...for why tape measure results slow down the longer you train, and why it's no big deal
I have a theory about our best friend, “The Law of Diminishing Returns” that just may take all the fun out of falling into despair over Mother Nature’s tendency to reward you with slower and slower growth, the longer you work out. I’ve arrived at an epiphany regarding diminishing returns, and it came to me in the elegant simplicity of rudimentary geometry. Come, grab a cup of coffee, or your favorite protein shake, and let us geek:
All theories start with a premise, and mine is no different. The premise of my theory is that all muscle growth can be quantified in terms of
increasing the cross-sectional area of any given muscle –or, more generically, an entire limb. The actual mechanics of muscle growth is not really critical to understand. Yes, muscle fibers grow in length, and through stretching, we can lengthen tendons and ligaments, but 99.9% of us measure muscle growth with a tape measure. In doing so, we are essentially looking for increases in the
circumferential measurement of a muscle belly or bellies. People don’t measure the length of their biceps/triceps –they measure the girth. I’m going to completely disregard the concept of tracking lean mass increases for this exercise, because this method is not subject to the kind of false interpretation we all assign to tape measure results (and it would render this entire thesis moot; for those of you looking for an excuse to tune out, it can be found in your bathroom scale and skinfold calipers). Either your lean mass is going up consistently or it is not.
On the other hand, it is not uncommon at all for people to work out for a period, take measurements, workout for another period of similar length (and hopefully greater intensity), and take more measurements, only to be disappointed that they did not elicit as much growth the second time around as they did the first. Invariably, with each visit to the tape measure, the results are not as potent as those which preceded it. For example, During my first six months of training, I might add two inches to my thigh measurements, but the second six months of training only yields 1 ½ inches. Between months 12 and 18, I might only add another inch. My knee-jerk reaction is to assume that my gains are slowing down. My knee-jerk reaction is wrong.
At this point, the seasoned bodybuilders are thinking, “just go by lean mass increases, the tape measure can be tricked by creatine bloating, bodyfat reduction/addition, water retention, the phases of the moon, etc.” Again, this is true –if you are consistently gaining lean mass, then that is far better proof that you are growing than any tape measure will proffer. But still, we obsess over tape measure results. Needlessly, I might add, and here’s why:
As a muscle grows (ostensibly after being scared into growing by lots of mean, unforgiving trips to the gym), it becomes thicker. Whether by addition of new muscle fibers, or by increasing the size of existing muscle fibers, or by converting satellite cells to contractile tissue is –as I have already pointed out- not really important. What matters is that the growth can be expressed as an
increase in cross-sectional area. In a perfect world, this increase (and here’s where the proverbial “rubber” of my theory meets the practical “road”) would be constant. Under ideal circumstances (assuming every conceivable training, dietary, genetic, and recuperative variable were met
perfectly), one should be able to continue adding muscle fibers and increasing the cross-sectional area of a muscle in steady, constant amounts. The first six months of training swelled the muscle with 1 square inch of new fiber (or whatever), the second six months added another square inch, and the third and all future six month intervals would also add 1 square inch. Of course, nothing like this happens in reality –there is an efficiency value to be considered as well. But let’s not get ahead of ourselves. For now, assume that you lived in this perfect world, where you could continuously add the same amount of muscle fiber (or whatever) repeatedly, interval after interval. Armed with this physiological fact, you would be justified in claiming that you are growing at a constant rate. But the tape measure would say otherwise.
Because the tape measure is a circumferential value, and linear additions to cross-sectional area
do not translate to linear circumferential increases. Now for the geometry that proves it. We know that Circumference=Pi times Diameter. We also know that the area of a circle (I know limbs are not perfectly cylindrical –indulge me) is equal to Pi times the square of the radius. Let’s put a hypothetical muscle though some “perfect” growth and see what happens:
If you start with a 14 inch bicep, you can derive the cross-sectional area fairly easily by dividing by Pi (to get the diameter), then dividing the result by 2 (to get the radius), then squaring the result and multiplying again by Pi.
A 14” biceps has approximately 15.6 square inches of cross-sectional area. Now let’s do six months of alternate DB curls, barbell curls, and chinups. At the end of this six months, you hit the tape measure and are delighted to be the proud owner of 15” biceps. First of all, congratulations on being such a mass monster. Let’s run the numbers again.
Your new 15” biceps has approximately 17.9 square inches of cross-sectional area. In other words, you added 2.3 square inches to the cross-sectional area of your biceps. Those of you geeking along with me (and skipping ahead) can already see that another six months, and another 2.3 square inches of growth will not yield another beautiful inch on the tape measure.
Six months have passed, and you managed to elicit exactly the same amount of muscle fiber synthesis as you did during the first six months. You’re hoping for another inch on the tape measure, but it just isn’t there. Because adding another 2.3 square inches to your previous 17.9,
your biceps now have approximately 20.2 square inches of cross-sectional area, which translates back to 15.9 inches circumference –a tenth of an inch less tape measure growth than your first six months.
HORRORS!
Just for kicks, another six months of “perfect” growth will get those guns up to
22.25 square inches of cross-sectional area, yielding 16.8 inches on the tape measure. Again, this latest six months of punishing yourself in the gym has rewarded you with little more than ¾ of an inch of growth –almost a quarter inch less than the very same amount of growth gave you after the first six months.
Now let’s complicate things by taking away the perfect linear gains. In reality, even if you are hitting on all six cylinders, meeting every diet, training, and recuperation challenge to the best of your abilities, your body will still respond with less growth activity than it did at the beginning. I call this the efficiency facto. All things being ideal, most people are only likely to reproduce 75% of the growth they accomplished in the previous six months –and they have to bust their azz tirelessly to make that happen. If there were no intervening efficiency factor eroding our ability to gain muscle, we would all be Ronnie Coleman. It would only be a matter of time, and persistence. But reality dictates that a guy starting with 11” biceps is never going to build those things up to Mr. Olympia proportions without steroids. It simply does not happen. So if a person’s growth response trajectory already has a built-in decay, adding the corrosive effects of less-than-perfect efficiency amplifies that curve. Let’s apply the efficiency curve to our hypothetical muscle above, and see what we would get from two years of training in the real world:
Start:
14 in biceps = 15.6 sq in area
Six Months:
15 in biceps = 17.9 sq in area (2.3 sq in gained)
Twelve Months: 17.9 + (75% of 2.3) = 19.6 sq in =
15.7 in biceps Eighteen Months: 19.6 + (75% of 1.7) = 20.9 sq in =
16.2 in biceps Twenty-four Months: 20.9 + (75% of 1.3) = 21.9 sq in =
16.6 in biceps.
The tape measure increases for this two-year growth period (assuming 75% efficiency, which is probably ridiculously generous) would be: 1 inch, .7 inches, .5 inches, and .4 inches respectively. If this individual were to keep training at full-tilt, never allowing the workouts to become routine, and acing
everything to the best of their abilities, at 75% efficiency, their gains would eventually grind to a perceptible halt (after 4.5 years, to be exact), and they would plateau at
17.5 inch biceps.
The Law of Diminishing Returns expressed in simple mathematics. Using this foundation, one can easily predict the kind of growth that is possible for any given individual. There are only two variables to consider: initial growth response (assuming your body responded at maximum growth potential), and your individual growth efficiency factor (which is eroded by genetics, slacking off in the gym, bad dietary habits, lack of recuperation, overtraining, how long you spend ogling Ros’ avatar, and a million other influences, the mitigation of which comprises the great sport of bodybuilding). That, of course, renders this an absolutely dismal guessing game, no more clearly defined than before we started, but with an important lesson to take away in the process, and that lesson is this:
Even if you could maintain perfect, linear muscle growth from one measurement period to the next, with 100% efficiency, it is physically, mathematically impossible to produce constant, linear increases in tape measure results. If you do manage to elicit a bigger change on the tape measure later during your training than you did at the beginning, that is more likely because you weren’t really growing at your maximum potential at the beginning.
So stop beating yourself up over diminishing tape measure results (what? It’s just me? Oh, okay. Then don’t start). Nothing you do –legally- will help you stretch the tape measure the same amount each and every time you take measurements.
If that doesn't send you rushing to the store for a good bathroom scale and a skinfold caliper, I don't know what will
