Since the Royals have had a dearth of quality ballplayers for the past generation, there aren't any players to seriously consider for election into the baseball Hall of Fame. So let's instead speculate about the Royals Hall of Fame. Let's first see if there are any guiding standards by which to abide, and then apply those standards to current players.
Here is a table showing the position players. I restricted each players' stats to their time with the Royals. I doubt the Royals considered performance with another team when evaluating Royals Hall of Fame possibilities.
There is a large range of values. My first instinct is to look at fWAR. My first instinct might be stupid. Anyway, Cookie Rojas finds himself in the Royals Hall of Fame with only 6.2 fWAR. Alex Gordon had 6.6 fWAR this season alone. George Brett had the most at 84.6 fWAR. I don't think using fWAR makes any sense.
What about offensive value? Nah, not really. Those values (wRC+) range from 79 to 133. There is a range of defenders there. From Frank White to John Mayberry, defense is just as variable as wRC+. About the only thing I can see is longevity. Cookie Rojas played the fewest games with the Royals on that list, but it still amounted to almost five and a half seasons. He was with the Royals from 1970-1977, and his best season came in his first full season as a Royal. John Mayberry logged a similar number of games, but the rest are all far above 1,000 games with the Royals. So, I'll look for longevity first. Then I might look at fWAR or something.
Here are the pitchers, again restricting to their time with the Royals.
Except for closers-extraordinaire Quiz and Monty, all the pitchers were (mostly) starters who logged at least 1,000 innings with the team. The lowest amount of fWAR naturally belongs to those two closers, and it seems like there is a bit less of a range in fWAR. Interestingly, Gura, Quiz, and Monty were the only ones whose ERA beat their FIP, and they were the ones who relieved the most. For current Royals pitchers, I'll look at role, innings pitched, and fWAR. Mostly.
So now let's see the Royals' current position players. I took some liberties with this list. I eliminated guys who have barely played (like Terrance Gore and Christian Colon) and recent free agent signees Alex Rios and Kendrys Morales.
Alex Gordon, obviously. He's logged more time with the Royals than Rojas and Mayberry and accrued more fWAR than Mayberry, Patek, and Rojas. If he left the Royals right now, I think he'd still get in. If he plays a full, healthy season at his true talent level in 2015 and decides not to exercise his player option, his case will be even stronger. Only Brett and White were Royals for life, so playing for other teams isn't much of a concern. Gordon should get in easily.
Salvador Perez and Alcides Escobar. If both players play out the rest of their contracts, including option years, at somewhere around their career stats, they should both get in based on longevity. Escobar needs two seasons to reach the "bar" for games played, and he's basically Freddie Patek in terms of offense. His baserunning is excellent. Escobar just needs to play. His fWAR right now is more than Rojas.
Perez was a homegrown guy who has a chance to spend his career with the Royals if the team decides to re-work his contract in a few years. As long as, you know, Ned Yost doesn't kill him. However, if Perez' workload doesn't decrease and he falls apart, he could miss out on the Royals HoF. I think he'll get in because of his Wild Card walkoff hit and his reputation. He could miss out if his offense never rebounds.
Lorenzo Cain, Jarrod Dyson, Mike Moustakas, and Eric Hosmer. Cain has trouble with playing time, and Dyson has been used strictly in a part-time role. Those guys probably won't clear the longevity threshold, though their actual worth on the field clears the Rojas line. Moustakas and Hosmer just haven't been good enough. If they stay through their arbitration years, they'll likely clear the longevity barrier. I don't think their defensive value is strong enough. Then again, Rojas is there.
Omar Infante. He won't be with the team longer than four years total.
Time for the pitchers. Again, I took the liberties of eliminating new guys and guys who haven't pitched much. I also eliminated some of the I-29 reliever shuttle guys like Tim Collins and Louis Coleman.
Honestly, it's tougher for the pitchers. The Royals have a longevity bar that's going to be tough to clear given the injuries that happen to pitchers these days.
Greg Holland. If the Royals hold on to him for 2015 and 2016, and he performs at the same level he has, he'll still fall short of Quiz and Monty's IP numbers. However, he'll approach 200 saves with the team while pitching at a ridiculous peak performance level. There's a chance his peak numbers might be enough for Holland to slip in. If Holland stays with the team now and after his arbitration years, he has a pretty good chance to make it in.
Wade Davis. This really depends on how the Royals see his 2014 season and Davis' role going forward if Holland is traded or not traded. He probably won't have the longevity unless the Royals extend him. Yordano Ventura and Danny Duffy fit here as well. It's not because of their talent. It's because they are both injury risks due to velocity and history, respectively. Injuries could easily keep them from reaching longevity thresholds, but it's so early in their careers that it's hard to say much about them. We're all waiting for Kelvin Herrera to fall apart, but if he takes over the closer role long-term after Davis and Holland leave, and holds on to it for a long time, he has a shot.
Guthrie and Vargas. Free agent guns-for-hire who won't have the longevity or the performance.
So here's the summary. Gordon should be a Royals Hall of Famer without needing to add anything to his resume. Escobar and Perez need to log more time with the team but have a decent chance if they don't fall apart. Greg Holland has a shot if he maintains his peak and the team doesn't trade him. The others are all longshots or have no shots at all.