How many bases does a runner advance if a fielder throws the ball out of play after touching the base?

When a fielder throws the ball out of play after touching a base, the runner is awarded two bases from the point of the throw. This rule is designed to penalize the defensive team for an errant throw and to give the offensive team a chance to advance the runners further.

In this case, the key factor is the location of the throw when it goes out of play. Since the throw is deemed to have occurred prior to the ball becoming dead, runners advance based on the rules surrounding the type of throw that led to the ball going out of play. Thus, the correct interpretation is that the runner gains two bases from the location where the ball was thrown out of play, ensuring fairness and consistency in how advancements are handled in baseball situations.

In other scenarios, different rules may apply, such as advancements due to other types of dead ball situations or specific rules regarding plays at the plate, which is why the other options do not apply in this situation.