I occasionally see something come up where a user will ask about speed work and someone responds saying that they don't have the base to support it. Would someone be able to explain this to me? How do you tell if someone does not have enough of a base to support week/day x?

What would happen if you went through with week/day x if you didn't have the proper base for it?

Hopefully someone can give a more comprehensive answer than I can, but generally the books I've read advocate that certain types of speed training only be a certain percentage of your weekly mileage.  If that percentage is only 8%, and you're running 10 miles per week, then .8 miles would be your maximum for that type of training.  That might not be worth your time, when you could be focusing on building your base.  The theory is that base building, and easy miles prepare your body and are a form of injury prevention in the long run.  Your chances of injury increase when the percentage of your miles that are speed work increase.

On the other hand, we've seen more than one runner on this forum continue to get faster and faster without ANY speed work, simply because they're running easy miles.  I'm sure there's a limit to the benefit of lots of easy miles, but most beginners aren't anywhere near that limit.

I am a proponent of starting speed work very early in your running.  It doesn't have to be anything formal.  Finish the last quarter mile faster than the rest of the run.  In the middle of a run, pick up the pace a bit.  Of course, this doesn't fit the definition of "speed work" in most people's minds but you start learning how to have more than two gears (jog and sprint).  You start building extra neuromuscular strength.  You add a bit of fun to the run.  Once you can run for 3 miles without stopping, I think you can begin doing formal speed work.  An easy one is a tempo run.  Jog one mile.  Then run one mile hard.  Not all out but hard.  Then jog a mile.  Presto.  You just did your first tempo run.  

My other thought is that it is easier to get hurt doing nothing but increasing your easy miles relentlessly than it is to get hurt doing speed work because speed work hurts.  You'll be in some discomfort and you'll have to pull back.  There are some guidelines out there about what percentage of your weekly mileage should be faster running and I'm sure it varies by individual but I think a decent guideline is no more than 20% total with no more than 10% in any given workout.  (I'm excluding marathon pace runs but if you have been running long enough to be able to run 10-12 miles at a planned marathon pace, then you've likely figured most of this stuff out).

Now, if you're talking about someone who is running 10-15 miles per week and wants to head to the track for something like 12 x 400, then yeah, they don't have the base to support it.  In that case, you're talking about someone doing 20-30% of their total weekly mileage in one speed session and that's quite over the top.

onirocdarb-I have read what your citing in a couple of books, basically to the effect of "unless you can handle 30mpw don't do speed work"

I don't know if I get the statement, I know what they are trying to say, and where they are trying to go...if your just outta c25k, don't kill yourself trying to do intervals or hill repeats.

I second learning your different gears are a good thing. I am not the fastest runner, but my first few attempts at strides was a huge breakthrough for me as far as from moving from the shuffle to a 'wow I am moving' pace.

Then there was my tri-friend who talked me into the 30 minute LTHR test at the track last night. Dry heave fun party yay! WTF that is not fun.