Short game drills for a quick improvement?
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I would start with targeting your full swing and worry about short game and putting later. Both @saevel25 and myself have given you a pile of homework, start there. There are no magic bullets and quick fixes, trust me, I would have found them by now!
Attacking everything at once will impede your progress and looking for quick fixes won't get you anywhere. Take the links we have posted and GET TO WORK! LOL.
A fun way to practice short game is to play with one ball. Toss the ball off a practice green then try to get up and down to a specific flag. I will usually do this after full swing work at a range. I try not to repeat the same shots either. I will work my way around the green so I get up and down hill chips and pitches and putts.
Honestly, if Jacob Smith is a 27 hdcp, he's losing MOST of his strokes on and around the green. Boogielicous' advice is pretty sound. The other thing I would recommend is a lot of putting practice in the 2' - 5' range. A 27 hdcp player likely misses more than half of these during a round.
Chip off the green with a goal of getting down from anywhere or any lie in 3 shots. One chip and two putts. Sometimes you might get lucky and get up and down in only 2. Other times, you'll blade it across the green and take 4 or more to get it in the cup. Keep practicing, around the greens is the easiest and quickest way to reduce score.
One more tip: When my wife started playing 4-5 seasons ago, we started with a SW around the greens. I gave her nice uphill lies to chip from. We worked on the hands forward, weight forward and ball-first contact. When they started 'popping' off those lies, she understood a very basic theory of golf: Ball first contact with a descending blow makes ball go UP!
"At minimum" one day. Not trying to be a smart alec but everybody is different. I see plenty of people that have short game mechanics so poor that it would take quite a while of practicing the "right way" to change those mechanics for them to ever be any good at it.
Other people are halfway decent with mechanics that would at least work for certain types of short game shots early on, but they make terrible decisions on what kind of shot to hit and end up turning what should have been a fairly low difficulty shot into a high difficulty shot. Takes them quite a while to figure out that they are not Phil Mickelson.
When I hear somebody talk very often about flubbing a 60 degree wedge I shake my head.
That said, EJ and the guys are right. I never saw a high handicap player that didn't have a whole lot of improving to do on full shots.
I loved this drill from tom watson short game book :
putt à tee 2 yards into the green and pitch to it with everything from a sw to 7 iron or so. dont aim a flag, just look at the ball behave.
I did this drill from 5 yards from the tee, then 10, then 15, then 20 taking out progressively long clubs that didn't fit the end of the green.
The best about this drill is to find that no matter what club, the BS is the same for each yardage you need to carry the ball. only the run changes. It really gets chipping easy.
It will take time, but make a game of it and have fun practicing. Check out these videos to help.
My take on short game is it's a case of 'been there, done that.' This means practice, (and lots of it) from a bunch of different situations. Chipping from the fringe to targets of varying length and with different clubs is good practice. Using your SW from a bunch of different lies (both tight lies and from the rough) is good practice.
And then when you start hitting greens from the fairway, you might find yourself with 30'+ putts all the time. Then, you really need to practice that shot, too.
It's all about practicing different shots so when a similar shot presents itself during a round, you recognize it as something you've practiced a bunch of times and can pull it off with reasonable accuracy.