# Scientific paper by R.Tobin on steroid use

Im doing a review of a scientific paper about steroid use in baseball and its effects, but am struggling to understand a section.
(paper is "On the potential of a chemical Bonds: Possible effects of steroids on home run production in baseball")

"It is therefore reasonable to assume
that a 10% increase in an athlete’s muscle mass will
also increase the force exerted by those muscles by about
10%. The increases in maximum voluntary force found in the
weight-lifting study of Ref. 18 were even greater, possibly
because of steroid-induced behavioral effects that led to
more intense effort.18 In view of those results, my assumption
that the increase in force is proportional to the increase
in muscle mass is conservative. If we assume that the length
and technique of a batter’s swing remain the same, it follows
that the work done by muscles on the bat, and therefore the
kinetic energy of the bat, can also be increased by about 10%
through the use of steroids. If the bat’s mass is constant, the
speed of the bat as it strikes the pitched ball will be roughly
5% higher than without the use of steroids. Because we are
making rather rough estimates here, it will not make much
difference if the batter uses a slightly heavier or lighter bat."

The problem is where does he come up with this 5%? is it a simple formula? or is it in reference to the muscle increase without steroids - which is 3%, still leaving an unaccounted for 2%

$$1.05 \simeq \sqrt{1.1}$$