If the starting pitcher injures himself, or becomes ill, he need not complete pitching to the first batter. A substitute pitcher would also not need to complete pitching to the batter at bat if he injures himself, or becomes ill. Either pitcher would not be relieved from having to complete pitching to a batter if the batter is substituted for in mid-count. They would simply need to complete pitching to the sub, or retire the side, in the case of a reliever. And, if I eject any pitcher before he can complete his pitching requirements then not only can you change pitchers, I expect you to do so.
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