The concept of accidental strength is based upon the notion that, as trainees, we can be unaware of weaknesses we possess. You may be diligently tracking your training and noting trends as they appear, but sometimes there can simply be unknown variables affecting your progression. Due to the fact that we cannot train every movement every time we train, and that the principle of training economy will dictate that we make use of the movements that we know will produce the results we desire, we have a tendency to stick with the same movements whenever we train. A powerlifter will bench, squat and deadlift, an Olympic lifter will do the clean and jerk and snatch, a strongman will drag and carry, etc.
In selecting certain movements to train, we are in fact doing so at the exclusion of other movements. This necessitates us to ask why it is that we chose not to do these movements. I present that there are two basic reasons to not do a movement, the first being that we know it does not benefit us, and the second being that we do not know if it benefits us. Arriving at the first conclusion necessitates experimentation, in that we must have attempted the movement with enough frequency/sincerity to know that, despite our best efforts, it is not helping our progress. Everyone is different and will have their own movements that do not work. For me, the best example I can think of is bent over rows, which, no matter how many times I have tried, simply do not help me get bigger or stronger.
In the case of the latter reason we are not trying something, we owe it to ourselves to attempt the movement in the hopes of achieving accidental strength. We may find that, despite the fact that one has a strong bench and overhead press, the incline press is a very weak movement for this person. They have never been in a position where they have needed to move weight in this fashion due to their strong horizontal and vertical pressing ability, and have been able to compensate with one or the other when the need arose. When forced into a less than ideal mechanical position, thus removing the lats ability to contribute, the weakness manifests itself, and in turn represents an opportunity to grow stronger. By strengthening a weakness in this less than ideal position, it allows one to display greater strength in an ideal position.
A secondary contributing factor to accidental strength is the reality that no person is a beginner, intermediate, or advanced lifter. I am moving away from these terms, and instead contending that one is a beginner, intermediate, or advanced trainee of specific lifts. What I am getting at is that, if a lifter has spent years training as a powerlifter, it is quite possible that they are an intermediate or advanced bencher, squatter, or deadlifter, but when you give them a strongman log to overhead press, they are in fact a beginner log presser. The ramifications of this reality is that one has a much greater potential to grow exponentially in this new lift compared to one they have mastered, due to the nature of “beginner gains” and rapid adaptation to a new stimulus. This advanced bencher may need to spend years adding an extra 5lbs to their bench, but they can add 20lbs to their log press in a matter of months, if not weeks, which will have significant carryover to their ability to press in general.
Some exceptions may apply
To take a personal example here, as I have noted previously, I am training for a strongman competition. Despite spending years training the powerlifts, and having a fair degree of success with my best comp lifts at 181 as 502/336/601 (and current gym lifts of 545 squat for a double, 340 bench and 620 deadlift for a double at 200lbs), I have never trained any of the strongman lifts. One of the events I am training for is the axel clean and press. The first time I tried to find the maximal amount of weight I could axel clean, I got as high as 190lbs. I could not get anything higher than that to my chest, despite my best efforts. The next time I trained the lift (2 days later), I managed to get 210lbs to my chest. That is a 20lb PR in 2 days time, simply because I got better at the movement. Adding 20lbs to my max deadlift takes about 8 months. Meanwhile, my ability to clean bigger weights has a positive impact on my ability to generate power, which is a positive quality in most athletic and strength endeavors.
Pursuing accidental strength is a surprisingly easy task. When I structure a training program, the first lift of the day is the lift I am intentionally training that day for the sake of growing stronger (IE: the squat, bench, deadlift, or overhead press). This means that the first movement of the day is both a training movement and a measuring device. I train this movement to grow stronger, and if I am stronger on this movement than I was last week, that means I am training correctly. The second movement I perform is a supplemental exercise that I train for heavy volume with the intent of making that first movement stronger. If this was the day I benched, then this supplemental exercise could be 5x10 benching, overhead pressing, incline pressing, etc. This is a great place to put into practice the pursuit of accidental strength. Instead of sticking with the tried and true, use a movement that you haven’t used before. If you always bench medium grip, go close. If you’ve never used dumbbells, use them. Use chains, use bands, go crazy. Give it an honest effort, not just 1 training session. If, after a month, your first lift has stalled or regressed, do something else. If, however, your primary lift continues to increase while you train this supplemental lift, congratulations, you have grown accidentally strong.