I’m assuming you can prove 15 > 18...
15 can be bigger than 18. 15 hundred dollar bills is much more than 18 twenty dollar bills.
Wherever we land on this, I think it's reasonable to say that Tiger's 82 tour wins is mind boggling. It's more than DJ (20), Rory (18), Day (12), Spieth (11), Thomas (11) and Koepka (7) combined.
Looking at the all-time tournament wins list, Tiger and Phil are the only guys in the top ten who are younger than Jack (who will be 80 in a couple of months I think). Among players born since 1950, there are 2 in the top 10, 3 in the top 29 and you have to get down to 34th to find someone younger than Tiger (DJ with 20). The top 50 has 12 people born since 1950. Those are:
Tiger, Phil, Vijay, Davis Love III, DJ, Greg Norman, Crenshaw, Ernie, Rory, Nick Price, Jim Furyk and Curtis Strange.
Sliding back to 1940, you can add Jack, Tom Watson, Johnny Miller, Ray Floyd, Lanny Wadkins, Hale Irwin, Hubert Green and Tom Kite.
So 20 of the top 50 were born in 1940 or later. The remaining 30 were all born before that. Seems to me like winning lots of tournaments was easier back in the past. Counts by decade of birth in the same list (top 50)
1980s - 2
1970s - 3
1960s - 3
1950s - 4
1940s - 8
1930s - 5
1920s - 4
1910s - 8
1900s - 8
1890s - 7
1880s - 1
There are 53 here because 4 people are tied for 50th on the list (17 wins apiece). The 1880s and before didn't really have much to play for and the 1980s are potentially not yet done getting onto this list (Adam Scott has the most of those in the 1980s, but not in the top 50 with 13 wins, so he needs 4 more to break into the top 50). 1970s are potentially not done too. Zach Johnson and Bubba Watson have 12 wins apiece, so 5 more to break into the top 50. From the 1990s, Jordan Spieth and Justin Thomas are highest with 11 each.
Allowing for all this, there certainly does appear to be a pretty solid trend. Tournament wins have been getting harder and harder to come by as time has gone by and the game has grown in popularity and global reach. Where else have we seen this? Oh right yes - with majors too.