 In keeping stats to compare one pitcher or pitching staff to another, runs have been divided into a few different categories to help make a more fair and accurate comparison. So with that in mind, let's take a look at the difference between runs allowed, earned runs, and un-earned runs. Runs allowed are the simplest because it is all inclusive. Every run scored is a run allowed by the defensive team, regardless of how or when the run is scored. In terms of individual pitchers, the run will be charged to the pitcher who allows the base runner to get on base in the first place. Even if a batter singles, the pitcher is replaced with a relief pitcher, and then the next batter hits a home run. It's the first pitcher who will be charged with the run of the hitter who singled. The relief pitcher will then be charged with the run scored by the batter who hit the home run. This may seem unfair to the first pitcher, and there are stats to try to rectify this, but those numbers like left on base percentage and leverage index are a discussion for another time. Under runs allowed, there are two more types of runs, earned runs and un-earned runs. All runs allowed are one or the other. Whether a run is earned or not is affected mainly by two things, errors and past balls. If we have an inning in which there are no errors or past balls, all runs scored in that inning are earned. If there are runs scored in an inning that there was an error or a past ball, however, things get a little bit more complicated. The rulebook states that the official score should reconstruct the inning without errors or past balls. If the runs still score in this reconstructed errorless inning, then the run is earned. But if it does not score, then the run is un-earned. So for example, let's say that the first two batters of our inning fly out and then a third hits a routine ground ball to the shortstop, who commits an error and allows that batter to reach first base safely. The fourth batter then hits a home run and the two runs score. The next batter strikes out to end the inning. Our official score would then replay this inning as if the error had never happened. Our first two batters would have flown out and without the assistance of the error, our third batter would have grounded out to the shortstop for the third out in the inning and no runs would have scored. This means that those two runs that scored are un-earned. You will notice that the order in which the events take place can have an effect on the classification of the runs as well. Let's say we have the same inning, only the first batter. Let's say we have the same inning, only it's the first batter who hits the home run. The next two batters fly out and the next batter advances to first base by way of an error on the shortstop. With the runner on first base, the next batter strikes out for the third out. We have the same events but because they occurred in a different order, reconstructing the inning means that the lead-off home run would have been hit anyway, followed by the two outs and a ground out to the shortstop. We have one run allowed and that run is earned. Let's cap things off with one final example of a past ball. Let's say we have a runner on second base with two outs. A past ball moves the runner to third base and the batter at the plate singles with a weak ground ball that makes it to shallow right field and the run scores from third base. The next batter then strikes out. In reconstructing the inning, the rulebook states that the pitcher should be given the benefit of the doubt when it comes to runners advancing. So we've got our runner on second base, without the past ball, that is where he is when the single is hit into right field and because we are giving the pitcher the benefit of the doubt, the runner will stop at third base in our reconstructed frame. The next batter strikes out, leaving two runners on base and no run score, meaning our run was unearned.