If you look at the Royals offense strictly on runs scored they are not doing all that badly. At 4.36 runs per game they are 14th in baseball, and 9th in the American League. That puts them as a pretty average offense. I will also say that they have played a tough schedule, so when I look at the offense from 30,000 feet it makes it seem like everything is okay. The individual components are another thing entirely, but for today I want to look at the distribution of run outcomes and see what the offense has done.
From the chart you can see that the Royals have mostly been scoring well above or well below their average. With an average of slightly below four and a half and a fairly normal distribution you would expect the most common outcome of a game to be in the four or five run categories, the two closest to average. That is not the case. The most common out come is three runs or two runs, and six and nine have happened more often than four and five. This is a pretty skewed distribution.
Last year the distribution did have some of the same characteristics if you look at the next chart, but there were a lot more four run games, and a maximum of 11, which the Royals have already matched and exceeded this year. The five, six, and seven run games last year showed up more often than one or two run games, but so far this year they only equal the two run game total. What this says to the optimist and statistician in me is that as our sample of games for 2013 grows, this distribution will become more normally distributed. For that to happen it would mean a lot more four to seven run games in lieu of one to three run games. Also, the Royals have a winning record (dead on their Pythagorean expectation to boot) despite all of the low scoring games, so this could indicate a lot of good to come.