## Run Distribution-20 games

Ok, everyone, I've been around for a while, but this is my first post with graphs/pictures, so go easy on me if I don't do this correctly.

I was reading an interesting post over an fangraphs.com about run distribution.  In it they link to a previous article done by Dave Studeman over at The Hardball Times a while ago, which I read, but is a bit more involved.  The basic concept gets to something that I've seen Rangers fan discuss for a while:  Total runs scored is a good way to tell if an offense is good or not, but it always seems that the Rangers offense isn't quite as good as total runs suggest.  Now, undoubtedly, part of this is due to the RBiA effect.  These two links come up with another aspect of offense to consider:  variance.  Which is another way to say, sure scoring 30 runs in a game is great, but it doesn't help you the next game when you only score 2 runs.  So as a way to chart this, Studeman looked at teams from 2000-2004 to see how many times each team would score a particular number of runs.

"For instance, if your league averaged five runs a game, and your team scored exactly five runs in every game, it would typically have a .600 winning percentage instead of .500, even though it had scored the average number of runs. That is the power of looking at distributions instead of averages."-Dave Studeman

To make a long story short (though the article is very interesting if you have the time), the most important runs scored (in terms of getting wins) are the 2nd-5th runs scored, followed by the 6th and 7th runs.  What I wanted to know was, how does this hold for the Rangers.  First, here is the Rangers run scored distribution (Rangers) and runs allowed distribution (Opponent):

Now then, assuming that worked, what does that mean?  For those who didn't go through the Studeman article, the biggest thing to note is that this is skewed to the right.  Obviously, small sample sizes apply.  Anyways, a large part of the right skew is due to the fact that the Rangers simply score (and allow) a lot of runs.  However, it is also worth noting that the Rangers have scored 5 and 6 runs the most this season (40% together), more than they have scored less than 4 runs together (25%).  This is good in the sense that scoring more runs is good, but does lend some credence to the idea that the Rangers are boom or bust with their run-scoring.

Another topic I wanted to delve into concerns the fact that the Rangers allow runs in a similar manner to how they score them, namely a lot.  So, how does this change the importance of the number of runs scored from earlier (2-5 are most important, then 6 and 7)?  This is pretty striking, especially compared to league average, but remember that we're only 20 games in:

This is only a cumulative look at wins.  It doesn't mean that the Rangers win 90% of the games they score 12 runs in.  It means that in the Ranger wins, they have scored 12 or less 90% of the time.  Why is that useful (since most teams have a high winning percentage when they score 12 or less runs)?  Compared to the league average winning percentage for 2000-2004, the Rangers don't win very many (or any so far) games when they don't score 5 runs.

As a final note to this novel:  It could be argued that the Rangers feel the need to swing for the fences so much because their pitching is bad and thus they have to score 5 runs in order to win.  Remember though, that consistently scoring an average number of runs results in more wins (usually) than scoring the same number of runs with more variance.  There are some teams who are the exact opposite.  They score less runs, but get more wins out of the runs they do score.  While a majority of that is good pitching and defense, we can now see that there is another aspect that matters: consistency.

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