Before answering your question, one should think about what we really refer to or want to refer to with the term ‘efficiency’, particularly in freediving. Despite some simplifications my approach to your question required a bit of a lengthy text, sorry about that. My take on it in brief: elite freedivers will cover depth with less energy expenditure (thus greater ‘overall’ efficiency) compared to those new to the sport, primarily due to more efficient technique (think of duck dive, finning, and turn) and hydrodynamic posture. Dry land activities to further increase this overall efficiency? Maybe, I think of working on your relaxation, technique (video analysis of a previous dive), and possibly strength training and dietary nitrate supplementation.
In a laboratory setting, ‘gross efficiency’ of cycling can easily be measured as the ratio of mechanical power output (Watt or J/s) over total energy expenditure (J/s). To measure isolated efficiency of the musculoskeletal system, i.e. ‘net efficiency’, the ratio of power output over [total energy expenditure minus resting energy expenditure] can be used. These measurements will give you a different value (net efficiency is higher than gross efficiency) hence be careful interpreting efficiency numbers without context. There exists other ratios as well, though gross efficiency is the most commonly used. Energy expenditure can be estimated based on indirect calorimetry (respiratory gas analysis), though note that exercise intensity should be low enough to exclude considerable anaerobic energy contribution.
These efficiency measures estimate the percentage of the total produced energy that is translated into external work. This is influenced by multiple components. Amongst others, the process efficiency of chemical energy production through substrate (glucose and fat) oxidation in the muscle, its translation into muscle contractile activity, and the translation of muscle contractile activity into mechanical power output (i.e., mechanical work output to generate a pedal stroke to propel the bike forward). Efficiency of myocellular energy production can be slightly improved by dietary nitrate (think of red beet root, lettuce) consumption. As a quick side note, also note that per molecule of oxygen, glucose oxidation provides more energy than fat oxidation. Gross and net efficiency can also be determined by the amount of muscle fibers you are recruiting for this cycling movement to occur. Are you only contracting the muscle fibers that are required for an efficient pedal stroke to occur, or are you also contracting other muscles/muscle fibers not contributing to this movement? As you mentioned, substantial scientific data indicates strength training to increase cycling (or running) efficiency. The underlying mechanism has not been elucidated yet, but hypotheses point to training-induced decrease in muscle fatigue (particularly type I fibers) and hence lower type II muscle fiber recruitment (which are less metabolically efficient), and improvement in stability of movement coordination.
Now taking it a bit further than ‘efficiency’ in its restricted meaning: the distance you will cover by providing a certain power output on the pedals of your bike is amongst others determined by rolling resistance and air resistance. How ‘efficient’ the generated power output translates in cycling ‘performance’ (distance covered) is thus determined by aerodynamics and hence your position on the bike which determines your frontal area.
Now let’s take this thought process to freediving for depth. In contrast to cycling, freediving requires a series of more complex movements: duck dive, finning, freefall, turn, finning, and finally a glide to the surface. As in cycling, we think about the efficiency of cellular energy production and efficient muscle recruitment (not tensing muscles that are not contributing to the action) to, for instance, displace a given amount of water by a finning movement. Then there is the technique of your finning (or duck dive or turn) that comes to play; are you efficiently pushing the water away in the right direction (distally) to propel your body forward? And of course, very important, the hydrodynamics, determining the distance that you will cover with a given displacement of water by finning as well as determining the speed of freefall induced by gravity forces. Are you as hydrodynamic as possible, or is, for example, your elbow of the arm with which you pinch your nose to equalize too lateral from your body instead of close to your chest? What about the position of the lower body, the fins, etc. The latter all influencing the ‘frontal area’, which in this case does not refer to the area covered in a frame from a picture looking direct at you (cycling), but from a picture taken from above your head. Besides the energy produced to propel you forward, in freediving also the basal energy production plays a significant role in your overall performance, therefore making gross efficiency a more interesting parameter than net efficiency in freediving. This is why performance declines when cold, shivering in essence constitutes of inefficient muscle contractions not generating power output/mechanical work but only heat.
Could we measure ‘overall’ efficiency (here referring to energy production + distance covered) in freediving? As there is considerable anaerobic energy production during freediving, collecting the air from the lungs upon surfacing for indirect calorimetry would not be valid I am afraid (at least not without a good strategy to estimate the anaerobic energy production). In practice, max depth performance without blacking out (if hypoxia would be the limiting factor, that is) already gives you quite an indication, doesn’t it? And for submax performances, SpO2 (are some oximeters waterproof already?) and possibly capillary lactate measures can provide you some good indications as well – but then again, not sure whether there would be a need for this in practice. However, if waterproof oximeters would exist (measuring at the earlobe), it would be interesting to play around with different strategies regarding food intake, weights, the amount of finning kicks prior to freefall, recovery breaths, etc. and evaluate to effect on oxygen saturation.
So to come back to your question: I think improvements in hydrodynamics, technical execution of your duck dive, finning, and turn, and relaxation by far outweigh modest improvements in isolated efficiency of the musculoskeletal system. And then of course we have other parameters such as oxygen storage capacity, capacity to equalize, sensitivity to CO2, and flexibility that may determine your max depth performance…
