The exploits of Cy Young are immortalized in the annual award bearing his name. Each year, the top hurlers in both leagues are given this award, but not without some controversy over the merits of one pitcher versus another.

“Pitcher A had more wins than Pitcher B. But pitcher C had more strikeouts and less run support. Pitcher D played for a pennant-winner, but he pitched half his games in a canyon of a ballpark, while Pitcher E has the lowest ERA of them all and pitched half his games in a bandbox.” Its enough to make a sabermetrician’s/fan’s/award voter’s head explode.

I’m here to offer a simpler prize for pitchers. Its the “π Young Award”, to be given to the moundsman whose season ERA is closest to π. In case you need a refresher, π is:

“a mathematical constant whose value is the ratio of any circle‘s circumference to its diameter; this is the same value as the ratio of a circle’s area to the square of its radius. π is approximately equal to 3.14159 in the usual decimal positional notation.”

Why choose “π” as the basis for an award? Well, I believe that “3.14” is a wonderful constant that SHOULD be celebrated whenever and wherever possible. And of course, you can’t spell “pitching” without “pi”.

In terms of baseball measures, 3.14 lends itself well to ratios and some percentages. It is in fact a horrible WHIP, to which Tim Byrdak can attest (2006). On a happier note, a pitcher would love to have a K/BB ratio of 3.14, and pitchers as famous as Nolan Ryan (and as ho-hum as Pat Jarvis) have nailed that ratio in a given year. But ERA is the measure that has stood the test of time, and for better or worse, its the barometer on which the valuation of a pitcher is quite often based.

Though it is a constant, a pitcher’s getting to there is a journey of randomness due to the myriad combinations of innings pitched and earned runs that are possible. That would build a little excitement for the award, as pitchers cross over and under the magic 3.14 number throughout each season, like a mathematical version of a Star Trek “Neutral Zone”. Can’t you just see the folks at MLB Network playing it up? “Who will get the ‘π Young Award’ in 2011? If Roy Halladay gives up 27 runs in his next 2 innings, he’d be at 3.12 for the year! But if Rick Porcello can somehow give up only 2 runs in his next 27 innings, then he’ll be in the hunt too! Stay tuned folks.”

While compiling a 3.14 ERA may not seem that special (the last time it would have led either league? The American League in 1950), it would have placed you in the top 10 in most years, especially during the DH/steroids era. It turns out that an approximate 3.14 ERA can be most easily achieved by pitching some multiple of 14⅓ innings while allowing an equal multiple of five earned runs (it calculates to approximately 3.13953488445106 if you really need to know, and if you’ve read this far, you do), yielding the following table:

Most pitchers (and managers) would sign up for that.

Thanks to the wonderful Baseball Reference.com Play Index, I can tell you that there have been 81 pitcher-seasons ending with a 3.14 ERA (regardless of innings pitched). For those of you who love decimal places, this group includes anyone who ended up with ERAs between 3.1350 and 3.1449 (as rounding would bring them up and down, respectively, to the magical 3.14).

Houston’s Bob Knepper achieved “π nirvana” twice within a three-year period, pulling off 3.14 ERAs in 1986 and 1988 while Mel Parnell (1948), Paul Foytack (1957) and Jerry Koosman (1970) came closest to π (to six decimal places) when each yielded 74 earned runs over 212 innings, for an ERA of 3.141509.

At this point, it must be stated that it is extremely unlikely that any pitcher will amass just the right number of innings pitched and earned runs allowed to really nail the π ERA down even further than Parnell, Foytack and Koosman did. Here are the ten closest combinations to 3.14159265 (which is as far as I’m willing to take π without getting to know it better, meeting its parents, etc.):

You’ll note that the three closest combos feature innings pitched totals that haven’t been seen since the days of Old Hoss Radbourn, Christy Mathewson, and Mr. Cy Young himself.

At this point, you may be wondering … have there been pitchers whose entire careers have come very close to “π-dom”. Why yes, and as with the single season list, we are considering those with ERAs between 3.135 and 3.145):

Cory Luebke is the absolute closest to the 3.14159265 magic number, but given his active status, that is bound to change both very, very soon and very, very often. The next closest, in an amusing coincidence, is the 1974 NL Cy Young Award winner (and the first reliever to win the award) Mike Marshall. Finally, former Baltimore Oriole Mike Cuellar amassed the most innings of “π ball”.

Now it wouldn’t be a VORG post without a statistical cherry on the top (mmm . . . statistical cherries …..). The first Cy Young Award was given in 1956 to Don Newcombe. So, lets retroactively bestow the 1956-2010 “π Young” honors to those players whose ERA ended up closest to 3.14:

So, let’s get the bandwagon started for the newest pitching award . . . The “π Young”.

Great post!

Both Rich Garces and Bartolo Colon thought that they had a shot at this award, but they were confusing it with the Pie Young award, which is given to the pitcher who consumes the greatest quantity of pie in a 162 game season.

Thanks much!

Felix Pie was just confused by this whole matter …

LOL.

Surprised at no 22/7 approximations but I guess you need to work the 9 in there somehow and those numbers won’t give it to you.

You have to multiply the 9 in later. ERA is earned runs per 9 innings, so it would be 22 earned runs per 63 innings.

An even closer fraction approximation of pi is exactly halfway between 22/7 and 3.14 even. 3.14 is 157/50, so cross-multiplying, that would be 1099/350 and 22/7 is 1100/350…so to split the difference, it would be 2199/700. Well, we’re obviously not going to get 700

innings…what about 700 outs? That’s a reasonable 233.3 IP…but since it’s “per nine innings”, it wouldn’t work out properly. Not for a single-season, anyway. Since we always have to multiply by nine anyway, a pitcher who pitched exactly 2100 innings for his career and gave up 733 earned runs would have a career ERA of 3.14142857, which would be closer than anybody on the list of actual players. We might be able to tweak it even closer by adding or subtracting a single out from that career total, but why mess with something that is both extremely close and not too hard to envision due to the use of round numbers? (But of course it has to be for a career due to the presence of the 733, which is a prime number.)With the Felix Pie reference, we’ve come full circle…

well-done, Mauer.

Ember … I hear ya’ …. giving up 7 earned runs in 22 innings makes for a 2.86 ERA. 🙂

love the idea and love the effort on this one .

don’t think i will be able to watch jose valverde close out games this year ,

without thinking of this award and this article .

Thanks much … it was a labor of love …

Hi, dianagram! I’m a fellow Scrabble enthusiast, baseball fan, and (in this case, most relevantly) math geek. You’ve commented on my livejournal blog, but somehow I’ve only just discovered this wonderful blog.

In hopes of contributing to this discussion from five years ago, I’ll point out something you likely already know: the methods of “continued fractions” (see Wikipedia) allow us to find those values of earned runs and innings pitched that lead to approximations of pi.

We first note that an ERA close to pi is equivalent to an ER/out ratio close to pi/27 = 0.116355283… . (Using outs allows us to avoid using fractional innings pitched.)

p/q is a “best rational approximation” to pi/27 if there’s no fraction with a smaller denominator that’s closer to pi/27. It’s relatively straightforward (again, see Wikipedia) to find those convergents and semi-convergents of pi/27 that yield the best rational approximations. They are:

ER Out IP ERA

0 1 0.3 0

1 5 1.7 5.40

1 6 2.0 4.50

1 7 2.3 3.86

1 8 2.7 3.38

1 9 3.0 3.00

2 17 5.7 3.18

3 26 8.7 3.12

5 43 14.3 3.1395 [this appears in your blog entry]

22 189 63.0 3.1429 [this is equal to the famous approximation 22/7]

27 232 77.3 3.1422

32 275 91.7 3.1418

37 318 106.0 3.14151 [this appears in your chart]

69 593 197.7 3.14165 [as does this]

106 911 303.7 3.141603 [as does this]

249 2140 713.3 3.1415888

355 3051 1017.0 3.14159292 [this is equal to the spectacular approximation 355/113]

2024 17395 5798.3 3.14159241

2379 20446 6815.3 3.14159249

2734 23497 7832.3 3.14159254 [this takes us past Cy Young’s career IP, so let’s stop here]

I’d be absolutely delighted if a pitcher ended his career with 355 ER allowed in 1017.0 IP.