In baseball, the fourth out is a legal out made by the defense after three outs in a half-inning already have been recorded. According to the rules, the third out does not cause the ball to become dead; if the fielders make a subsequent out that prevents a run from scoring, this out will supersede the apparent third out, thus becoming the recorded third out. For statistical purposes, the apparent third out is "undone" and the fourth out's result is recorded instead. This is not the same as Four Strikeouts in an Inning.
When runs score
No run may score in which the third out is a force out or on the batter before he reaches first base. Put in other words, force outs count before runs are scored. It is common that a runner reaches home plate a moment before the third out is made by force out. Such a case is routine; the runner doesn't score but is counted as left on base. It is also common that the third out might come on a non-force tag out after another runner reaches home plate. By extension of these two rules, the "fourth out" covers the case where the third out is not a force out, but a subsequent out is. Since the force out counts before the run scores, it must also count before the third out.
The situations where a fourth out may be recorded are exceedingly rare, but some examples follow:
Example: An appeal force out
Suppose bases are loaded with two outs, and the batter hits a single. The runner from third base touches home, scoring easily. The runner from second base touches third and attempts to score, but is thrown out at home plate. Meanwhile, the runner from first base, on his way to third base, misses second base. Now we apparently have three outs and one run scored. RULING: The fielders have a viable appeal play at second base. If they are alert enough and understand the rules regarding fourth outs, they may make a live ball appeal that the runner missed second base. If such an appeal is made, the runner from first base is out on a force out, because he failed to touch his force base (second base). Since no run may score on a play where the final out of the half-inning is a force out, this out prevents the runner from third from scoring. Thus the runner from third is marked as left on base and his apparent run does not count; the runner from second is also left on base, and his out is nullified; only the runner from first is out on the appeal force out, which now becomes the actual third out.
Example: A non-appeal out
Suppose there are runners on second and third base with two outs, and the batter hits a ground ball to third base. The runner from third scores, but the runner from second base is tagged out for the third out. Since the runner from third reached home plate before the third out was recorded, and the third out was not a force out or on the batter-runner before reaching first base, we seem to have three outs and a run scored. However, suppose that the batter-runner fell down on his way to first base and was injured, unable to walk. Then suppose that the fielders throw to first or tag the batter out. Since no run can score if the last out is made on the batter before he reaches first base, this fourth out prevents a run from scoring. Thus the runner from third is marked as left on base and his apparent run does not count; the runner from second is also left on base and his out is nullified; the batter-runner is out, which now becomes the actual third out.
Example: A quick fourth out
There are runners at first and third with two outs. The runners are attempting to steal on the pitch. The batter grounds to the shortstop. The runner from third base reaches home; then, the shortstop tags the runner who has rounded second (third out). The shortstop then throws to first base, which beats the batter-runner for the fourth out. The fourth out is on the batter before he reaches first base, so it replaces the apparent third out and nullifies the run.