Looking through the list of goalies in the Hall of Fame sorted by birthday, there seems to be a repeating pattern. Several goalies will be inducted that were all born over a short time period. That will be followed by an extended dry spell, before another cluster of similarly-aged candidates gets enshrined. This is followed by another gap, and the cycle repeats.
This doesn't particularly apply to the oldest goalies in the Hall of Fame (Hugh Lehman, Georges Vezina, Hap Holmes, Clint Benedict and George Hainsworth), all of whom were born between 1885 and 1895. Then again, things were quite different back then in hockey's early days, with several different professional leagues, teams folding and moving all the time, and some goalies having very atypical career curves, often playing many years of amateur hockey before breaking into the professional at an advanced age.
The first group of Hall of Fame goalies who spent the large majority of their careers in the National Hockey League were born around the turn of the 20th century: Roy Worters (1900), Alec Connell (1902), Tiny Thompson (1903), and Charlie Gardiner (1904). After those four, it took a decade to produce the next Hall of Famer (Turk Broda in 1914).
Broda was quickly followed by Brimsek the following year and Bill Durnan the year after that to create the trio of goaltending legends that dominated the NHL in the 1940s. In the decade after Durnan, Chuck Rayner (1920), Johnny Bower (1924) and Harry Lumley (1926) were born. Lumley and especially Bower made most of their Hall of Fame cases after the previous "Big Three" had retired.
Perhaps the best goalie cohort of all was the 1929-1931 group, which includes Terry Sawchuk, Jacques Plante, Gump Worsley and Glenn Hall. In the wake of that dominating quartet there was a gap of eight years until the next Hall of Famer, and even then the next two inductees born (Ed Giacomin in 1939 and Gerry Cheevers in 1940) are both among the weakest goalies enshrined, with Hall of Fame cases largely built on taking advantage of an unbalanced league.
It took 12 years after Hall until the next no-doubt first-ballot Hall of Fame netminder came into the world in the person of Tony Esposito in 1943. Once again, he was quickly followed by a couple of others: Bernie Parent in 1945 and Ken Dryden in 1947, with Billy Smith arriving not far behind in 1950.
The next decade (1951 to 1961) didn't see any goaltenders born who would eventually be considered Hall of Famers, and that is probably not likely to change either with the games played leaders from that period including Mike Liut, Greg Millen, Andy Moog, Kelly Hrudey and Don Beaupre.
With 1962 came Grant Fuhr to break the drought, but 1965 was the real money year for goaltending ability, producing three first-ballot Hall of Famers in Dominik Hasek, Patrick Roy and Ed Belfour. All goalies born in 1965 combined to play a 4,687 games in the NHL, well ahead of any other year on record, and Tom Barrasso may still have an outside chance at making it four Hall of Famers from one birth year.
Yet again the feast and famine pattern looks like it will continue, with Curtis Joseph the only goalie born from 1966 to 1971 that is likely to be even seriously discussed by the Hall of Fame committee, and although some goalies have significant portions of their careers remaining the only guaranteed Hall of Famer born since 1971 remains Martin Brodeur.
What is causing all this? Is it merely that the random allotment of goaltending ability just happened to result in some groupings close together? That's likely part of it, but it's not particularly probable that a similar pattern would have repeated itself essentially four times in a row.
Factors that may have had some impact are the level of league scoring, the size and level of parity in the league, and changing league rules or revolutions in goalie training or techniques. Certain periods seemed to be set up better than others to create Hall of Famers, either because lower scoring levels led to lower GAAs and higher shutout totals or because an unbalanced league made it easier to rack up wins on the top teams.
Beyond that, it seems apparent that opportunity would have played a significant role, especially in smaller leagues with only 6 or 12 starting jobs available. In reality it was likely even more restrictive than that, given the required level of team success typically needed to produce a Hall of Fame career. With two or three teams dominating the standings year after year throughout much of the NHL's history, goalies usually either had to be fortunate enough to be signed by those elite clubs, or else they had to play well enough for long enough on one of the league's bottom-feeders that they were eventually given the chance to don the sweater of a Cup contender.
I'd say that the most likely explanation is that a few elite goalies have a tendency to monopolize awards and gravitate towards the best starting jobs in the league, making it that much harder for the guys coming after them to put together the trophy case and team success that the Hall of Fame has historically required for entry.
I don't rate goalies based on traditional accomplishments like Vezina Trophies, postseason All-Star selections and Stanley Cups, but many people do, including apparently most of the Hall of Fame voting committee. In that type of evaluation method, I think it is important to consider the strength of a goalie's teammates and the quality of goaltending peers he was competing against, and to consider not just how many times a goalie won an award but also how many times he got close to winning. After all, the best goalie in a particular season and the best goalie in the league are not always the same thing. There are additional useful ways to verify how well a goalie was rated by his contemporaries, if you consider that to be an important piece of information, such as looking at observer accounts and other primary sources, salary/trade history, international selections, coach and player polls, etc.
That said, I still maintain that a careful analysis of historical statistical performance remains the best method to properly evaluate the accomplishments of a netminder, with care taken to adjust for team factors during the parts of the league history that were more unbalanced than others.