If players can control their speed on longer putts and lag the ball well, then they do possess the skills needed to control their speed at other lengths. That means that the differences are probably in effective practice, mindset and understanding the importance of speed control at all lengths of putts.
Here's a link to an article about Jordan Spieth's preparation for a round. He works on getting putts past the hole, but within 3 feet. He prepares for his round by working on his speed control.
After you read that, go watch this video on Jordan's skill set at controlling his speed on putts.
Before we go any further in this discussion, I want to talk about some offshoots at being poor in controlling your speed from 5 to 15 feet. When you miss putts from that range, you start thinking you might have a flaw in your stroke, so you begin to work on your mechanics during practice or even during competition. If you aren't getting accurate feedback as to why you're missing putts, you should know that mechanics isn't always the reason. The second problem that arises from players with poor speed control is, they think they are poor green readers. After walking with two of my players last spring on back to back days, I realized that they read putts quite well, but they weren't very skilled at delivering the ball to the hole at the speed that matched their read. You cannot be a great green reader if you can't deliver the ball to the hole at the correct speed.
The concept of getting the ball to be slowing down around the hole is pretty easy to understand when you're 45 feet away from the hole. You know you want to give it a chance, but the odds aren't great that you'll drop the ball in the hole. So, you balance the idea of giving it a chance with keeping it close to the hole. Most good players think 1' to 2' feet is an acceptable second putt from 45'. Why then, isn't that an acceptable distance for a 2nd putt from 10 feet? So many times I watch young players' putts lose steam and fall off the line when they are a foot or two from the hole. They end up just low of the front edge or perhaps a bit past on the low side. The read was probably perfect, but the speed of the putt ran out prior to the hole. Other players I've watched get really jacked about having a ten footer for birdie and they hit their putt 3' to 4'' past the hole. The ball holds it's line beautifully, but the line doesn't match the putt the player envisioned.
The boys I watched at the Stacy Lewis and the Wyndham Cup were very good at hitting putts that would be 1' to 2' past the hole when they were within that distance of 5' to 15'. Their putts didn't run out of steam and break off before they got to the hole. Nor did their putts motor past to stop 3 feet past. These boys controlled their speed at 5', 10', 15', 20' and on and on. That is probably one of the skills that has allowed these boys to be the highest ranked players of their age groups.
This week, I've heard from two of my players about speed. One wrote to tell me she had a ton of birdie putts stop a roll short. Another told me she lipped out so many putts. Then today, I worked with one of my students who was rolling it great, but making nothing. I decided the golf gods were clearly telling me to get busy and come up with a drill that helped players with this skill. Here you go.
Speed Control Challenge:
1. Put a tee down at 10 feet.
2. Read the putt and decide on the aim point.
3. Put an aim stick down on the aim point you chose.
4. Place a golf ball 1 foot behind the hole; another 2 feet behind the hole and a third 3 feet behind the hole. If the putt is left to right, place them in the middle of the cup on the line the ball would enter the hole or each slightly more right. If the putt is right to left, place them in the middle of the cup as the ball would enter or slightly more left.
5. Using the aiming stick you placed when you read the putt, putt 3 balls that finish at the first ball if they don't go in the hole. Did your aim work for that speed? Did the balls hold their line? Were you able to hit 3 balls at that speed? Now do the same thing, but if the balls don't drop in the hole, they should end at the second ball that is 2' past the hole. Once again, ask yourself the same three questions: Did your aim work for that speed? Did the balls hold their line? Were you able to hit 3 balls at that speed? Now finish by hitting 3 balls at the speed that puts them at the 3rd ball or 3 feet past the hole. Ask yourself the same 3 questions.
6. If you continued to use the aim stick on all putts, how did the different speeds affect your putt's chances to drop in the hole? Go through the same challenge, but this time, adjust your aim for each speed.
7. Decide which speed is best for the hole holding the ball. In other words, a putt that is traveling 3 feet past will go in only if it hits the cup right in the middle, while a putt hit at the speed to be a foot past will catch the hole toward the edges, not just in the center.
8. Finally, after you decide which distance past is your optimal distance (probably between 1' and 2'), lay an aiming stick down behind the hole and make sure that all putts would be there if they didn't fall into the hole.
This might make sense to do with a tee in the ground instead of using the hole. With a tee, you will get good feedback on speed on almost every putt. However, I think it's important that you understand the role the speed has on both holding your line and on catching a piece of the hole and dropping in. By using the cup, you're keeping it real.