Muscular strength is a measure of the maximal amount of force that a muscle can produce in one contraction. Muscular strength is muscle or muscular group as well as movement specific and must be measured and accounted for using a variety of testing that should be specific to the desired performance. Muscular strength increases with an increase in muscle cross-sectional area and with an increase in the bodies ability to activate all the neurons (nerves) that go to the specific muscle so as to contract the entire muscle and not just a section of it.
Muscular strength relates to movement efficiency because a greater strength means less “effort” is needed in order to produce particular movements and to produce a given amount of force. For example, a stronger person will find it easier to lift an 80 Kg barbell than a weaker person, even if they both can lift it. This rate of perceived effort correlated highly to fatigue, which can clearly affect performance, as technique becomes poorer. Furthermore, a stronger person can focus more on their technique in order to produce the same force or power than a weaker person. this helps in sports such as cricket, baseball, or golf, where the distance a ball is hit can have a great impact on the performance. An athlete with greater muscular strength will be able to hit the ball further, with a lower effort level and greater focus being given to technique.
Another way that strength relates to movement efficiency is that it helps to improve posture, and can help increase the biomechanical efficiency of the bodies movements, especially through stabilisation. For example, 100 m sprinters often work very hard on developing their core strength (abdominals and lower back) in order to stabilise their torso when sprinting to increase their force output and maintain better streamline. This then improves their performance.
Measuring muscular strength through 1RM testing, dynamometers, and other devices (see here) can help to predict performance, as long as the testing done is specific to the sport. For example, it would be helpful to do a 1RM test for the clean and jerk for a weightlifter or to do an internal rotation force est using a dynamometer for an arm wrestler. However, as the sport becomes more complex and varied the testing will not be as reliable a predictor. So, for example, if strength testing was done for rugby league it would not necessarily predict performance, as many other variables are involved in such performances. Even if you were only using the test to predict the effectiveness of tackling, as more than muscular strength is required to perform such skills in competition.