John gave you great advice about the Sigma 150-600 and Canon 100-400 lenses in order to get more reach. As long as the softball game is in the daylight (most are depending upon region of country) or in a well illuminated park, then either will work.
One caveat is the 70-200 (especially the f2.8 version) focuses extremely quickly while the EF 100-400 will be noticeably less responsive and the Sigma 150-600 is even more so. Be prepared to slightly adjust your shooting style with either of these lenses (or pretty much any other longer zoom lens) because you will need to anticipate the action and be on target a moment before you need to capture. The only lenses I use that are faster focusing than my EF 70-200 f2.8 are the "great white" primes including the EF 300 and EF 400 f2.8. I sometimes shoot day games with an EF 200-400 f4 with built in 1.4X extender and it is a bit slower focusing than the 70-200 even with the 1.4X extender switched out.
That doesn't mean the Canon 100-400 or Sigma 150-600 are bad choices because many people shoot sports with them, it just means you have to accommodate their characteristics when moving from your 70-200 lens.
Another lens to consider that is available used is Canon's EF 400 f5.6. I bought one of these back in 2005 when I bought my first 1 series Canon body and I would nominate it as the Canon lens that most outperformed its reasonable price. It focuses very quickly and provides excellent image quality while being relatively light and has a nicely integrated hood. Even though I have Canon's excellent EF 400 f2.8, I will still sometimes use the EF 400 f5.6 during a day game because its light weight makes it a pleasure to use and it will provide focus acquisition on par with the EF 70-200 f2.8 It is simply easier to design a high performing prime than a zoom so if you can give up the versatility of the zoom for longer reach, this low cost prime does a great job.
If you are interested in the EF 400 f5.6, I will try to dig out some older soccer photos I shot with it to give you an example but the results are very good. It is an amazing piece of glass, especially when you consider the low weight and relatively low price so consider a used one in good condition.
Photos below were captured with EF 70-200 f2.8, EF 200-400 extender lens f4, EF 400 f2.8 (2 of them), and the last from the outfield fence using an EF 800 f5.6 which is WAY too much reach when shooting from the dugout or near field area! So for normal work, you won't need anything beyond 400mm if you are close to the field and fast focus is a great attribute in any fast moving sport.
And on edit, two examples of soccer using the EF 400 f5.6. As you can tell, I still really like this lens even though I own several more expensive Canon tele primes 🙂
Rodger
