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Color by Numbers: Too Much of a Good Thing?

Posted By William Juliano On May 26, 2011 @ 11:26 am In 1: Featured,Baseball,Bronx Banter,Yankees | Comments Disabled


How many times when you were growing up did your parents tell you not to eat too much ice cream? You’ll spoil your appetite, or maybe even get sick, they warned. After all, too much of even a good thing can be bad, they reasoned. Did you believe them? Neither did I.

Apparently, home runs are baseball’s version of ice cream because the conventional wisdom of late has suggested that hitting too many is a bad thing. From broadcasters to beat writers to even the players who knock them out of the park, a common lament about the Yankees’ offense has been it relies too heavily upon the home run. According to those “in the know”, more runs would be scored in the Bronx if the Yankees did less bombing and more bunting, or something along those lines. Although such a philosophy seems inherently illogical, many around the game still espouse it, so let examine the main arguments more closely.

The easiest way to test whether too many home runs can be a drag on run production is to determine the correlation between the two statistics. Over the last decade, the Yankees have exhibited a mild, but meaningful positive link between homers and runs, while all of baseball has experienced an even stronger relationship between balls leaving the park and runners crossing the plate. Of course, every statistician will tell you that correlation doesn’t mean causation, but at the very least, there is good reason to suspect that home runs inflate, not depress, the amount of runs scored.

Correlation Between Runs and HRs, Yankees and MLB, 2001-2010

Yankees R/G HRs MLB R/G HRs
2010 5.302 201 2010 4.380 4613
2009 5.648 244 2009 4.610 5042
2008 4.870 180 2008 4.650 4878
2007 5.975 201 2007 4.800 4957
2006 5.741 210 2006 4.860 5386
2005 5.469 229 2005 4.590 5017
2004 5.537 242 2004 4.810 5451
2003 5.380 230 2003 4.730 5207
2002 5.571 223 2002 4.620 5059
2001 4.990 203 2001 4.780 5458
R= 0.4434 R= 0.8244

Note: R is the correlation coefficient, which ranges from -1 to +1. A score of 0 implies no relationship, while scores approaching each parameter imply an increasingly meaningful direct (positive) or inverse (negative) relationship.
Source: Baseball-reference.com

To be fair, most people who would prefer to see the Yankees score via small ball or timely base hits fret more about the percentage of runs scored via the homer than the actual number of home runs. According to the theory, scoring a disproportionate number of runs with muscle leads to an overreliance on the home run, which furthers results in an unsustainable offensive approach. Once again, we can test this argument by determining the relationship between total runs scored and the percentage of tallies plated by the homer.

Percentage of Runs Scored Via the HR, Yankees and MLB, 2001-2011
Source: Baseball-reference.com

As you can see from the chart above, the percentage of runs scoring on a home run in baseball has steadily decreased over the past decade. However, the Yankees’ rate has seemed to fluctuate without any noticeable relationship to runs scored. In fact, the year the Yankees scored their highest run total in this span was also when they recorded the lowest percentage of runs scored via the home run. Because of this randomness, we can’t definitively determine a link between total runs scored and those coming on homer, at least not for the Yankees. Using aggregate team data for all of baseball, however, reveals a strong positive correlation between total runs scored and the number crossing the plate via the homerun. Why doesn’t this relationship hold for the Bronx Bombers? Perhaps that’s a post for another day.

Correlation Between Total Runs and Runs via the HR, MLB, 2001-2011

Year R/G %R from HR
2011 4.17 32.3%
2010 4.38 34.4%
2009 4.61 35.5%
2008 4.65 34.5%
2007 4.8 34.2%
2006 4.86 36.1%
2005 4.59 36.2%
2004 4.81 37.0%
2003 4.73 35.9%
2002 4.62 35.8%
2001 4.78 36.8%
R= 0.7507

Source: Baseball-reference.com

Correlation Between Yankees’ Run Total Relative to MLB and Runs Scored via the HR, 2001-2011

Year vs. MLB R/G %R from HR
2011 130.7% 49.4%
2010 127.2% 38.2%
2009 128.9% 41.0%
2008 108.9% 35.7%
2007 131.3% 34.3%
2006 124.1% 39.0%
2005 125.0% 44.0%
2004 120.5% 43.4%
2003 119.1% 41.8%
2002 127.0% 41.2%
2001 108.6% 40.2%
R= 0.2397

Source: Baseball-reference.com

Based on the data presented above, there really is no reason to believe that too many home runs are hampering the Yankees’ offense. But, what about the often repeated argument that even if an overabundance of homers doesn’t limit run production in the regular season, it will eventually catch up to the Yankees when they face better pitching in the playoffs? Is it really more difficult to score runs with a home run when facing an elite pitcher? If so, the Yankees might be better off trying to manufacturing runs so they’ll be better prepared to win in October.

Percentage of Runs Allowed on Homers by Ace Pitchers, 2010


Source: Baseball-reference.com

The list above is composed of each league’s 10 best pitchers in 2010 (based on WAR) along with the percentage of runs they allowed via the home run. From Josh Johnson at 17.6% to Johan Santana at 46.3%, there is a wide range of rates, suggesting that ace pitchers are not unanimously averse to being touched up by a long ball. In fact, the accumulated totals of the top-10 in each league are pretty much in line with each respective league average.

We’ve shown that home runs and runs scored via homers have a positive correlation to total offensive production. In addition, evidence from 2010 suggests that ace pitchers are not immune to being scored upon via the long ball. In other words, there really is no such thing as too much of a good thing, at least when it comes to home runs. Nonetheless, no analysis, regardless of how thorough, is likely to dispel what has become a very popular misconception. So, instead of trying to convert the remaining holdouts, I say let them eat cake…and save the ice cream for the rest of us.

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