I usually don't like to get into specifics about in what order certain balls should be played. Not that it's not important because it is. But bad pattern play is often a by product of the way the table layout is viewed & analysed. I'll get back to that but as to the above; 4, 7, 14 is much preferable over 4, 14, 7. However, after the 1 you shot the 15 which in hindsight you think was the wrong shot. Actually it was the correct shot. What you did with the CB off of the 15 was bad but shooting the 15 at that point was definitely the best shot. You basically had five relatively easy stop shots to get close, perfect position on the break ball from there.
Go back & take a look. !5, 11, 4, 7, 14. Not much can go wrong. Each ball leads perfectly to the next with the correct angle & minimal CB movement. Maybe I'm nit picking a little because the pattern you described above is also connect the dots & is very workable. The only reason I like the 14 last over the 11 is because you really can't get a bad angle on the 14 to where you can't easily get on the 5. If you get a little off angle on the 11 ( particularly if you get too far above it ) then getting good on the 5 could be a problem.
Putting aside patterns, I'd be real interested in knowing what your thoughts were right from the beginning of that rack. From the beginning of the run actually. Going back to the 1st rack, after you broke the balls you had 3 very specific problem areas. In order of importance they were the 1, the ball on the left rail right below the side & the 4 on the right rail. A plan to deal with those areas needs to be developed before you even take your 1st shot. You shot 7 straight open, easy shots without doing anything to address those problems. Those open balls have to be used in ways that attack problem areas, as quickly as possible. Often this will entail shooting a shot or trying for position that you're maybe not comfortable with. You mentioned maybe a lack of confidence sometimes may cause you to pass up what you think is the right shot. Shoot it anyway. That's how the uncomfortable becomes comfortable, doing it over & over. Think back to when you 1st started playing pool. Always trying something new & trying to master it. If that process stops happening then stagnation sets in.
Good Luck