1. Was he ever regarded as the best player in baseball? Did anybody, while he was active, ever suggest that he was the best player in baseball?
No.
2. Was he the best player on his team?
He led Cleveland’s pitchers in win shares in 1903, 1905, 1907, and 1908.
3. Was he the best player in baseball at his position? Was he the best player in the league at his position?
He never led AL pitchers in win shares, although he finished second in 1908. He was third among major league pitchers in win shares that season, but that was his only year among the top six in win shares among MLB pitchers.
4. Did he have an impact on a number of pennant races?
He had 35 win shares in 1908, when Cleveland lost the pennant by half a game, and pitched a perfect game in the heat of the pennant race. Otherwise, Cleveland wasn’t close to winning the pennant during Joss’ career.
5. Was he good enough that he could play regularly after passing his prime?
For Joss, this question is not relevant. He died of meningitis at the age of 31, so we don’t know what his decline would have been like had he lived.
6. Is he the very best baseball player in history who is not in the Hall of Fame?
No.
7. Are most players who have comparable statistics in the Hall of Fame?
By similarity scores: John Ward, Larry Corcoran, Deacon Phillippe, Jeff Pfeffer, Noodles Hahn, Hooks Wiltse, Dizzy Dean, Jack Coombs, Candy Cummings, and Fred Toney. Three of the ten are in Cooperstown, but Ward also had a career as a shortstop, and Cummings is in as inventor of the curveball. However, Joss’ lifetime ERA+ of 141 is the best of the bunch; nobody else has one higher than 131. Similarity scores don’t help us here.
Career win shares, contemporary P: Sam Leever 212, Jack Chesbro 209, Deacon Philippe 206, Wild Bill Donovan 202, Bill Dineen 200, JOSS 191, Jack Taylor 183. Chesbro is the only one in Cooperstown, and he’s considered one of the Hall’s mistakes. Otherwise, these aren’t Hall of Famers.
Best three seasons, contemporary P: Vic Willis 101, Clark Griffith 94, Eddie Plank 89, Jack Powell 89, JOSS 88, Jack Taylor 85, Bill Dineen 81, Babe Adams 81, George Mullin 80. This isn’t BBFHOF territory, either.
Best five consecutive seasons: Vic Willis 138, Bill Dineen 134, Eddie Plank 133, JOSS 131, Jack Taylor 124. This isn’t the best company for Joss, as he’s just below the cutoff line.
8. Do the player's numbers meet Hall of Fame standards?
His Black Ink score of 19 is only 99th, and his Gray Ink score of 143 is just 102nd. Those are not good marks. However, he does place a decent 42nd in HOF Standards, at 47.0.
9. Is there any evidence to suggest that the player was significantly better or worse than is suggested by his statistics?
Joss pitched in the deadball era, which makes his raw numbers look better. Also, he had no decline phase to lower his career numbers.
10. Is he the best player at his position who is eligible for the Hall of Fame?
No. There are many other pitchers better than Joss who aren’t in the BBFHOF. There are pitchers better than Joss who haven’t even received votes in the BBFHOF elections.
11. How many MVP-type seasons did he have? Did he ever win an MVP award? If not, how many times was he close?
There was no MVP award during Joss’ career. He finished second in win shares among AL pitchers in 1908, however.
12. How many All-Star-type seasons did he have? How many All-Star games did he play in? Did most of the players who played in this many All-Star games go into the Hall of Fame?
There was no All-Star game in Joss’ era. Baseball Magazine started naming its all-league and all-American teams in 1908. Joss was one of the five pitchers on its all-AL team that season, but failed to make the all-American team that year.
Joss had only two seasons in which he was among the top five AL pitchers in win shares. He was sixth one other year, and seventh two other times. But three or four All-Star-type seasons is very low for a pitcher.
13. If this man were the best player on his team, would it be likely that the team could win the pennant?
I don’t know. Joss had only two seasons when he was among the top five pitchers in the AL in win shares. However, those were the only seasons when he was among the top ten in the AL in IP and games started. I don’t know why he wasn’t used as often as other leading pitchers in the league.
14. What impact did the player have on baseball history? Was he responsible for any rule changes? Did he introduce any new equipment? Did he change the game in any way?
He pitched a perfect game in 1908. He’s also known as the player Cooperstown waived its ten-year requirement for.
Joss has the best WHIP of any major league pitcher in history, and the second best ERA of any pitcher. He’s twelfth in adjusted ERA+ among major league pitchers.
15. Did the player uphold the standards of sportsmanship and character that the Hall of Fame, in its written guidelines, instructs us to consider?
As far as I can tell.
CONCLUSION: A player with a career as short as Joss’ needs a huge peak in order to deserve induction into the BBFHOF. Joss had very good rate stats, but suffers in the win shares measures because he usually didn’t pitch as many times per season as his contemporaries. As he doesn’t come close to having the best peak among pitchers of the twentieth century’s first decade - he didn't make Baseball Magazine's list of top five pitchers in 1908, his best season - Joss does not deserve induction into the BBFHOF.
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