The incident you linked to wasn't a nuclear explosion: the rocket the nuke was sitting on exploded. FTA:

"The W53 warhead landed about 100 feet (30 m) from the launch complex's entry gate; its safety features operated correctly and prevented any loss of radioactive material."

(I am not a nuclear engineer)

If you have a ball of fissile material, there are two sizes that are interesting to you. There's the point at which the material goes critical: on average, every neutron emitted causes the emission of more than one neutron. However, there are two types of neutron emission: prompt neutrons (released immediately when an incoming neutron breaks apart an atom), and delayed neutrons, released eventually by the decay of fission products. If you're producing one prompt neutron on average, then you're at prompt criticality.

Nuclear reactors prompt-subcritical but delayed-critical. Because the exponential growth of neutrons in a delayed-critical material is relatively slow, it can be managed by futzing with control rods.

If undisturbed, a supercritcal fissile mass will explode. The question is, how energetically? If it's delayed-critical, not very. The time scale characterizing the exponential growth is large compared to the time required for the explosion to propagate through the mass, so the mass will explode with not much more than the minimal amount of energy required to render it subcritical again. This is messy, but not what you think of when you imagine a nuclear explosion.

If the mass is prompt-critical, then the exponential growth is much faster. Even once the mass has released enough energy to explode, it still takes time for the mass to expand enough to be rendered subcritical. In that time, a prompt-supercritical mass will undergo many more generations, resulting in an actual nuclear explosion.

To get an actual nuclear detonation, then, you need to get your fissile material from subcritical to prompt-supercritical as fast as possible, so it doesn't predetonate unimpressively. This is a tricky task, requiring carefully shaped explosives, and pretty unlikely to happen by chance.

No it wasn't a nuclear explosion, but it certainly could've been and the fallout would have been very bad. You're way oversimplifying it. Did you watch the documentary a few weeks ago? I'm just saying I did and they interviewed the people involved including the guy who dropped the socket. They also go over just how unsafe these facilities were and a couple of other incidents of even worse magnitude.

> This is a tricky task, requiring carefully shaped explosives, and pretty unlikely to happen by chance

It's not "by chance," the warhead is carefully designed to make it and everything needed is already there, there are no missing parts. The "software" maybe doesn't activate the parts optimally or at all if there's luck but nothing is missing inside.

In the given case, "only" the rocket body exploded (with the fully functional warhead on it) even if it's not designed to do so, and only because of one single fallen small piece of metal (a single socket).