Christy Mathewson, Grover Cleveland Alexander, Smokey Joe Wood, Eddie Cicotte, and Dutch Leonard (a sub-1 ERA in 1914!). That being said, there was little doubt about who deserved the top honor here.
Walter Johnson 1913 (14.3 bWAR)
With all due respect to Cy Young, Walter Johnson is probably the greatest pitcher who ever lived. The JAWS metric as well as the fan EloRater on Baseball-Reference agree with me. No pitcher threw more shutouts, led his league in more categories, won more MVPs or produced a more Hall of Fame-worthy career (according to Bill James) than Johnson. Young won a lot more, but he also lost a lot more, so that argument cancels itself out.
Already the game's premier power pitcher by 1913, the 25 year-old Johnson won his first major league pitching Triple Crown with his 36 wins, 1.14 ERA and 243 strikeouts. He paced the Show in almost every pitching category imaginable, and his bWAR total is the highest of any pitcher since 1900
Even for the Deadball-era, some of his statistics are otherworldly. For instance, his 259 ERA+ ranks as the fifth highest in the modern era, surpassed only by Pedro Martinez, the aforementioned Leonard, and Greg Maddux (twice). . His 0.78 WHIP was the lowest produced during the Twentieth Century, only to be broken by Martinez's record-setting 2000 season. His eleven shutouts put him at eighth all-time, tied with Mathewson, Sandy Koufax, Dean Chance, and Ed Walsh. His 1.14 ERA stood as the record for any pitcher that surpassed 300 innings in a season until Bob Gibson squeaked by him (1.12) 55 years later. Early in the year, Johnson delivered 55 and two-thirds consecutive scoreless innings, still the AL record though later broken by Don Drysdale.
And while most pitchers are automatic outs when they step into the batter's box, Johnson was no slouch with a bat in his hands. Though never to be confused with Babe Ruth, Johnson had a reputation as a good-hitting pitcher and acquitted himself well at the dish that season with his 110 OPS+. Not too shabby.
The Big Train rolled to his first of two MVP awards (he won again in 1924) that year, back when it was called the Chalmers Award. Johnson outpolled accomplished hitters such as Shoeless Joe Jackson, Eddie Collins, Tris Speaker, Home Run Baker, Nap Lajoie, "Wahoo" Sam Crawford, and Ty Cobb. It didn't hurt that his Washington Senators won 90 games and compiled the second-best record in the American League, either. Had there been any formal award recognizing top pitchers, he would have won them in a landslide. As it is, he became the first pitcher in baseball history to receive an MVP award, paving the road for the Lefty Groves, Roger Clemens's, and Justin Verlanders that followed.
There are no splits or game logs available for this season, so unfortunately I can't provide any fun facts (other than the ones listed above, of course).
Best Offensive Season of the 1910s--Ty Cobb (1911)