1900s Players Who Likely Merit the Honour
Russell Bowie is far and away the player with the most notable career from this era. He had several seasons that are simply massive, with his best being 1901, when he scored 24 goals despite missing one of his team's eight scheduled matches. The next-highest goal-scorer had 10 goals. Bowie scored more goals in seven games than the entire Quebec team did in eight games. The result it a TPAK of 8.57, which is far and away the best single season for the data set I currently have, which goes up to 1926. He also has the third-, seventh- and seventeenth-best seasons as well. I haven't done the calculations for Wayne Gretzky yet, but it's possible Bowie might approach the Great One's level of dominance. He was that good.
As you can see, the Hall of Fame committee did quite a good job at honouring the very best players from this decade. Among these very best players, only Harry Smith and Herb Jordan have not been recognized by the Hall. I've posted about Smith before; Jordan has likely been overlooked since he played for Quebec in an era when Quebec rarely had a championship team. Jordan was sometimes the only really good player on his team.
1900s Players Who Might Merit the Honour
Among the maybes, most have been honoured by the Hall already. I would personally draw the line after Alf Smith. I think he deserves the honour, while Bruce Stuart probably does not. Hod's brother has too many mediocre seasons on his resume to be considered one of the best of his era, in my opinion.
This line would mean that both Fred Lake and Billy Breen deserve to be in the Hall of Fame. I would certainly support the induction of Breen, a Winnipeg hockey superstar, but Fred Lake is something of a surprise here. Lake started his pro career as something of a nomad, playing mostly left wing in the IHL, then later in Manitoba. He then joined the Ottawa Senators in 1909, and played point (the second-most important defensive position) for a defensively dominant team for several years, and these seasons are really what elevate his career to this level.
1900s Players Who Likely Don't Merit the Honour
Here is where we see where the Hall of Fame committee went wrong, as seen by this method. Tom Hooper was inducted due his playing for the Kenora Thistles, alongside Tommy Phillips and Si Griffis (two legitimate Hall-of-Famers), and Billy McGimsie (who's also in but probably doesn't quite deserve it). If the team really had that many of the very best players at the time, they would likely have won more than they actually did.
Fred Scanlan was apparently a matter of completing the Montreal Shamrocks line with Harry Trihey and Art Farrell, and only Trihey really comes close to deserving the honour.
George Richardson was an OHA player who later fought and died in World War I. War heroes have a history of being honoured by the Hall of Fame, regardless of what their hockey career actually entailed. Later events make their career seem better that they actually were.
Jimmy Gardner had a long pro career, but a mid-level one. However, he played an important role in the founding of the game most historic franchise, and this association apparently made his playing career look better in retrospect.
Billy Gilmour is a puzzler. He really only had a couple of good years in Ottawa, and they were only good, not great.
Fred Whitcroft is another head-scratcher. He made as big name for himself for a brief period by signing with the Kenora Thistles in 1907, and then heading to Edmonton to play for the pro team there, playing in three Stanley Cup challenges all told. But he has little more than name recognition going for him; he was a good player for a few years, but not nearly at the level needed to be considered one of the best of his time.