Perfection?

One of the most famous baseball quotes of all time is attributed to famed sportswriter Red Smith. There have been various versions used by Smith, but it essentially goes like this:

Ninety feet between bases is perhaps as close as man has ever come to perfection.

The problem is that the distance between the bases isn't 90 feet at all. What is the 90-foot distance all about? Well, the key is that a 90-foot square (generally called a "diamond") is used to help lay out the bases on the infield. But the bases aren't all the same size (home is a very special shape) and they are not all placed in similar locations relative to the corners of the 90-foot diamond.

In a prior blog entry (which I encourage the reader to review), I discuss the little-known fact that the rules of baseball require that home, first, and third bases each nestle neatly in their respective corners of the 90-foot diamond, but second base is centered on its corner of the diamond.

Here's a diagram (not drawn to scale) from the official rule book that shows the situation:



So, while the infield is laid out on a 90-foot diamond, the shortest distance between consecutive bases is clearly less than 90 feet.

So what are the distances between bases? To answer this question we first need to first define these distances as the shortest length between one base and the next.

It seems that we have four distances to determine: home to first, first to second, second to third, and third to home. However, the layout of the bases is reflectively symmetrical. That is, one can draw a line running through the center of home base and through the center of second base such that the left side and right side of the infield are mirror images of one another. Thus, the distance between home and first is identical to the distance between third and home. And the distance between first and second is the same as the distance between second and third. So, there are actually only two distances to calculate, not four.

Let's calculate two distances that are often covered by base stealers: first to second and third to home. Obviously the dynamics of stealing second base are quite different from those of stealing home, but still it should be interesting to compare the actual distances covered.

The easiest distance to calculate is that between first and second base. The shortest distance between first and second is represented by the double-headed red arrow in the diagram below, while the double-headed blue arrow is identical in length to one side of the 90-foot diamond:



All one needs to know to determine the length of the double-headed red arrow is the size of first and second base (which, of course, is also the size of third base). Each base is a square, 15 inches on a side. So, we need to subtract the full length of first base and half the length of second base (remember it is centered on its corner of the diamond) from the 90 foot double-headed blue arrow to determine the length of the double-headed red arrow:

distance between first and second = 90 feet - 15 inches - 7.5 inches
distance between first and second = 90 feet - 22.5 inches
distance between first and second = 90 feet - 1.875 feet
distance between first and second = 88.125 feet or 88 feet 1.5 inches

Now we are left with the more difficult calculation: the distance between third and home. The problem is the rather strange shape of home base. First, a bit of an aside to explain why it is that we have such an awkward-looking, five-sided home base.

For a number of years prior to the turn of the century, home base was a square, 12 inches to a side. Like first and third, home was nestled snugly in its corner of the diamond. However, in 1900 home plate was changed to its modern shape. Spalding's Official Base Ball Guide of 1900 explained the reasons behind the change:

With the plate placed in accordance with the form of the diamond field, that is, with its corner facing the pitcher instead of one of its sides, a width of 17 inches was presented for the pitcher to throw the ball over instead of 12 inches, the width of each side of the base. But this left the pitcher handicapped by having to "cut the corners" as it is called, besides which the umpire, in judging called balls and strikes, found it difficult to judge the "cut the corner" balls. To obviate this difficulty, the Committee [of Rules], while keeping the square plate in its old place—touching the lines of the diamond on two of its sides—gave it a new form in its fronting the pitcher, by making the front square with its width of 17 inches, the same as from corner to corner, from foul line to foul line. The change made is undoubtedly an advantage alike to the pitcher and umpire, as it enables the pitcher to see the width of base he has to throw the ball over better than before, and the umpire can judge called balls and strikes with less difficulty.

Now back to the calculation. In the diagram below, the shortest distance between third and home is represented by the double-headed red arrow. Note that this double-headed arrow runs from the home-base side of third to the closest corner of home plate. As in the above diagram, the length of the double-headed blue arrow is 90 feet.



Now for the hard part. What is the distance represented be the double-headed green arrow? The following diagram should help us determine that important information:



Distance C is what we are trying to determine. But C is the sum of distance A and B. To calculate A and B, we simply need to apply the Pythagorean Theorem. Remember that? Here's a refresher: In a right-angled triangle, the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides.

By the way, have you ever noticed that near the end of The Wizard of Oz, the Scarecrow, in an effort to show off his new honorary degree of Th.D. (Dr. of Thinkology), incorrectly states the Theorem? His butchered version is "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side." Check it out:



But we've stalled long enough. Back to the math. First let's calculate distance A:

A² + A2 = (17 inches)²
2A² = 289 inches²
A² = 144.5 inches²
A = 12.02 inches

Now distance B:

B² + B² = (8.5 inches)²
2B² = 72.25 inches²
B² = 36.125 inches²
B = 6.01 inches

And so the double-headed green arrow (C) can now be calculated:

C = A + B
C = 12.02 inches + 6.01 inches
C = 18.03 inches

All that is left to do is to subtract the full length of third base (15 inches) and distance C (18.03 inches) from the 90 foot double-headed blue arrow to determine the length of the double-headed red arrow:

distance between third and home = 90 feet - 15 inches - 18.03 inches
distance between third and home = 90 feet - 33.03 inches
distance between third and home = 90 feet - 2.7525 feet
distance between third and home = 87.2475 feet or 87 feet 2.97 inches

Finally, let's compare the two distances between bases:

distance between first and second = 88.125 feet or 88 feet 1.5 inches
distance between third and home = 87.2475 feet or 87 feet 2.97 inches
difference = 0.8775 feet or 10.53 inches

And so we have our answer. Indeed, the distance between bases is very different. In fact, the distance between third and home is over 10½ inches shorter than the distance between first and second.

Sorry, Mr. Smith.

Who's on First? Where is Second?

The Tampa Bay Rays' new logo (unveiled after the 2007 season) is wrong.





It's not that I don't like the design. Actually, the new look is nice. It's sharp, straightforward, and (dare I say it?) classy.

And it's not that I'm disappointed that they've dropped the "Devil" from their name. In fact, the devil's still there. Indeed, the devil's in the details. Look closely at the positioning of second base. It's in the wrong place.

Rule 1.06 of the Official Rules of Major League Baseball states:

First, second and third bases shall be marked by white canvas bags, securely attached to the ground as indicated in Diagram 2. The first and third base bags shall be entirely within the infield. The second base bag shall be centered on second base.

And here's that "Diagram 2":



Home, first, and third bases are each neatly nestled in their corners, but second base is centered smack dob on its crook of the diamond. Strange, but true.

Well ... maybe not that strange. Perhaps an explanation is in order.

Though the earliest rules of the game did not explicitly state where the bases were to be positioned, early diagrams showed that each was to be centered on its corner of the infield diamond. It was not until 1874 that a new foul line rule made this clear:

The foul ball lines shall be unlimited in length, and shall run from the center of the home base through the center of the first and the third base to the foul ball posts. ...

Then, in 1875, the rulemakers moved home base (a 12-inch by 12-inch square like first, second, and third) so that it was completely in foul territory, with the front corner of the plate touching "the foul ball lines where they meet at the home base corner." This surprising positioning of home lasted just two seasons, after which two major changes were introduced.

First, the season of 1877 saw home base move once again, this time to a position wholly in fair territory, with its back corner touching the intersection of the first and third base lines. With the exception of the rule that altered the shape of home to its now-familiar five-sided shape, the positioning of home has remained right there. And second, that same year, the first, second, and third bases were increased in size to 15-inch by 15-inch squares.

Finally, in 1887, the positions of first and third bases moved such that "the center of the first and third bases shall be on the lines running to and from the foul lines, providing that each base be entirely within the foul lines." The reason for the change was simple. Prior to 1887, a batted ball hitting the portion of first or third that was in fair territory was a fair ball, while a ball hitting the foul portion of these bases was foul. With just one umpire on the field (the two-umpire system was not introduced until the late 1890s) having to make a split-second call as to what part of the bag was hit was exceptionally difficult. By moving the bases wholly into fair territory it rendered the point moot: any ball touching a base had to be fair.

Of course, there was no need to move second, as it had nothing to do with fair and foul balls. So it was left where it had long been: centered on its corner. It would have been nice for second to have been moved for the sake of symmetry (and for the Rays), but it was not done and ... well ... here we are.

Now, to be fair, the Rays were not the first to make the mistake of placing second base in the wrong place. Even though second base has stayed put for over 120 years, there have been numerous incorrect representations of the diamond.

A few that come to mind include ...

the 1939 baseball centennial logo (worn as a patch by every major league player in 1939):



the cover art on the Macmillan Baseball Encyclopedia:



the primary National League logo:



the Chicago White Sox shoulder patch (thanks to Mark Fimoff for alerting me):



and shame on the Northwest Baseball Umpires Association ... you'd think the officials would know better:

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Update of September 24, 2011:

While I've found numerous examples of this common error over the years since I originally posted this entry, this one seemed particularly egregious. Here's what the Baseball Writers' Association of America's "Manager of the Year Award" looks like (or, at least, what it looked like when Mike Scioscia received his 2009 award):



Arrgh!