How important is speed to putting? If you roll your putts at the wrong speed, nothing else matters. You will have far too more three putts.

Most golfers don't think about speed quantitatively. They don't know why they did  it and go only so far as to hope they won't do it again. Their mistake is not understanding that controlling speed is a skill, just like all the others in golf, that can, and should be, worked on and improved. Most golfers think about controlling the line of their putts. While this may not sound bad, it really is a way to ensure that your putting never improves. Trying to “make” a ball do anything usually involves a mechanical responese of the hands, fingers, and forearms, none of which are helpful in executing rhythmic, repeatable putting strokes. 

Your ball tracks (their shape, size, and direction) is a function of the speed. On the course, misses probably would have been blamed on misreading the break, pulling it just a little, and hitting the putt poorly respectively. The truth of the matter is that all misses were simply the result of rolling the ball the wrong speed.

It is easier to see errors in line than errors in speed. Golfers get so concerned about line that they forget how fast of how far the putt needs to roll, and different putt speeds will always give you a choice of ball tracks (unless it is one of those few dead-straight putts). Because the ball is much less than half the size of the hole, even straight putts offer a choice of makable Aimlines, since you can aim a little to the left, a little to the right, or dead in the middle and still find the hole.

There are even more Aimline choices on breaking putts than on straight putts, and there are countless combinations of Aimlines and speeds in between.

When you're looking a putt, which element do you consider first? Line or speed? Since the line is the more instinctive, it would make sense to choose line first and then determine the correct  speed for that line. 

And there is. Rather than focus on line or speed, I've found that the best way is to imagine neither the Aimline nor the speed but the entire ball track you expect your putt to roll on. Because you can't correctly imagine a ball track without your mind including both line and speed.  

If you can imagie the ball track you want, starting on the Aimline you have chosen, your subconscious will include the speed.

 Years of experiments have shown me that the optimum speed for making putt is one that would, if the hole were covered or miss, roll the ball 17 inches past the back edge. 

"17 inches past" has become known as the optimum putting speed that produces the optimum ball track and makes the most putts, it's a terribly important number to know. There's another advantage to rolling putts at the 17-inches-past speed, you're much less likely to leave putts short.

Speed is the number-one principle in putting，every putt is a new experience,  and because everything is new, controlling the speed of your putts will always require every bit of your focus and attention. In fact, ball tracks (which include your aimlines and speeds) are just about the only thing you should think about when putting.