The tempo of the back-and-thru swing sets the size, as Tempo-Slow has a Large backstroke compared to Tempo-Fast with a Short stroke, but both strokes can generate exactly the same FORCE for one same distance of roll. The brain instinctively can produce the exact same distance roll with two different tempoes. So there is a certain range of tempo where strokes can produce the same distance while the sizes of the strokes change with each change in tempo: there is always a combination of Tempo-1 plus Size-1 that matches the force of Tempo-2 plus Size-2. A slow tempo with a large stroke can exactly equal the impact velocity at the bottom and the force of a faster tempo and a shorter stroke.
You can experience this directly by first noting that a given stick of a fixed length "naturally gets swung by gravity of our big ROCK planet" with only one always-the-same tempo of total timing from top to top of swing, no matter whether the SIZE of the stroke is short or large. Tempo does not change even though the size of stroke changes, at least not when the pendulum is swinging solely due to gravity back and forth. The LENGTH of the pendulum forever sets only one TEMPO for a gravity pendulum, and all SIZE strokes by gravity with that one-length pendulum always take the same total time from top to top, and so have the same TEMPO even when the SIZES of strokes go from short to longer to longest. What changes with the SIZE changes is the pendulum's velocity right at the bottom of the stroke. Longer swings get going faster before reaching the bottom, so longer equals faster, and faster impacts at the bottom equal farther rolls.
The brain knows this and knows that given one's familiar putter head mass, the FORCE of impact and the distance depends solely upon the size of the stroke (which sets the speed of impact of the mass of the putter head, as "force" is mass times its speed at impact).
Specifically, the brain knows with exceedingly fine precision exactly how long your arms swing in gravity, and if you swing a putter a little bit, the brain then also knows how arms-plus-putter swings in gravity also. By that, I mean that the brain knows from the tempo that goes with the length of the swinging thing (arms or legs or arms-plus-putter unit) exactly WHEN the putter head is supposed to coast to the top of the backstroke and WHEN the putter head reaches the exact bottom of the pendular arc and WHEN the putter head coasts to the top of the thru-stroke; AND the brain also knows each different possible SIZE backstroke and exactly what velocity of the putter head right at the bottom of the stroke that size will result in (and there is a complete dial of backstroke SIZES and each of their impact velocities at the bottom , all known precisely by the brain / body but not the mind); AND the body knows exactly how much mass is in the arms plus putter and hence exactly how much impulse is needed to toss the whole exactly to a given SIZE backstroke so the putter head coasts to the top of the pre-determined backstroke SIZE with great exactitude, the same way a tennis player can always toss his service ball to exactly the chosen height. The body is wired to all of this knowledge, and yet the mind is utterly uninvolved and ignorant about the existence of this knowledge and in fact does not know the details that the body knows and would have to take a class in college physics and make at least a B in the class and then work out all the measurements and formulae with a calculator in order to know what the body is simply wired to always get correct.
If the tempo stays the same, one size backstroke of a pendular stroke sends the ball only one same distance over and over, and an increase in size is the ONLY way to make the force greater (by making the impact speed greater). But if you change to another tempo, one the golfer handles more quickly than the OLD ROCK would do, the SIZE of stroke still sets the force and a quicker tempo can generate the same force as a slower tempo but will set a shorter size compared to the slower tempo's larger size. The brain knows nonconsciously all about what tempo and what size backstroke will generate the peak speed at the bottom, and can hit exactly the same peak speeds using different tempoes and diferent size strokes.
This means that the brain simply gets a short memo in advance about what the tempo will be for this specific putt. While it's usually best not to be switching the channels on the tempo very often, it certainly can be done, especially if the golfer has some basic familiarity with the odd tempo and if the golfer does not stray too far from the base casual (slow) tempo of normal relaxed motion. The range of increase of tempo is limited before the stroke gets too violent and touch suffers, so a general idea that the range of tempo should stay within about 25% of the beginning base tempo seems about right. Don't double the relaxed tempo; just step it up a little at a time but not more than about half way to doubled.
Since the brain is first about "safety" when the body moves towards a target object / barrier in space (and only then is the brain about success), it takes the tempo to be used for the stroke in light of the available distance in space "only to and not too violently past" the object (reference distance -- i.e., the hole) and limits the SIZE of the backstroke to insure safety. This limit coincides quite nicely with 100% of the size that gets the ball all the way to the hole, and thereby avoids spastic overshoot without causing missing short. The point is to preclude 105% too-big a backstroke size.
The brain is trained by the world over years to wire the body up so that the wiring connects the space with the limit -- it's completely non-mental and only physical. All animals that move have to have this body trained to the limits of the world, or else they get hurt and fail too often to survive.
This all means that with "whatever" reasonable tempo to be used, the brain still sets the size of the backstroke for the space at 100%. A slow tempo means that 100% is "big" while a fast tempo means that 100% is "short". Who cares? The body just rhythmically goes back with one dose of the chosen tempo to 100% of the appropriate size, and once that part of the swing is attained at the top of the backstroke, then repeating this same chosen tempo going forward from top of backstroke thru impact and on to top of follow-thru simply generates the anticipated putter head peak speed at impact that the brain intended by limiting the size where it did. The backstroke size has built into it the impact speed, as the brain assumes the golfer will use the same pendular swing-swing tempo both directions for a rhythmical action.
This is how the brain manages a "swing back and swing thru" action: the tempo sets the size and the "rhythm" of the back-and-thru swing is simply two doses of the same chosen tempo. The "rhythm" combined with two doses of tempo "gets and spends" the safe-successful backstroke force.
Fundamentally, then, the intentionality to move nicely all the way to a space destination (to and not too far thru) is what selects the backstroke limit / size given the chosen tempo. The intentionality to the space accurately perceived is what activates the trained-in wiring connecting to the appropriate stroke-size limit and hence impact force that is enough but not too much.
This "knowledge" of the stroke size is embodied, and simply results from the intentionality to move all the way to but not too far past the given space. It's automatic, takes less than 0.25 second to express itself, persists as long as the golfer remains intentfull to the space, and does not require any special subjective sense of "feel" or practice strokes or even much prior experience with putting on greens.
Once the brain has set the limit, the RHYTHM of the back-and-thru natural and instinctive swinging merely "gets and spends" the force of the stroke. "Intend" or "determine" to go all the way but not too far past the space, then make a rhythmic back-and-thru of two doses of the same tempo. One potato back, one potato thru to finish. How fast this happens is the tempo.
Back to reality, then. On short putts, you can speed up the tempo somewhat above the base relaxed slow tempo, and at all step-ups in tempo the same equal back-and-thru rhythm not only never changes, but is actually always required to "get and spend" the backstroke sizes set by the brain's (more properly, the nonconscious brain wiring of the BODY itself, not the "mind" of those old antiquated "sports psychs") reaction to the space given the chosen tempo.
Any stroke that -- when using the relaxed tempo -- requires a size that does not extend past the rear foot in the stance will feel too slow and perhaps too large for the short space (usually inside 8 feet of so). Because the tempo is OPTIONAL but the rhythm for any tempo is MANDATORY for a swing-swing instinctive stroke action, the golfer has permission to speed up the tempo, shorten the stroke, and make the action moderately more violent requiring moderately more muscle tone and form to control the more robust forces of swinging the arms and putter faster.
That's usually a welcomed increase in muscle tone, as this replaces the "too slow too loose too large" sensation that accompanies the too-slow and short stroke inside the stance with more deliberate form and felt-movement "control".
But even so, don't take the bait that a faster tempo should call for any "deceleration" or any faltering in the basic swing-swing RHYTHM. Stick to the rhythm, especially when upping the tempo, so the thru-stroke doesn't falter out of some "mind-sponsored" fear that the faster tempo with cause too much force. It won't. The intentionality to space still limits the size and force, so the faster tempo doesn't cause too big of a (spastic) backstroke.
You have to believe that, have experience with that, and not mistake that when it comes to the top of the backstroke and any question arises in the "mind" about WHETHER to simply repeat the same tempo going forward. The "mind" after all is completely ignorant and disbelieving about the body's being intelligently trained to the world's physics, and so rather stupidly believe that only the "mind" is capable of managing something as sensitive as "touch". But sticking to the rhythm in finishing the stroke -- whatever tempo is used to start the stroke must be the only tempo for the thru-stroke --is the ONLY POSSIBLE TIMING that spends the force of the size-limited backstroke, and anything cautious or tentative is a "choke stroke."
So, forget tempo and think "smooth rhythm back and thru", whatever the reasonable tempo.
And then there's this: once you're inside 10 feet or so, with the possible exception of steep slope and slick green speed from above the hole, it is practically impossible to face a situation where you really care much about going too far past the hole. Don't worry about that; worry about not getting the ball all the way to the front lip of the hole -- that would be the same as not even taking your shot, but just adding one to the scorecard for the heck of it.
And when the "touch" inside 10 feet is in fact a dicey problem, part of the issue can usually be helped out by some intelligent use of the entire hole when deciding the line, and then tightly defining the permissible delivery speed to the hole. That done, dicey putts for touch end up at the time of executing the stroke requiring a nice smooth rhythmic action thru impact. Short putts often have a "straight start" issue that masquerades as a touch issue: some fault in actually getting the ball started dead straight on the chosen line of the read spoils the putt, not really something about tempo or rhythm for touch, even though many golfers misinterpret a little poor line control as being a touch-caused problem in the putt.
Correctly identifying the real problems of putting is a problem due to the somewhat jumbled confusion about what got done properly and what causes what that plagues the vast majority of golfers. But clarifying line and distance control helps the golfer attain much greater consistency and success, and "outs" the issues of skill or lack of skill fitting the consistent stroke and touch to the surface read and aim. Golfers who stroke straight where aimed with the intended delivery pace will become much better readers of putts more quickly than others.
So, don't sweat the tempo so much (inside a given range). Just form the intentionality to the space and make a smooth rhythm and let the body's impulse in the backstroke toss the putter as far back as the body wants to toss it, and then finish the forward stroke by repeating the same tempo just used in the backstroke, as that is the back-thru rhythm. Then you will "feel" more in control.
Now that you're free to speed up a bit, focus on what tempo helps you REALLY REALLY start the ball EXACTLY STRAIGHT where the putter face was aimed according to the read. Ultimately, putting is both stroking down that line of putter face aim plus the tempo-rhythm impact speed of touch. So the integration of the tempo-rhythm for touch with the biomechanics of square, online impact that sends the ball exactly where the putter face was aimed is always the goal -- both together, line and touch.
And helpfully, a nice "back-and-thru rhythm with a well-familiar tempo" actually contributes greatly to making on-line impact, since with a clear timing pattern the golfer really knows very well what is supposed to be where when. The putter head is always coasting to the top of the backstroke always at the same moment in the tempo, always reaches the impact-point at the bottom and middle of the forward stroke on exactly the same moment, and then coasts to the top of the follow-thru at the end of the tempo, no surprises anywhere or "anywhen."
But, hey, inside the range where "too far past" is not a big deal, get the LINE dead straight anyway you can. I like doing that with a "smooth rhythm", but you can play the game off the sheet music quite a bit if you feel like it.
Putting Coach and Theorist