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Color by Numbers: Too Much of a Good Thing?

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.

Categories:  1: Featured  Baseball  Bronx Banter  Yankees

Tags:  color by numbers  william j

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1 kenboyer made me cry   ~  May 26, 2011 11:04 am

William, I throughly enjoy reading your pieces and diving into the analysis. I am not a sabermetrician, but you break it down for us passionate fans "of the gut" style.

Thank you.

AND, ice cream with cake is even better.

2 William J.   ~  May 26, 2011 11:36 am

[1] Thanks...and what better for the gut than a nice healthy bowl of ice cream (with a little cake on the side too)?

3 ms october   ~  May 26, 2011 12:14 pm

i was hoping you would tackle this topic william.
very good stuff.

although i am not a big ice cream lover and i am perfectly happy scoring runs via the hr.
i mean if manager binder himself realizes they are hits i don't see why everyone is so up in arms about them.
i sort of think it is the perception that more stuff is happening while playing "small ball" that leads people to think it nets more runs - "oh they are stealing, and bunting, and hitting it the other way to move the runner - they must be scoring."

4 RIYank   ~  May 26, 2011 12:55 pm

Yay! Good job, William.
My hunch about why the correlation between runs scored and % of runs from HR does not hold for the Yankees is: small sample size.

5 joejoejoe   ~  May 26, 2011 1:32 pm

Here are the per game run totals of the Yankees this year, by frequency.

15 runs - 1 time
13 runs - 1 time
12 runs - 2 time
10 runs - 1 time
9 runs - 2 times
7 runs - 4 times
6 runs - 7 times
5 runs - 10 times
4 runs - 6 times
3 runs - 7 times
2 runs - 2 times
1 run - 1 time
0 runs - 4 times

The Yankees average 5.2 runs per game but they are just as likely to score 3 or fewer runs per game as score 9 or more runs in a game. Is there any evidence that a less homer dependent offense that scores fewer runs could produce more wins by scoring more consistently in individual games?

6 Chyll Will   ~  May 26, 2011 1:43 pm

You might have to also consider who is relying on themselves to hit homers when they could almost obviously produce at a better rate doing something they're far more capable of. Everyone has the potential to hit a home run, but certainly not at the same rate. So if Derek and Brett are going up to the plate and swinging for the fences each time, is that really something you can ignore or not be concerned about based on just present production? Brett still has potential to hit double digits consistently, Derek not so much. Up and down this lineup, you have guys who can pop it at any moment, but half of them probably shouldn't being trying so hard to do so, as the case may be.

7 William J.   ~  May 26, 2011 2:07 pm

[3] It definitely seems like perception is the issue. It's kind of like when bad hitters get reps for being clutch simply because we only remember the unexpected event (i.e., there one big hit instead of there many more expected outs).

[4] Sample size is a good starting point. For example, if you throw out 2007 (when Yanks had highest BABIP and one of highest BAs with RISP), the correlation doubles. In many ways, the Yankees offense has been a relative outlier to the rest of baseball, so some deviation from the norm isn't surprising.

[5] I actually posted something on that topic yesterday (put into graph form what you displayed above). In one of the charts, the Yankees run distribution over the past five years is depicted. One thing to keep in mind is the changing the run evironment also needs to be factored into this equation. http://t.co/lpsPheA

[6] I think many people are confusing two arguments. There is nothing wrong with hitting alot of HRs, but there could be negative ramifications from trying to hit them. I think Tex' steady evolution into a dead pull hitter (http://t.co/JUE6NsM) might be an example of that tradeoff, but I am not sure if any other player currently fits the profile.

8 William J.   ~  May 26, 2011 2:08 pm

[7] Make that "their" instead of "there"! I hate that mistake.

9 Chyll Will   ~  May 26, 2011 2:26 pm

[8] Well that's neither hear nor their... >;)

10 SteveF   ~  May 26, 2011 6:05 pm

You would expect an older team to score more runs via the home run (as a percentage) than you would a younger team. I recall reading some study somewhere about how hitters age. Doubles decline and home runs increase. Strikeouts and walks increase. Batting average declines.

All three of those factors increase the difficulty of scoring runs on non home run type events.

On the plus side, it's been show that non-sequential (homer heavy) offenses seem to do slightly better (i.e. they get closer to their regular season average) at scoring runs than their more sequential counterparts in the post-season.

The first study was probably something done by Bill James and is likely very old and outdated by now (though probably still relevant). The second was something I read on Baseball Prospectus five or so years ago. No idea if things have changed since then.

11 Mr OK Jazz Tokyo   ~  May 27, 2011 12:31 am

[0] How dare you, William. A "real" baseball man like Jim Riggleman says "We do the little things and play the right way. Some call it Small Ball..we call it SMART Ball". So go back to your Ma's basement and crank some Foghat while you crunch numbers,stat boy!

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