Based on general solid fuel missiles, you can assume around a 20% total failure rate, either failure to ignite or catastrophic failure during boost (this would be higher for liquid fueled missiles, which are far more twitchy, as can be seen in civilian launches), assuming a good PM process is in place, which is a rather large assumption especially for Soviet/Russia systems. Call the actual failure rate 33%.
Warheads are VERY reliable. They are heavily tested, at least in the U.S. inventory (one reason the nuclear stockpile is so damned expensive to maintain) Failure, as in no detonation, would be no more than 5%.
The real question is accuracy. The over Pole launch is very different from anywhere test are conducted. I always thought they should fire some missiles w/o physic packages over Antarctica just to get some sort of feel for the bias issue, but the politics of that are such that it won't ever happen. The real problem would be in the counter-force weapons, which need to be pretty much dead on. Population targets, well, a 2,000 meter miss with a 450KT warhead doesn't really matter all that much.
There is also the fact that most of the strikes against population/strategic targets, at least on the Western side, would be SLBM, many of which would not require an over Pole flight path which would greatly improve accuracy. U.S. SLBM are also MIRV.
When you throw in counterforce strikes, other enemy action (a SSBN getting potted by the odd fast attack boat) and the fact that a number of crews just flat won't launch their weapons, it would be a surprise if 25% of the total weapons actually hit their targets. That is mainly why there are enough weapons to kill the Planet five or six times over..