo agoOh, I thought this was going to be about the old trackball arcade game. Or perhaps it is? Same sort of rules? The maths is going so far over my head I can't hear the whoosh.
- gs17 6mo agoI expected that too, but it's about the inspiration for the game, I guess. I was trying to figure out how you encode computation in the game.
- delichon 6mo agoAdd multiple decoys and the missile math tends to become an argument for the importance of preemption. Han shot first for a good reason.
- busterarm 6mo agoCareful. Preemption takes many forms, some of them many would find unpalatable.
- gos9 6mo agoUnpalatable preemption is generally better than reentry vehicles coming down your chimney.
- phkahler 6mo agoThe 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.
- busterarm 6mo agoI agree, but some of them are more obvious. Like not giving 100 billion dollars to someone who actively wants to kill you.
- wat10000 6mo agoA thought experiment: would the world be a better place if the US had preemptively attacked the USSR in the 50s or early 60s when it was possible to do without more than “get[ting] our hair mussed” as General Turgidson put it?
- XorNot 6mo agoBut it's also the basic l basis of deterrence and the destabilizing nature of ICBM defense: relying on interceptors presumes the war happens.
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- OhNoNotAgain_99 6mo ago[dead]
- heyitsmedotjayb 6mo agoWould 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...
- ErroneousBosh 6mo ago> And then again how they change when all your L band radars are destroyed... Connection reset by Yugoslavs with microwave ovens
- jsw97 6mo agoThe 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.
- grafmax 6mo ago"Our" adversaries, huh? There are more people in our country than pedophile billionaires, but it's this group starting the wars, murdering civilians, and producing generations of "adversaries".
- GeorgeWBasic 6mo ago"Our adversaries" are in the US government, or is this not crystal clear by now?
- RobertoG 6mo agoThis is a problem with a know solution, already applied by many in the world: don't start wars. Specifically: don't start wars thousand of miles away of your borders.
- vasco 6mo agoIf 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.
- u_sama 6mo agoGreat nerd title, the maths made me nostalgic as I haven't seen a Sigma/Pi in a few years
- owenmarshall 6mo agoTwo 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-823148 https://www.jpost.com/israel-news/defense-news/article-82314...
- jvanderbot 6mo agoAh 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 6mo agoThis 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 6mo agoNo, 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? There are lower cost ways to intercept already on the market and being rolled out. See for example: https://www.defensenews.com/global/europe/2025/09/11/uk-to-produce-ukraine-designed-interceptor-drones-supply-thousands/ https://www.defensenews.com/global/europe/2025/09/11/uk-to-p... This whole "cost analysis of patriot vs drone" examines the worst case scenario at a fixed point in time and ignores layered defenses, the effect of combined GDP, learning, diminishing capabilities of attackers, and improvements by defenders.
- srean 6mo agoGame theory would be useful for these kinds of modeling. Perhaps the government should have and advisory body that employs the smartest mathematicians for running these scenarios. Of course a lot of randomness needs to be modeled too. Wonder what would be a good name for such a body :) Paradoxically, if anyone leaks unpalatable information from the inside that would be a problem for the government. https://en.wikipedia.org/wiki/Daniel_Ellsberg https://en.wikipedia.org/wiki/Daniel_Ellsberg https://en.wikipedia.org/wiki/Ellsberg_paradox https://en.wikipedia.org/wiki/Ellsberg_paradox https://en.wikipedia.org/wiki/RAND_Corporation https://en.wikipedia.org/wiki/RAND_Corporation
- Maro 6mo ago" .. the smartest mathematicians for running these scenarios .. " https://en.wikipedia.org/wiki/John_von_Neumann https://en.wikipedia.org/wiki/John_von_Neumann > Claude Shannon called him "the smartest person I've ever met", a common opinion. > Von Neumann founded the field of game theory as a mathematical discipline. > .. leading him to a large number of military consultancies and consequently his involvement in the Manhattan Project. > In 1950, von Neumann became a consultant to the Weapons Systems Evaluation Group.. > In 1955, von Neumann became a commissioner of the Atomic Energy Commission (AEC), which at the time was the highest official position available to scientists in the government. > In his final years before his death from cancer, von Neumann headed the United States government's top-secret ICBM committee..
- srean 6mo agoThe Martian. Towards the end of his life as cancer metastasised in his brain he would ask his visitors to give him sums to do to reassure himself that he was still there. Towards the end he wasn't and couldn't. One of the saddest things.
- quotemstr 6mo agoThe 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 issues The 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.
- myrmidon 6mo agoYou 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.
- tonnydourado 6mo agoGotta say, did not know direct energy weapons were actually leaving science fiction and entering the real world yet, but it seems they're. It's obviously not star trek level, but it's way more advanced than I expected
- hedora 6mo agoThey are, but only have a range of 1.2 miles in earth's atmosphere. Since they're on the ground, and presumably near the target (not the launcher), that means they're aimed at the warhead just before it hits the ground. I looked up the numbers, and, interestingly, ICBMs have to slow down before they hit their target. In the midrange flight, they travel at 15,000 mph, but at re-entry the warheads are only traveling at 1900 mph, or 0.58 miles per second. So, in the best case (the warhead is headed to the laser), the laser only gets 2.5 seconds of dwell time to intercept it. This rapidly decreases as the distance from the laser to the target increases (to 0 seconds of dwell time at 1.2 miles). Also, if the ICBM fires multiple warheads, or chaff, then you'd need to scale up the number of lasers or scale down the dwell time linearly, assuming they're all conveniently aimed within a small fraction of a mile of the laser (again, I'm assuming best-case). Current direct energy weapons have only been demoed against UAVs, probably for this reason. edit: my math is completely wrong: Modern nukes are optimally detonated at about 5000 ft above ground level. So, you get about 0.33 seconds of dwell time, assuming the attacker doesn't just set the warhead to detonate at a non-optimal (but still devastating) 1.2 mile altitude. https://remm.hhs.gov/zones_nucleardetonation.htm https://remm.hhs.gov/zones_nucleardetonation.htm
- femiagbabiaka 6mo agocould 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
- OrangePilled 6mo ago"Lessons US and Gulf could learn from Ukraine’s air defence warriors" https://www.thetimes.com/world/russia-ukraine-war/article/us-welcome-ukraine-help-air-defence-lkdr7d6j6 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-defenses-war-76c91cad24bb98dd201f8f37a93c3464 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-shahed-drone-middle-east.html 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-intercept-targets-middle-east-2026-03-20/ https://www.reuters.com/world/europe/ukraine-deploys-units-i...
- Maken 6mo agoWhat the USA learned from Ukraine is that the Shaheds are amazing and they want them too [1], apparently. [1] https://en.wikipedia.org/wiki/Low-cost_Uncrewed_Combat_Attack_System https://en.wikipedia.org/wiki/Low-cost_Uncrewed_Combat_Attac...
- energy123 6mo agoWhat is the steady state? Assume you have two competent superpowers, both researching missile offense and defense, over the next 1000 years. What are the asymptotics of the interception rate from 0 to 1000?
- bob1029 6mo agoThe steady state would look like a sinusoidal signal. This is more of a cycle than a hill climbing thing.
- energy123 6mo agoAre you sure there isn't a structural advantage to either offense or defense that will reveal itself with more iterations, and we won't converge to either 0% or 100%?
- adampunk 6mo agohttps://en.wikipedia.org/wiki/The_bomber_will_always_get_through https://en.wikipedia.org/wiki/The_bomber_will_always_get_thr... That’s the steady state. Interceptors are expensive; missiles are (relatively) cheap. There’s no sine wave or cat and mouse game. If you’re trying to defend against a peer, missile defense loses.
- energy123 6mo agoI'm talking about interception probability, not the relative cost. I get that interceptors will probably be more expensive indefinitely (unless we start putting lasers into orbit to get around atmosphere, or something unexpected like that).
- adampunk 6mo agoWell there the cost plays a part! It’s not independent. If I can build 1000 missiles for every 1 interceptor, the probability of interception hardly matters. This actually was why we planned to put lasers in space: the economics of one nuclear-pumped laser reflected through Unobtanium were better than any other interceptor. And even that if the effect worked (it didn’t, they could not prove lasing and fired an engineer who blew the whistle on that), the system could be defeated by a staggered salvo.
- jmyeet 6mo agoPardon 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.
- captainswirly 6mo ago[flagged]
- nerfbatplz 6mo agoTechnically Iran fires SRBMs and MRBMs not ICBMs. They intentionally gimp their missiles to avoid advertising ICBM range as a way of placating Europe.
- captainswirly 6mo ago[flagged]
- Maken 6mo agoICBM means the missile is able to be launched into other continent (more than 5K kilometers in range), not about its effective warhead. Iranian missiles are fast and efficient, but their effective range is essentially being able to target Israel and the Gulf States, which means they are not ICBMs. Also, the one country in the Middle East who does have ICBM missiles and can target Europe is Israel, not Iran.
- echoangle 6mo agoThe IC in ICBM mean Intercontinental and specifies the range, not how impressive it looks in videos.
- vaporwario 6mo agoNot sure if it applies exactly but this discussion brings to mind this saying... "The loser of a knife fight dies in the street. The winner dies in the hospital."
- koakuma-chan 6mo agoWhy does a ground based interceptor cost $75M? High idiot index?
- hedora 6mo ago$1M, but we can only make 600 / year, globally.
- koakuma-chan 6mo agoFrom the article, "Each GBI costs approximately $75 million, and as of 2024, 44 are deployed across Alaska and California [3]."
- hedora 6mo agoI'm quoting the missile cost. I think they're quoting the launchers + a few missiles. (Also, lower bounding the cost improves the argument that they're too expensive to be practical.)
- O3marchnative 6mo agoAuthor here. The $75M is specifically for Ground Based Interceptors (GBIs). This is the U.S.'s ICBM mid-course interceptor. There are other interceptor types in the current U.S. arsenal: Patriot PAC-3 (~$4M): Nations burnt through 600-800 in the first few days of Operation Epic Fury. There are reports that they're being used for drone defense. SM-3 (~$10-30M): Ship-launched SM-6 (~$4-5M): Ship-launched THAAD (~$12-15M): Terminal phase, high altitude GBI (~$75M): intended for interception of ICBMs (reported as the hardest type of missile to intercept) Each type of interceptor is optimal for certain type of threats, which is yet another constraint on the optimization problem.
- mrguyorama 6mo agoIn what world would a specialized, niche, high precision, high readiness rocket meant to loft a very advanced interceptor munition into an extremely high velocity interception ever be cheap? These things are closing at like mach 20. Physics says that's hard to do. That means it's expensive. For reference, $75 million is in the realm of a Falcon 9 launch, which is a very cost optimized platform that doesn't have to place a very very precision instrument payload in a very very specific point in space to prepare it for a high energy, extremely difficult interception.
- fisherwoman 6mo agoThose rockets are lobbed in high arcs and glow in the sky then slowly fall down - they are so slow they almost look like flares. Your so-called missile defense does nothing at all against a real missile like Iran's supersonic ICBMs which can exceed 24,000+ km/h.
- sgtsteaks 6mo agoWhat are you gonna do when Iran destroys the missile defense system itself, oops already happened
- contravariant 6mo ago> Note that a more complete model would multiply each term by P(track)_j — the common-mode detection-tracking-classification factor developed in the previous section — but the standard WTA formulation assumes perfect tracking. I'm not sure that is a useful model, or more complete. I don't think you can assign interceptors to undetected missiles, so considering their effect on the value is rather pointless. It's effectively a sunk cost. Multiplying with the probability also makes no sense from an optimisation point of view. Why would you assign lower value to a target about to be hit simply because you were unlikely to detect the missile? The tracking probability only shows up in the meta game described at the end, where one side is trying to optimise their ability to hit valuable targets and the other is trying to optimise their ability to prevent that from happening.
- EGreg 6mo agoWhat happened to Iron Beam / lasers and those vaunted "space lasers" dubbed "star wars"?
- hedora 6mo agoApparently, Iron Beam still exists (or at least was demoed in 2024). Originally, the lasers were going to be mobile, but now they have to be stationary, so it will work like the game Missile Command, except you have unlimited ammo, but no concurrent shots, and the missiles can't be rotating (like a rifled bullet would). That's much more feasible-sounding that I'd assumed (coming from low expectations). https://en.wikipedia.org/wiki/Iron_Beam https://en.wikipedia.org/wiki/Iron_Beam
- EGreg 6mo agoI seriously can't wait for this technology. It can be purely defensive, and shoot down all aerial attacks - drones, etc. over your country's airspace. So... no wild weasel, no successful air raids, etc. We're back to ground invasions, and frankly, a country can defend against those a lot easier. And it also means countries not lobbing missiles at each other, and at oil fields and igniting them, or destroying shipping etc.
- jandrewrogers 6mo agoThe US has deployed operational anti-drone lasers for a few years now, though not widely. They are still quite new but they have several kills. This is probably operational field testing for fine-tuning the design prior to producing them at scale though.
- maxglute 6mo ago>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.
- dgroshev 6mo agoThat goes both ways. Terminal manoeuvring gets difficult as speeds increase, too. Besides, higher tier threats are intercepted outside the atmosphere, where it would be prohibitively expensive (in mass and accuracy) for RVs to manoeuvre. Your SSPK is way WAY too low. Also, the math on interceptions changes completely with multiple KKVs per interceptor (see NGI). Decoys don't work even at the highest end (ICBMs), see Chevaline's history and its rapid decomissioning for an example of just that.
- maxglute 6mo agoTerminal maneuvering vs interceptor kinematics difficult don't scale same at same rate with speed increase, a few Gs on reentry is magnified on interceptor end, the physics is not fair between attacker/defender. Higher threats are not exo atmosphere & midcourse that NGI targets, actual speculative high end threats (since we talking about speculative NGI capabilities) are hypersonic glide in upper atmosphere, which NGI can't target. It's even more extreme intercept problem, the intercept math for those class of threats is on paper even more lopsided against defender. NGI basically ensure US keeps pace with modern penetration aids proliferation, i.e NKR tier adversaries if they ever improve RVs + decoys from shit tier to mid tier. Chevaline was 50 years ago, not really relevant example, since issue was really economics of decoys vs just spamming mirv. Regardless, NGI trying to maintain 3/4/5 interceptor ratio instead of 30/40/50/100s against exo threats, which on spectrum is low/medium end. It does 0 against actual future highend threats of glide phase interception, an entirely different category.
- jcul 6mo agoReally interesting. Forgive my ignorance, but I thought Israel's "iron dome" offered a very effective defense. Is this just from short distance missiles from neighbouring countries? This article seems to indicate it's very difficult to achieve a high success rate against multiple missiles. Admittedly I probably need to read up on this more.
- icegreentea2 6mo agoThere are multiple tiers of missile (and ballistic missile defense). Especially with ballistic missiles, the longer the range, the faster the inbound warhead will be in the terminal phase (roughly). So longer range ~= faster meaning more difficult to intercept. "Iron Dome" is the name generally used to describe Israel's lowest tier set of defenses. Very roughly Iron Dome is designed to defend against stuff that you could plausibly fire from the back of a truck, and have a max range of around ~50km. Very roughly, these were intended to take on something like GMLRS (realistically, massed volleys of unguided rockets) - these are rockets that one or two people could conceivably manhandle, and are traveling in the neighborhood of Mach 2-3. One of the key innovations of Iron Dome is its ability to quickly ascertain and design on which rockets were unlikely to strike valuable areas, and only engage the actually threatening ones. The next tier up is David's Sling, and then Israel's wider set of high performance anti-ballistic missile systems. Returning the the range <-> speed thing, we'd need something like a medium range ballistic missile to get from Iran to Israel. For something like the Shahab-3, that's like ~Mach 7 during re-entry. If we step up to IRBMs (so something that China might use to strike at Guam), we're probably talking like Mach 10.
- jcul 6mo agoInteresting stuff, thanks for the long and detailed response.
- ozgung 6mo agoAs an alternative formulation of the same problem, maintaining peace has linear cost, completely solvable in linear time and rewards are unbounded for all parties.
- inaros 6mo agoI spent some time reconstructing the current US missile defense interceptor numbers. This was done from open source DoD data, CSIS P-21 procurement exhibits, and CRS reports, that are are in depth, non partisan, objective policy analyses written by experts at the Congressional Research Service (CRS) specifically for U.S. Congress members. Also used Lockheed/RTX financial disclosures. The numbers are pretty bad… Way worse than the headlines suggest. But anyway nowadays, investigative journalism has been decimated....For example experts like Kelly Grieco at Stimson estimated that at 12 day war consumption rates, the entire US interceptor stockpile depletes in 4 to 5 weeks. We are now in week 4... As of December 2025, CSIS documented delivery of 534 THAAD interceptors and 414 SM-3. The 12 day War burned through around 150 THAADs (that is 28% of inventory) and about 80 SM-3s. The current war has been drawing down from that already depleted starting point for 25 days straight... Gulf states reportedly expended around 600 to 800 PAC-3 MSE interceptors in the first 72 hours of Epic Fury alone, and that is more than the entire global 2025 production ( about 620 units). Meanwhile THAAD production is 96 per year….with a recent Lockheed commitment to quadruple to 400 per year, but that will only deliver these additional missiles after 2027 or later. For example the sole ammonium perchlorate supplier for every US solid rocket motor runs one plant in Utah, and the sole HMX/RDX source is a WWII facility in Tennessee… The US has procured roughly 270 PAC-3 MSE ( the Patriots ) per year since 2015, but has diverted around 600 to Ukraine over four years. The exact remaining US stockpile is not known with the same precision as THAAD/SM-3, so they could not have more than 3000 before Epic Fury... But it is known as I said above, Gulf allies burned through 600 to 800 or more PAC-3 MSE in the first 72 hours of Epic Fury alone from their own stocks. Since they have zero domestic production capacity, and will be competing with the US for the same Lockheed production line that only makes about 600 per year, Iran really has them by the balls. By the way, the cost so far in munitions is 20 billion ( check references…). Then on Intelligence... Iran has 13 satellites of their own, and it is known to be receiving intelligence from the Russians. This data allows them to know exactly how many Patriots or THAAD were fired so far. They are also probably customers of MizarVision, a Chinese AI startup, that has been cataloguing every significant American military asset in the Middle East. Every base, every carrier strike group, every F-22 deployment, every THAAD battery, every Patriot missile position, tracked, labeled, analyzed, and posted publicly. So... Unless the US escalates to a Ground Invasion (most likely scenario…), or negotiates a deal with Iran, if Iran can keep their industrial production of missiles, or maybe move them far up and inside tunnels in its Northern Mountains, and...if the USA does not escalate to a ground invasion due to the political risks, they can actually win this war both from the political and strategic aspects, as incredible as that might seem. Who is truly screwed are the Gulf countries, as their stocks of US missiles get progressively depleted… And they wont get a refill soon. Russia strategic interests are in helping Iran, since it weakens the US and strengthens their hand in Ukraine. What might make it worst for the Iranians is the Chinese view of this. I speculate they will prefer to help the US and its economy, by forcing the US to do a great commercial interesting deal for them, then using their strong leverage on Iran to come to an agreement. Strategically, over the next four to six months: Russian wins, Iran wins (despite all the destruction), China wins, Israel loses, the US loses. Trump truly is the biggest loser... "Are We Running Out of Missile Defense Interceptors?" - https://www.csis.org/events/are-we-running-out-missile-defense-interceptors https://www.csis.org/events/are-we-running-out-missile-defen... "‘Race of attrition’: US military’s finite interceptor stockpile is being tested" - https://www.defensenews.com/news/your-military/2026/03/06/race-of-attrition-us-militarys-finite-interceptor-stockpile-is-being-tested/ https://www.defensenews.com/news/your-military/2026/03/06/ra... "The Depleting Missile Defense Interceptor Inventory" - https://www.csis.org/analysis/depleting-missile-defense-interceptor-inventory https://www.csis.org/analysis/depleting-missile-defense-inte... "Over 5,000 Munitions Shot in the First 96 Hours" - https://www.fpri.org/article/2026/03/over-5000-munitions-shot-in-the-first-96-hours-of-the-iran-war/ https://www.fpri.org/article/2026/03/over-5000-munitions-sho... "A Chinese AI Startup With 200 Employees Is Mapping Every US Military Asset in the Middle East — In Real Time" - https://breached.company/mizarvision-chinese-ai-satellite-us-military-tracking-2026/ https://breached.company/mizarvision-chinese-ai-satellite-us... https://www.mizarvision.com/ https://www.mizarvision.com/
- blueblisters 6mo agoGaming this out for peer adversaries is mostly moot, right? The post-Cold War strategic balance has mostly hung on MAD. And Russia, in particular, has responded to any attempt at building missile shields with more capable missiles. It's likely more relevant for asymmetric conflicts that involve conventional weapons, and would enable an otherwise less resourced adversary to become a near peer. Dennis Bushnell from NASA presented this deck in 2001, and is quite prescient about UAVs and distributed warfare. https://alachuacounty.us/Depts/epd/EPAC/Future%20Strategic%20Issues%20-%20Future%20Warfare%20Circa%202025%20-%20NASA.pdf https://alachuacounty.us/Depts/epd/EPAC/Future%20Strategic%2...
- CamperBob2 6mo agoEh, he threw so much random stuff at the wall that some of it is bound to stick. An early slide in his presentation says there will be "no pixie dust," but that's 90% of what follows.
- tug2024 6mo ago[dead]
- deepsun 6mo agoAnd that is the answer to Fermi paradox "why we don't see any other civilizations in the galaxy".
- solatic 6mo agoThe math and economics on missile defense are broken. If your adversary uses nuclear-tipped missiles: within hours if not days, you are virtually guaranteed to suffer impact. Congratulations, New York is under a mushroom cloud. Lose. If your adversary doesn't use nuclear-tipped missiles, you have a war of attrition whereby the cost of interceptors is greatly more expensive than the cost of building the conventional missiles. Congratulations, you wrecked your economy, if you can even keep up production of interceptors for long enough. Lose. The only winning moves are to either use ground troops to invade and dismantle your opponents' missiles to prevent that risk from being realized, or to play mutually-assured destruction games trying to convince the other side that you're just an insult away from doing it anyway. And a Western world that seems desperate to keep boots off the ground is not playing that winning move.
- mikkupikku 6mo agoThe "if only one nuke gets through, you lose and the whole thing is pointless" is completely wrong. Even if surrender were mandatory after one nuke, all the other intercepted nukes would be thousands if not millions of lives saved.
- Brybry 6mo ago> the cost of interceptors is greatly more expensive than the cost of building the conventional missiles And the same thing is true with this comparison. The cost comparison is not interceptor vs conventional missile. It's interceptor vs conventional missile + the damage the missile would have done. Yes, you don't want to use Patriots to intercept Shaheds but that's an argument for using the right tool for the job. It's not an argument that the economics of interception are completely broken. Ukraine has interceptors that are cheaper than Shaheds.
- aftbit 6mo agoShot exchange is a huge problem, made even worse by the arrival of cheap drones. But you're implicitly assuming that the adversary is on roughly equal economic footing. If your defense budget is $800 billion and your adversary's defense budget is $8 billion, you can afford to spend 100x as much shooting down their missiles as they spend lofting them. There's also a danger in projecting linearly from the beginning of a war, where invading forces both tend to use more expensive stand-off munitions and also have to deal with more aggressive missile launches. As the defender's own air defense system gets degraded, the invader can switch from expensive long range stand-off munitions to cheaper stand-in munitions (like glide bombs) launched from much shorter range. Additionally, the invader will be able to diminish the defender's ability to launch missile strikes in the first place, either by destroying the launchers, the missiles themselves, or their production, thus reducing the demand on expensive high-capability interceptors. Drones and mines continue to offer asymmetric warfare options that are very hard to counter without a robust low side on the high-low mix. Ukraine are the world's leading experts in this currently, and hopefully are involved with US and Gulf forces to try to improve this shot exchange ratio. I am assuming nobody is using nukes though. That completely changes the picture. One must always assume "(some of) the missiles will get through". Traditional MAD does not require boots on the ground - merely the assurance that if Iran gets one nuke through and hits New York, the USA will respond with 100+ nukes. The real question then is what the other "large" nuclear powers (Russia and China, primarily) will do in response to that.
- Havoc 6mo agoThere is also a big real world experience element that is hard to account for mathematically. There are stories of ukrainian operators expressing bewilderment and BCC countries sending 8x interceptors at millions a pop at a 20k shaheed. The world doesn't seem to have acclimatized to well...how the world works now. There is a very fundamental disconnect at play here and I fear it'll get us all into trouble
- mattmaroon 6mo agoWell, it’s less about the value of the interceptor and more about the value of what the drones are heading for. If it’s a desalination plant that makes 20% of your freshwater, eight missiles are probably well worth it because a lot of people can die. Middle Eastern countries have much more condensed critical infrastructure and economic targets than we do. Iran has expected a war like this for decades and been continuously preparing, most of the other nations they have not.
- Havoc 6mo agoThat logic right there is why the US is going to lose. That math only works in isolation The Ukrainians don’t think about today’s tradeoff but also about tomorrows. They learned that when when a three day special operation turned into four years. You have to match your best defenses against the best expected incoming attack- across time- even if it means taking a hit. Yes desalination plant included The us doctrine of defend all the things all the time against everything has failed in light of modern drone warefare
- angelgonzales 6mo agoThe US already has “shoot the archer” doctrine which strategizes to target the site(s) launching cheap drones rather than the drones themselves. With US air superiority this seems feasible.
- 15155 6mo agoUkraine has no feasible means to actually act offensively, meanwhile, the United States is a nuclear weapons state. Pose a credible-enough threat and atomic deletion will ensue.
- enaaem 6mo agoYeah this is really bad news for Israel. America does not have the resolve for a major ground invasion, and Israel cannot intercept missiles indefinitely.
- MoonWalk 6mo agoWhatever that means.
- deleted 6mo ago[deleted]
- brcmthrowaway 6mo agoSo this is what RAND corporation spends all day doing.
- VerifiedReports 6mo agoWhat is that supposed to mean?
- egorfine 6mo ago[dead]
- egorfine 6mo ago> developed [] algorithm that solves instances with 10,000 [] in under 7 minutes on a Macbook Pro [] The prior state-of-the-art timed out at 2 hours Knowing how government IT procurement works, I'm afraid it's going to stay >2h for the foreseeable future even if the COTS solutions will bring this time down to a subsecond calculation.
- verisimi 6mo agoThe graphic shown has very '95 flavour.
- treebeard901 6mo agoChina, Iran and Russia can vastly out produce missle interceptors. Drones, hypersonics, etc. They can also manufacture launchers faster and cheaper than they can be countered. $30k drone vs interceptor at millions. The U.S. and Israel will not accept the current regime staying in power. Neither side wants to stop the war. Israel, Europe, the U.S., gulf states and others in missile range of Iran will not want the current regime to remain in power. What happens next? Full invasion? Regime change Iraq style?? Here is a highly probable outcome before next year. Iran continues breaking the Iron Dome and firing on "allied" targets and infrastructure. The U.S.refuses or cant sustain a full invasion (because it is a death trap). What happens next? It is obvious Israel will use tactical nukes on Tehran and other targets in Iran. It is going to be their only option.