Great question! Comes up all the time and I have trouble getting golfers to focus on this, as this really could save lots of strokes. YE Yang basically shot himself in the foot several time because he doesn't know about all this. Elk made a big boo-boo in the 2010 PGA Championship on the final hole -- same reason. Golfers need to figure this one out!
Part of it is setup / biomechanics, and part of it is how to operate the body, and part of it is cognitive know-how.
When putting up a steep slope, the body is most often on an uphill slope, and that tilts the shoulder frame, lead-side higher. The body relates to vertical in gravity, and this means the brain considers the lead shoulder "high" in relation to the other shoulder. This has the unfortunate effect in the stroke biomechanics of a "quit" in the thru-stroke. Basically, the stroke is SUPPOSED to go FURTHER / HIGHER than wherever the lead shoulder starts out, but in this particular uphill-slope setup, the brain gets back to the original height of the lead shoulder and says "higher than the other shoulder, so let's just stop here." In fact, the brain needs to be overruled about gravity setup, and forced to pretend the lead shoulder is the same level as the other shoulder AND in the forward stroke the lead shoulder MUST continue higher than wherever it started out. So, here's the trick: take stock of the initial position of the lead shoulder in these uphill-slope setups and say to yourself, okay, this stroke has to move the shoulder 1-2 or more inches HIGHER than this starting position. The "old lore" in golf history is that the golfer in this situation needs to "chase the putt a bit uphill." Great verbal garbage, those old guys!!
Operating the Body
This means how to INTEND to the far target uphill. You have to intend NOT TO GO TOO FAR PAST the target even though it is far uphill. The body needs this, even if it confuses the mind about how things work. The mind basically has nothing to do wit it, and if the mind is confused about how the BODY operates, that's tough sh... The forming of this INTENTIONALITY is accompanied by some tension, determination, carefulness, etc., all of which is a bit "anal retentive," but it's a necessary step or phase that "tunes the body" to the space correctly and LIMITS the backstroke so you WON'T go too far past. That's peachy for the body, since once the load / force is limited like this, EVERYTHING CHANGES to relax, get rhythm, do a dance, and "get the full tempo backstroke size achieved" or you will surely be SHORT. It is inherent in the "limited force / size" the body chooses that there is simply no EXTRA force to allow you to go too far past the target. Typically, in keeping you safe form spastic movement and collision injury, the brain / body will "load" about 102-103% of the necessary force level to make sure you aren't SHORT, and arrive with a "soft landing" little extra, the way the hand securely takes hold of the door knob with a very mild collision and then grasping. But the brain / body will never give you enough force / size to cause injury (e.g., 108% or perhaps 113%), unless of course you have organic brain damage, suffer from spasticity, don't pay attention, or are drunk.
The mind is basically telling you to worry about stuff, and as I have been saying for years now, the MIND is about the stupidest spokesperson to address the issue of how the BODY works that you could possibly listen to, so ignore the mind and do the flippin' full-tempo BIG BACKSTROKE and then repeat the full tempo in the THRU-STROKE without the slightest hint of "quit" or deceleration slowing of the tempo timing, and also without any gassing or speeding up the tempo timing in the thru-stroke. If this "concerns" or "worries" your mind, then I repeat: ignore the fear and JUST USE THE FULL TEMPO TWICE back and thru.
Eventually you will learn that the "concerns" and "fears" have nothing to offer and that the tempo-rhythm is what the BODY insists you actually DO, no matter what you personally think or believe. It's just black and white: tune the body for force, then get and spend all the force, not less, and not more.
This always comes back to this question: Do you actually know what tempo and rhythm requires? Do you know your tempo? Do you have two swinging actions back and then thru? Does the backstroke tempo match the forward stroke tempo timing? Do you really not give a flip about how big the body makes the backstroke or do you "jump in" with your asinine mind's pitiful opinion on what's too big or too small or worrisome? Once you make the backstroke with tempo and the body forcve at the start of the backstroke "tosses" the arms and hands and putter into the tempo so that a "size" results, do you flippin' leave things alone and go ahead and use all the body gives you? Do you understand the physics of swinging things, in that the SIZE of the swing determines the velocity of impact, and that determines force and distance? If you get that straight, you will comprehend that the body force tuned to the space tosses the arms and hands and putter into the tempo so that the whole assembly coasts to a top of the swing under the retarding influence of gravity at a specific size based upon the energy of the toss back, and that the body knows in advance WHERE this will happen (that's why the force power is set at its level). Just toss the flippin' stroke back and stay out of it, but do so with some dancing musicality.
You will see the backstroke getting bigger, which is exactly the ONLY way to increase power without switching completely out of your normal tempo into something nutty and unpredictable and streaky and without structure in space. So, for heaven's sake, let the backstroke get bigger, and KEEP the usual back-and-thru smooth tempo and rhythm. That's where all the pay-dirt is hidden.
Once you get over the mind fear and stop messing up the sizing of the backstroke in tempo, you will be shocked to learn that the body never goes crazy past the target distance. That's the message of all neuroscience for movement over the past twenty plus years: "The Body is Trained by the World and Has Got Your Back and Won't Let Your Mind Hurt the Body." That's tuning to the space with concern and determination and carefulness. But once done, "The body's got your back" and you couldn't go too far past if you tried, no matter what the ignorant mind might fear. So quit fearing THAT and get onto the business of the full-sized stroke that actually uses all the limited body force and gets the ball all the way uphill to the target not any short AND not too far past either.
It helps to lay a club down behind the hole about 2 feet past the target cup to make sure you know the space properly, and then DON'T JUMP THE STICK, and instead BUMP AGAINST THE STICK.
As a matter of physics I have created a "conversion factor" about how much elevation change uphill translates into a level-equivalent putt. It works like this:
If the uphill putt tape measure from ball to hole is 50 feet, and the elevation change is 1.5 feet, that's a 3% grade and the ball not only has to have the energy for the 50 feet, but also needs energy to rise up off the planet into the air another 18 inches. If you took the 18" up energy and applied it to a level, not-uphill 50-foot putt, how far would that putt go?
Roughly speaking, the rule of thumb I came up with in the physics is for every 1" up, add 1 foot further for the level putt (details later).
Now, standing at the ball looking 50 feet away at a cup 18 inches higher in gravity than the ball, if you wanted to place a "virtual" target further past the actual hole, how far would it be? Answer: 18 feet further (1 foot for every 1" up). So the "level equivalent" putt is a 68-foot putt, but now it's definitely NOT uphill anymore (that will cause a double-cross that ACTUALLY goes 68 feet way past the cup). So you must PRETEND the putt is level and not uphill but is 68 feet long and then perform the neck / face turn to that "virtual" distance and watch your backstroke GROW BIGGER and get the size of the backstroke and the impact energy just right to go 50 feet to the actual hole. If you want to go all the way to the target uphill without the conversion, one way to do it is to notice that the green speed uphill is slower than the green speed normally registered, which is the speed over basically level surface. It's one way or the other, but not uphill with a virtual target further away AND over slower surface too.
This trick is really only appropriate for the situations you are describing: substantial elevation change and lengthy putt (which of course necessarily pair up in basic trigonometry with green slopes a bit limited in steepness).
So, KNOWING THIS, you won't fear the flippin' backstroke for a NEW reason. Basically, your mind won't shut the heck up and you as a golfer don't really believe the mind is all that messed up, when in fact it has NOTHING TO DO WITH THE BODY except mess up the educated, skilled, highly trained processes of the body tuning to space correctly and then using tempo-rhythm to get and spend the pre-determined force load.
Details for the physics of the conversion factor: A Stimpmeter raises a golf ball's bottom about 10-11 inches off the surface before the ball rolls out of the notch and accelerates to the end of the ramp, and the only factor that sets the off-ramp velocity is the release height of the ball, not the length of the ramp (see Galileo). So, if fortuitously, the ball happens to roll 10 to 11 FEET, then the Stimp green speed is said to be 10' or 11'. But for our purposes, it means that for every inch of elevation, the ball rolls "about" 1 foot. Okay, that's why it's a "rule of thmb" and not an anal-retentive calculation in a physics class. We're playing golf, not getting a grade. And the "rule of thumb" is WAY more than "good enough for government work" since all it's doing is satisfying and shutting out your crabby, juvenile delinquent jerk of a mind. Get rhythm, boy and send it smoothly ALL THE WAY.
Putting Coach and Theorist