Ok - I've done a little research and here is a partial answer. Of the 16 most active seasons since 1885 (see the Met Blog for years) with 14 or more named storms, the average date for the fourth storm of the season was August 2nd. The five seasons that had the latest start date for the 4th storm were:

1969 (18 storms) 8/14
2000 (15 storms) 8/19
2001 (15 storms) 8/22
1998 (14 storms) 8/24
1953 (14 storms) 8/28

With no storms on the horizon for the next few days, the statistical (and climatological) likelihood of 16 or more named storms for this season is just about zero, however, a total of 14 or 15 named storms this year is still statistically possible.
ED