August 21, 2012
Baseball and Base 3
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Zachary Levine, who somehow tricked an accredited university into giving him a mathematics degree, is in his third season covering the Astros for the Houston Chronicle. This is his second endeavor for Baseball Prospectus, the first being a conversation with Kevin and the Professor about shooting guns in Texas on Episode 49 of the Up and In podcast.
Henry Aaron's running buddies were nowhere to be found at Atlanta Stadium that night, Cliff Courtenay and Britt Gaston having been bailed out for a C-note apiece after rounding the bases with the newly crowned home run king back in April. Hey, trespassing is an expensive habit.
So Aaron stood alone on that August night, on the edge of history once again.
Expos Reliever Chuck Taylor was his victim, a fair fight actually, given Taylor's short-lived peak that same year. And with one swing of the bat in a game long since over, Aaron had done it.
Just months after passing Babe Ruth for the all-time home run record, he had reached the unreachable star. He was the first major leaguer to 1,000,000 home runs.
In a society that has embraced base 10 to the fullest (probably something to do with fingers), you have to wonder how baseball ever evolved this way. It is, to steal a word out of base 5, the quintessential embodiment of base 3.
As a refresher from some math class we ignored along the way, the base is essentially where the next digit flips. With the last digit of a whole number the unit digit, a base 10 world puts the tens to the left of that and the hundreds, thousands and so on.
Base 3 limits your vocabulary of digits to just 0, 1, and 2, because the digit 3 would just be a 1 in the next column over. It's the units place, then to the left of that, what we in the traditional Arabic numerals call threes, nines, 27s, and so on.
So just to pick a number, Craig Biggio's modern record 285 career plunkings sounds even more painful as 101,120 in the ternary system.
Baseball has its cycles of three strikes to flip to the next batter, nine innings to flip to the next game (seriously, why not a perfect 10?), and 27 outs to complete a perfect game. It's almost as if Abner Tripleday, in a creation myth as laughable as that other one pushed for so many years by the baseball poobahs, came to America from a base 3 land and invented our national pastime for us.
- 10 strikes and you're out
- 100 innings make up one game
- 1,000 up, 1,000 down for a perfect game
- And as of the first expansions, 10,000 home games and 10,000 road games to flip to the postseason.
Base 3, or the "ternary" system as the analog to base 2's "binary" descriptor, doesn't get a whole lot of love in sports or at large, especially when compared to some of the even bases.
In addition to the on/off, yes/no binary that serves as the basis for all sorts of technology, the hexadecimal (base 16 with 0-9 and A-F) is a common computing base. The most obvious examples of non-traditional bases in sport are found in tennis, which uses a modified base 4 to keep score within games and a modified base 6 within sets.
Baseball even shunned the ternary when it eliminated the ternary outcomes that Americans frown upon when in 2007, ties went away, leaving only the binary win/loss outcomes.
But baseball does nod a subtle nod to its mathematical roots in the only commonplace use in our culture of the ternary point—the "decimal" in "decimal point" implies base-10, but it's the same thing.
Saying a pitcher threw 8.1 innings—hahaha, who are we kidding, 5.1 innings—does not compute in our spreadsheets when we try to come up with a season total, nor does it make for easy math. You have to convert back to the decimal system in order to figure ERAs in the way one is intended to.
But it's straight out of the number system that forms the basis for the game, and while it’s only a bit of shorthand, it’s the only remnant out there.
So what if, in Abner Tripleday's world, we measured all of baseball in base 3?
First of all, the 1,000,000 home run club would be borderline sacred, or else might have been until Barry Bonds' alleged performance-enhancing drug taint caused his entry Sept. 3, 2006 vs. Les Walrond to be a lot less celebrated.
But some of the game's other elite levels and de facto Cooperstown barriers are blown away as well, making one wonder if what we consider obvious greatness is really just a product of the number of fingers we have.
What we call 3,000 hits now—a club populated by 28 men with all of those not allegedly bitten by the drug bug in or bound for Cooperstown—is really just the very arbitrary 11,010,010. So is the big celebration at 10,000,000 (what we call 2,187)? If so, that's not really much of a standard, with 181 celebrants plus a place being held for Adrian Beltre next month.
Despite a nosedive in his final season, maybe Pete Rose sticks around to try to get to 20,000,000 (4,374).
As for 300 wins, the ternary milestone of 100,000 (243) is probably more appropriate for the age in which we live, featuring larger rotations and further specialization.
Also, forget Denny McLain's 1968 feat. The real ultra-elite single-season level for the ultra-trivial statistic becomes 1,000 (27) wins—last attained by Bob Welch in 1990 and at least something that we can talk about for a couple months once in an Ubaldo moon, whereas the current 30 is a virtual impossibility.
The batting average milestone, which a study found was actually not so trivial with more players just making it than just missing, becomes much simpler. Hitting .1 is a sign of a good season—and actually now a really good season in that category. One hit every three at-bats, which is something that at the start of play Tuesday had only Andrew McCutchen, Melky Cabrera and Mike Trout reaching rather than 25 players for the decimal .300.
So in some cases, it actually gives us a much better sense of the elite.
Alas, seeing baseball through the lens of base 3 would never happen.
As we all know, pitchers' injuries happen in base 10. If pitchers started to go above what we know as 100 pitches just because that stops being a round number, it would be disastrous for the game—right arms pretty much just strewn over the ballparks of America, having fallen out of their sockets.
It just wouldn't be worth it.
Zachary Levine is an author of Baseball Prospectus.
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