Dear LT,
Great question! Let's sink in and answer it.
The short answer is: "Only one of them." The somewhat abbreviated answer is: There is only one reality, and humans sometimes misperceive it due to ambiguity of the sense perceptions, and neither one of the two perspectives is always the better or the best for sorting this reality out. It really depends upon using your perceptual senses to full and best advantage in this situation.
The perception of slope on a green depends upon a number of factors, so let's air them out and see what's going on.
If you perceive left as high from ball-down-the-line perspective but right as low from behind-the-hole perspective, then you also don't know which direction the fall line runs "uphill" thru the cup and / or whether the ball is a higher or lower elevation than the hole.
Assuming the green surface is uniformly flat-but-tilted between the ball and hole so there is no intervening undulation that would make a multiple breaking path, then correctly identifying which direction runs uphill thru the cup necessarily sorts out for you left-right along the line as high or low, regardless of perspective.
Unless your putt is dead straight, and hence either straight uphill from the 6 o'clock position or straight downhill from the 12 o'clock position, your ball is positioned either on the 3 o'clock side of the hole somewhere between 12 and 6 or on the 9 o'clock side of the hole somewhere between 6 and 12 in the clockwise direction around the hole. Uphill is on the side of your ball closest to 12 o'clock. Simple. On the 3 o'clock half of the clockface (east), 12 (north) is always to the right facing the hole from behind the ball and to the left facing the ball from behind the hole. On the 9 o'clock side (west), 12 (north) is always to the left from behind the ball facing the hole and to the right from behind the hole facing the ball.
So let's step back from the surface of ONLY the putt path and look at the broader picture of what is uphill and downhill in the general terrain and then return to ONLY the specific surface involved in the putt with the general terrain's overall slope direction in mind.
FACTOR 1: Pay attention to the direct line from ball to hole, as this helps you to decide clearly and unambiguously whether left or right is higher or lower. This "direct line" from ball to hole neatly divides the universe into high side and low side and connects the putt surface to the wider terrain.
FACTOR 2: What is the overall lay of the land in which the green as a whole is situated? This overall perception serves as the beginning "frame" for how you perceive the specific surface of the putt.
If the local highest ridge or hill is off to your right when facing the hole from behind the ball, and the local low area (creek, pond, etc.) is off to your left, then the general lay of the land runs from right downhill to left.
FACTOR 3: Does the green as a whole differ from the general slope of the terrain in which it sits? This involves you perceiving the general slope of the green as a whole and then comparing it to the perception of the terrain as a whole (Factor 2). Where is the highest fringe of the green and where is the lowest fringe of the green, in terms of elevation above sea level?
In order to perceive this accurately, you need good posture and a sense of the body level in gravity with respect to the zenith of the sky and the horizon of gravity-level. Good putters have good posture. Period. This perception really is an internal matter of how your body relates to gravity. Are you "balanced" in gravity on your feet and with your erect skeletal posture? Do you have a good sense of what is the highest point in the inverted bowl of the sky directly overhead on the line from the center of the earth thru your body straight up to the zenith of the heavens? Can you use this vertical posture of body including head and eyes to sense what is level horizontally in gravity, notwithstanding the tendency of the local environment and its oddities to fool you about that reality?
With good posture as described, you use the borders of your eyes and your inner ear sense of balance in gravity to check level horizontally. The corners of each eye make a line that seems level to you, not tilted in gravity in reference to the vertical line to the zenith. You feel in the neck and other body parts (shoulders, back, hips, knees, legs, feet) that your posture is balanced and not tilted.
FACTOR 4: Is the ball higher or lower than the elevation of the hole above sea level? or does it matter? It doesn't matter, as all this tells you is whether you are above or below the 3 or the 9, and not which side of the clockface you're on (east or west).
FACTOR 5: How do your left and right feet feel in the two perspectives? If your right foot feels higher when behind the ball, then when you move behind the hole the left foot needs to feel higher. "Higher" means the inner edge is bearing more weight than the outer edge, as the inner edge is downhill. This is actually only true when you aren't trying to make yourself stand vertically in gravity, and are instead standing up vertically off the slope. So you have to pay attention to which one you are doing. If you stand vertically in gravity against the slope, you will shift the weight to the uphill edges of your feet, sort of digging into the slope with that edge. So standing behind the ball facing the hole when standing against the slope into gravity-vertical, when the outer edge of the right foot bears most of the weight, then uphill is to the right. And when you change to looking from behind the hole to the ball, the outer edge of the left foot will then have to be the edge bearing most of the weight.
If the slope around the hole is mild, it is harder to "sense" uphill versus downhill when looking down at the green surface. This is mostly because you are trying to compare how "close" the surface looks to you at the hole when standing at the ball with how close the surface looks to you at the ball when standing behind the hole. Actually, it is even tougher, because you are trying to decide whether the ground to the right of the hole when standing behind the ball looks closer (or not) than the ground to the left of the hole, and then repeating this perceptual decision after moving to the new perspective behind the hole looking back to the ball, AND trying to recall the first set of perceptions and compare them to the second set of perceptions.
The consistency of your positioning and posture will matter quite a bit in trying to discern these subtle differences, just as a visual problem. For starters, you should stand the same distance behind the ball as you stand behind the hole. You should stand in both perspectives vertically into gravity regardless of the slope. You should tilt your head and eyes at the same angle more or less. And you should focus on the apparent closeness of the right versus left side of a line from ball to hole, either right at the ball or hole, or all along the dividing line. You can imagine the effect of not using these sorts of consistencies would have. For example, if you stand 5-10 feet behind the ball, your perception of higher / lower left / right at the hole will be from farther off than when you stand 2-4 feet behind the hole and look back at the ball. These differences will confuse you. If you stand with the slope at one perspective but against the slope vertical into gravity at the other perspective, you will reduce the signal comparing high and low left / right and standing with the slope will tend to make the downhill side look less downhill and more like the uphill side. If you squat behind the ball but stand behind the hole, you will get different perceptions.
Basically, if you get the fall line uphill direction right, and use the direct line from ball to hole to divide the universe into higher and lower, there won't be much room for ambiguity in the perceptions. You will have a broad sense of the local terrain, of the general slope of the green, and of the direction of the fall line thru the cup, all based upon good posture, visual orientation to level, the inner ear, and the feel of the feet against the surface slope.
This ambiguity usually only happens when the surface slope at the hole is mild, so the golfer does not get a loud and clear signal about the fall line or uphill / downhill thru the cup. When that is the case, step back to the wider terrain and start over with good posture and consistent employment of the senses in terms of posture and position, make a decision, satisfy yourself that the ambiguity from behind the ball and behind the hole is reduced or eliminated, and go with it.
Cheers!
Geoff Mangum
Putting Coach and Theorist
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