Figuring Earned and Unearned Runs in a Crazy Inning

I'm cross-posting this from Brew Crew Ball because I think it's a useful guide to determining earned and unearned runs in an inning involving errors, fielder's choices, and pitching changes. Since I wrote it for a Brewers blog, you'll have to excuse the pro-Brewers tilt. The earned run totals in the final paragraph are outdated, but the larger point holds true. I also have to thank my dad, who has covered 1800+ games for STATS, LLC, for checking my work.

---------------------------------------------------------------------------------------------

The fifth inning of last night's game officially took 51 minutes. The Brewers' half included eleven batters and two pitching changes and lasted 25 minutes. The Marlins' half had only one pitching change and ten batters but lasted 26 minutes. Since there were errors, pitching changes, and runs galore in the Brewers' half, it's worth talking about.

One of the most confusing parts of scoring a baseball game is determining whether or not runs are earned. Just as confusing is determining which pitcher in a multiple-pitcher inning is responsible for each run. Since the top half of the fifth inning contained just about every possible weird situation relating to earned/unearned runs, let's work through it and figure out how the runs were assigned.

First, two basic rules: if a batter reaches base because of an error or stays on the bases because of an error and then scores a run, that run is unearned. Also, if runs score after error-free play would have resulted in three outs, those runs are unearned.

Now, the full play-by-play of the inning:

Brewers fifth.
West pitching.
McGehee grounded out, third baseman E.Bonifacio to first baseman Cantu.
R.Braun safe at first on fielding error by shortstop H.Ramirez.
Fielder singled to center, R.Braun to second.
Penn pitching.
M.Cameron walked, R.Braun to third, Fielder to second.
Hardy grounded into fielder's choice, third baseman E.Bonifacio to catcher J.Baker, Fielder to third, M.Cameron to second, Hardy to first, R.Braun out.
B.Hall walked, Fielder scored, M.Cameron to third, Hardy to second.
Kendall walked on a full count, M.Cameron scored, Hardy to third, B.Hall to second.
Looper walked, Hardy scored, B.Hall to third, Kendall to second.
Sanches pitching.
C.Hart safe at first on throwing error by third baseman E.Bonifacio, B.Hall scored, Kendall to third, Looper to second.
McGehee doubled to left, Kendall scored, Looper scored, C.Hart to third.
R.Braun struck out.

Whew, that's a screenful. Sean West entered the inning having given up three runs already in the game, all earned. His role in this inning is the easy one to analyze:

Brewers fifth.
West pitching.
McGehee grounded out, third baseman E.Bonifacio to first baseman Cantu.
R.Braun safe at first on fielding error by shortstop H.Ramirez.
Fielder singled to center, R.Braun to second.
Penn pitching.

McGehee's groundout is self-explanatory. Braun's at bat is trickier: he should have been the second out of the inning, but he reached base. Remember this for later. Fielder's single is also a simple ending for West's night. He departed the game having allowed two runners to reach base.

Now, when Penn entered the game, there should have been two outs. However, Rule 10.16(i) says

When pitchers are changed during an inning, the relief pitcher shall not have the benefit of previous chances for outs not accepted in determining earned runs.

So even if there should have been two outs, Penn does not get the benefit of the error for determining his earned and unearned runs. It's probably easiest to examine his outing play by play.

• M.Cameron walked, R.Braun to third, Fielder to second.
  
  Braun and Fielder remain West's responsibility.
  
• Hardy grounded into fielder's choice, third baseman E.Bonifacio to catcher J.Baker, Fielder to third, M.Cameron to second, Hardy to first, R.Braun out.
  
  This is a confusing play, especially if you see West was charged with two runs in the inning. Since he was responsible for only two batters and Braun was out at the plate, shouldn't he only be responsible for Fielder from this point forward? The answer is no. It's easiest to think of this situation as if Penn came in with no one on base. In that case, Hardy would have come up with Cameron on first. His fielder's choice would then have wiped out Cameron. It's not Penn's fault Braun was on third base to be put out on the fielder's choice. Ergo, Cameron takes Braun's place as West's responsibility.
  
  
• B.Hall walked, Fielder scored, M.Cameron to third, Hardy to second.
  
  The first of West's runners scores. It's tricky here, too, because of the two perspectives on how many outs there should be. From West's perspective, Hardy's fielder's choice should have ended the inning. Thus the run Fielder scores against him is unearned. From Penn's perspective, Hardy's FC was only the second out of the inning, so he's still on the hook for future earned runs.
  
• Kendall walked on a full count, M.Cameron scored, Hardy to third, B.Hall to second.
  
  Since Cameron took over Braun's role as West's responsibility, this is the second of West's two runs to score. Again, the inning should be over from his perspective, so this run against him is unearned.
  
• Looper walked, Hardy scored, B.Hall to third, Kendall to second.
  
  Hardy is the first of Penn's runners to come around and score. Since from his perspective there should only be two outs, this run is earned against him.

Penn was finally pulled after going to a 2-1 count on Corey Hart. If Hart had proceeded to walk, he would have counted against Penn (see Rule 10.16(h)). Mercifully, he didn't walk, keeping things a little simpler.

Brian Sanches entered the game with the bases loaded and all three runners Penn's responsibility. The same rule that applied to Penn applies to Sanches, namely that from his perspective there should only be two out. Let's break his outing down play by play as well.

• Sanches pitching.
  C.Hart safe at first on throwing error by third baseman E.Bonifacio, B.Hall scored, Kendall to third, Looper to second.
  
  This error should have ended the inning from both Penn's point of view and Sanches' point of view. Thus Hall's run counts against Penn, but it is unearned. Hart is Sanches' responsibility.
  
  
• McGehee doubled to left, Kendall scored, Looper scored, C.Hart to third.
  
  Both Kendall and Looper reached because of Penn, so their runs are charged to him. Since the inning should have ended after Hart's at bat, neither run is earned. Both runners are Sanches' now, so close the book on Penn.
  
  
• R.Braun struck out.
  
  The inning finally ends.

The total damage? West is responsible for two runs, both unearned. Penn is responsible for four runs, only one of which is earned. Sanches gave up zero runs. In total, the team gave up six runs, only one of which is earned, right?

Wait! We're not finished yet. From the team's perspective, the inning should have ended with Hardy's fielder's choice, before any runs scored. So even though Penn got charged with an earned run in the inning, that run is marked down as something called a team unearned run. Marking it down as such avoids penalizing the team for putting in a relief pitcher. Remember how Penn entering the game "reset" the number of outs there should have been? If that was carried over to the team, it would effectively force the Marlins' pitching staff to record four would-be outs in the inning before runs became unearned. In short, team unearned runs undo for the team what Rule 10.16(i) does for a relief pitcher.

This can lead to some interesting "discrepancies" in team pitching totals. For example, examine Baseball-Reference's team pitching totals. Note that Cleveland has given up 284 earned runs this year. If you go to Cleveland's team page and sum up the earned runs for every pitcher, you get 284. Duh, right? Not quite. Take a journey over to MLB.com's team pitching totals. There you will note Cleveland as a team has given up 283 earned runs. The difference is one team unearned run on May 12. In that game Tony Sipp gave up an earned run, but it was a team unearned run. Since Baseball-Reference totals earned runs by summing up the earned runs of each pitcher, they end up off by one in this case, affecting the team's ERA. In this case MLB.com's total is correct and the Indians' team ERA is 0.02 lower than what Baseball-Reference shows. Baltimore is in the same situation.

Baseball's rules can be extremely complicated at times. I feel bad for anyone scoring the game last night.