Hebrews 11:1 is not really a definition of faith itself but rather a statement about what faith does. And the word translated "substance" should have been "transubstantiating" but they were avoiding it because of the doctrine of the Catholic church. Now faith is the transubstantiating of things hoped for... And this does mean that faith does change things as James Norman suggests it should. Faith is the changing of the substance of things hoped for.
 
http://www.fivedoves.com/letters/apr2011/michaelc427-6.htm
 
For me the biggest mystery about faith is not what it is or what it does but rather in the time element involved in its seen result. The examples given by James Norman do show how faith changes things and the implication is that we too should be able to see such results in our lives. However there are also examples in the Bible of those who have faith but see no obtaining of the promises.
 
Hebrews 11:
32.  And what shall I more say? for the time would fail me to tell of Gedeon, and of Barak, and of Samson, and of Jephthae; of David also, and Samuel, and of the prophets:
 33.  Who through faith subdued kingdoms, wrought righteousness, obtained promises, stopped the mouths of lions.
 34.  Quenched the violence of fire, escaped the edge of the sword, out of weakness were made strong, waxed valiant in fight, turned to flight the armies of the aliens.
 35.  Women received their dead raised to life again: and others were tortured, not accepting deliverance; that they might obtain a better resurrection:
 36.  And others had trial of cruel mockings and scourgings, yea, moreover of bonds and imprisonment:
 37.  They were stoned, they were sawn asunder, were tempted, were slain with the sword: they wandered about in sheepskins and goatskins; being destitute, afflicted, tormented;
 38.  (Of whom the world was not worthy:) they wandered in deserts, and in mountains, and in dens and caves of the earth.
 39.  And these all, having obtained a good report through faith, received not the promise:
 40.  God having provided some better thing for us, that they without us should not be made perfect.
 
Some had beautiful victories through their faith while others by faith accepted death and seeming defeat but obtained a better resurrection. Those receive not the promise in this life but will certainly have reward later.
 
Why is faith so important to God?
 
Here is what I think is going on:
 
Ever since Lucifer challenged God there has been this issue of whether God is truly good or not. God easily defeats Satan's attempt at co-ruler-ship in heaven, casting him and his other fallen angels from heaven and could easily dispatch with him for good and all in one fell swoop but He did not do that but why? Because that would only prove that God is superior to Satan in strength not in goodness also. Strangely, the issue apparently could not be entirely settled before we came along to help decide the truth of the matter. In a strange way, we each get to play referee in this huge contest. God and Satan each from the dawn of mankind have made their claims of what each would do for man. We must decide which of the two we believe and choose to follow with our entire being.
 
There are many in the NWO, Illuminati, secret society, pagan religions and ideologies, whatever one wishes to call them who actually believe that Lucifer is the good guy who wants to help mankind and God "Adonai" is the evil one who only wants to exploit man for His own selfish reasons.
 
Faith in what God promises us is the only way to vote for God. Anyone can claim they believe that God is good but unless they have put their life or something of value on the line in defense of that belief have they really voted for God? Go into any casino or racetrack and walk up to the payment window and tell them that you believed that the winning horse or number was going to come in before it did but that you didn't actually put in a bet or wager anything on it and try to collect the prize money. They'll laugh you out of the place. God needs our bet the same way and it has to cost something. Mere mental belief won't win a prize. But the payoff for a correct bet doesn't always come when we want it to either.
 
I have heard that some teachers of the "name it and claim it" kind of faith thought that if Paul had known what they had figured out that he wouldn't have had to be a prisoner so much because he could have claimed his victory and taken authority over the situation. Yet Paul who certainly had faith, also had troubles that he accepted as God's will. He told Timothy about how some rewards come quickly and some take more time even waiting until eternity. Same with punishments for wrong bets or behavior.
 
1 Timothy 5:
 24.  Some men's sins are open beforehand, going before to judgment; and some men they follow after.
 25.  Likewise also the good works of some are manifest beforehand; and they that are otherwise cannot be hid.
 
Bottom line is that faith is not measured purely by its results in this life but is willing to keep strong even in the face of apparent defeat because God will come through in the end and faith will come forth as pure gold tried in the fire unto praise honor and glory at His appearing.