Some people argue that long distance running helps get lactic acid out of your arm, especially the day after you pitch. The problem with that is there is very little if any lactic acid in your arm after a pitching performance. For lactic acid to build up, you have to perform at full effort for at least 20 seconds consecutively. Pitchers use one explosive burst for less than one second at a time and then rest for at least 12 seconds. There is no lactic acid build-up. The soreness in your arm is more likely caused from a bunch of micro-tears in your muscles from the repeated explosive movements.
Doing a series of longer sprints will get the blood flowing to these micro-tears just as well as a long distance run.