The very first discontinuity (not annotated on the graph) is 1910/1911--a relatively modest one by later standards--which marks the introduction of the cork-center baseball.
The next of the discontinuities, and perhaps the most famous, is the advent in 1921 of the so-called "rabbit ball", a ball juicing that resulted from the immense popularity of the emerging hero, Babe Ruth: the Babe's homers made the turnstiles rotate, so what was good for the Babe was made good for everyone. After that, one can see clearly--if the anomaly for WW II is mentally smoothed out--that the rise in power production during the four decades from 1921 to 1961 was remarkably steady.
The next obvious discontinuity is in 1977, the year MLB switched ball makers from Spalding to Rawlings; the new ball was substantially livelier. But if we again mentally "splice out" that jump, we see a continuing downtrend from the mid-60s, one that ran for about 20 years, to 1981 or 1982, before easing. (The spike of 1986/1987 was an anomaly no one has yet explained, but it was brief.)
The last discontinuity is the ball juicing of 1993 - 1994, which apparently ensued from a change made then in the ball-manufacturing process (it looks as if the change introduced the new ball roughly mid-1993). Subsequent to that jump, the trend looks like a continuation of the gradual upward movement.
MLB has steadfastly denied all of those ball juicings, no matter their obviousness or the actual events (manufacturing processes, for example) associated with them. Mind, except for (probably) the original rabbit ball, it may well be that the jumps were unplanned--incidental effects of innovations in the manufacturing process. But to deny that they did happen, when they happened, and that they were definite, discrete events requires a massive dedication to belief in the Tooth Fairy.
Because the ball-juicing discontinuities are critical, we can and should look further into the evidences for them. Of course, the very first consideration is that they are exactly what we are calling them: discontinuities. They are not increases, even rapid increases: they are each a sudden large jump from one season to another, with both the pre-jump seasons and the post-jump seasons being clearly continuous eras separated by an overnight (or, in fact, over-winter) abyss. No theory that relies on any gradual process, even a pretty fast-acting one, can possibly explain the "step" nature of those power jumps.