The Fuji X-T1 and baseball
Would you use a first generation camera, such as the Fujifilm X-T1, to take pictures for your nephew's baseball game? Well, it depends:
Do we have plenty of light? For this game, yes we did, it was high sunny midday.
Do we have a fast lens? Indeed, the great XF 50-140mm f2.8
Has the X-T1 been upgraded to the latest firmware? Sure.
In my short experience shooting sports, I say, taking good sharp pictures first and foremost, depends about the quality and quantity of the light that reaches the sensor to the camera. So shooting at noon, with a lens stopped at 2.8 the whole time, you can bet the sensor has plenty of light to quickly acquire focus. Everything else after that is about knowing how to handle continuous autofocus and being aware of filling the buffer after a burst of shots, meaning, after factoring the light, it is all about your technique, and less about the specs of the camera.
Photography can get pretty expensive. Choosing what camera to buy, what lens to buy, depends entirely in the conditions of the context you find most frequently requiring a camera. So for sports, you could have a long telephoto lens that at the long end opens at 5.6, and no matter how much light, or how fast a camera is, it'd be very difficult to get sharp pictures with a moving target… the lens is to slow.
If baseball is your thing, you'd need a telephoto lens. If looking to get sharp pictures in a burst, I'd recommend a fast zoom lens, f2.8 at maximum. And no matter is the camera is a bit old, if you will it to master its autofocusing features, you'd get plenty of keepers. So, yeah, I'd use an X-T1!