New and Improved “Pitching a Perfect (Square) Game” (now with extra squareness!)

Almost immediately after I posted about the Tigers-Mets game that ended with “perfect square” scores, reader Ember Nickel correctly pointed out that I failed to include “zero” as a valid “perfect square” score.  So, let’s recalculate our “perfect square” table:


HOME 0 1 4 9 16 TOT
0 129 1826 1408 324 19 3706
1 2668 167 2576 580 19 6010
4 1832 2932 159 838 56 5817
9 420 736 862 32 34 2084
16 26 39 69 15 1 150
25 0 1 2 0 0 3
TOTAL 5075 5701 5076 1789 129 17770

Now, we can extend the “perfect squareness” of the game by including hits and errors for each team, giving us six possible attributes to shoot for.  Sadly, in the Tigers/Mets contest, the teams’ respective linescores (16 runs, 20 hits, 2 errors for the Mets, 9 runs, 10 hits and 2 errors for the Tigers) only satisfied two perfect squares.  But there have been MANY instances of the hits, runs and errors for both teams all being perfect squares.

There are gaps in the recorded history of “linescores”, but the earliest “6 Perfect Square” game on record occurred on May 30, 1911, when Pittsburgh had 4 runs, 9 hits and 1 error to the Cubs 1 run, 9 hits and 1 error.  The 2010 season had 10 such games, the last happening on September 22, when the Phillies outlasted the Braves, 1-4-0 to 0-1-1.

The highest total of runs, hits and errors for the sum of the six perfect squares is 40.  It has happened twice, both times with the winning team have a linescore of 9-16-1 to the losers’ 4-9-1.  The dates in question were  May 28, 1977 and May 1, 1993.  The lowest sum for a six perfect square game is 3, and it happened when (not surprisingly) Sandy Koufax no-hit the Cubs on September 9, 1965 (Dodgers 1-1-0 to Cubs 0-0-1).

Going even FURTHER down the “perfect square” rabbit hole, we could see if any of these “6 perfect square” games occurred on a perfect square date, making it a “9 perfect square” game!  That is, the month, day and year are also perfect square numbers.  Now, I’ll save you the work and inform you that 1936 is the ONLY 4-digit year in the history of baseball which is a perfect square (44 times 44).

I’m sorry to say, there has never been a “9 perfect square” game if we use 4-digit years.  The closest we get is 8 perfect squares, as in the 4th month of 1936, when Brooklyn’s Bill Lee bested the Cubs’ Van Lingle Mungo 1-0. (1-4-0 to 0-4-0).  Unfortunately, the game took place on the 29th, not the 1st, 4th, 9th, 16th or 25th.

If we use 2-digit years, our chances improve dramatically, as we have the ’00, ’01, ’04, ’09, ’16, ’25, ’36, ’49, ’64 and ’81 seasons to shoot for.  And we do hit paydirt, twice . . .

On 9/4/(20)01, in the 2nd game of a doubleheader, the White Sox topped the Tigers, 4-9-0 to 0-4-1.  Then, on 9/16/(20)09, the A’s Trevor Cahill and two relievers limited the Rangers to one hit, as Oakland topped Texas, 4-9-0 to 0-1-0.

OK . . . I think we’ve exhausted the “perfect square” topic.  NOW we’ll move to prime numbers, in our next post.

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5 Responses to New and Improved “Pitching a Perfect (Square) Game” (now with extra squareness!)

  1. Ember Nickel says:

    Thanks for the update! :) Nice work.

  2. Pingback: Yankees and A’s considered Prime Number Suspects | Value Over Replacement Grit

  3. Señor Spielbergo says:

    “I’ll save you the work and inform you that 1936 is the ONLY 4-digit year in the history of baseball which is a perfect square (44 times 44).”

    It’ll be 2025 before you know it…

  4. dianagram says:

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