Is unanswered prayer a waste of time?

I don't know if there are any reliable stats on this topic, but it wouldn't surprise me if most Christian prayers go unanswered. (By "unanswered prayer," I mean not getting what you ask for.) That raises an interesting and important question: answered prayer has obvious value, but does unanswered prayer serve any purpose? 

i) At one level you might view prayer like dandelion parachutes and maple leaf whirlybirds. Even if most don't germinate, redundancy provides a margin so that a few are likely to germinate. More prosaically, if you already get less than you pray for, then the less you pray, the less you get. You get even less than if you prayed more often. Suppose only a fraction of prayers are answered. In that event, the "odds" of any prayer getting answered plummet if you pray infrequently. You fall below the threshold. 

Now, that's a rather mechanical way of putting it. I'm not suggesting that it's primarily about the odds. There is, though, an element of truth in the fact that you get more hits with more throws. On a dartboard, even when you miss most of the time, if you keep throwing darts, you'll get lucky, but if you rarely throw darts, your hits will be that much rarer rare.

Once again, I'm not suggesting that answered prayer is a matter of luck. Just using an analogy to illustrate the point. Analogies have disanalogies. 

And, of course, you don't know ahead of time which prayers will go unanswered. So it's not as if you could make better use of that time. 

ii) When several people pray for someone, and the prayer is answered, whose prayer was answered? Was everyone's prayer for that person answered? If they all prayed for the same thing, did God individually answer their prayers? There's a sense in which, if fifty people pray for the same thing, and God answers their prayer, God can't answer their prayer fifty different times since there's just one specified outcome. 

Or did God respond to just one or two prayer warriors–out of the sum total? If half the people prayed, maybe the prayer would go unanswered, not because it's about sheer numbers, but perhaps the prayers of some Christians are more efficacious. Some Christians are more saintly than others. (I don't mean "saintly" in the Catholic sense.)

iii) The habit of prayer creates a prayer-shaped life. Both answered and unanswered prayers contribute to a prayer-shaped life. It's not confined to a subset of "successful" prayers, but a life of prayer that conditions and regulates the Christian pilgrimage. 

v) Answered prayer affects the future, but so does unanswered prayer. For the time spent in prayer is time diverted from other activities. Even when prayer doesn't affect the future by directing a specific outcome (answered prayer), yet the act of prayer still affects the future regardless of the divine response. In a cause/effect world, what agents do with their time has a ripple effect. In his providence, God employs unanswered prayer as well as answered prayer to orchestrate the future.