I guess that I should preface my answer by noting that, although it seems active, we have only had two named storms so far - which is not that unusual. But its still an interesting question.

I looked at the past 60 years of data and looked for seasons that had at least two storms on or before July 15th but ended up with a season total of 11 storms (average season) or less. A total of 12 seasons out of 60 met the criteria - which is 20% of the time (a bit surprising). Here is the list:

1948 - 9 total
1957 - 8 total
1959 - 11 total (4 storms before July 15th)
1960 - 7 total
1966 - 11 total (3 storms before July 15th)
1968 - 8 total (3 storms before July 15th)
1972 - 7 storms
1979 - 9 total (3 storms before July 15th)
1982 - 6 total
1986 - 6 total
1989 - 11 total
1997 - 8 total (4 storms before July 15th)

The 1997 season had a 5th storm on July 16th, with only 3 more for the rest of the season - but that was also the year of the strongest El Nino ever recorded. I also took a look at it the other way, i.e., what were the seasons that had two or more storms by July 15th with a season total of 12 storms or more. I found 8 seasons out of the 60 - or 13% of the time, and here is that list:

1964 - 12 total
1971 - 13 total
1981 - 12 total
1995 - 19 total (3 storms before July 15th)
1996 - 13 total
2003 - 15 total (3 storms before July 15th)
2005 - 28 total (5 storms before July 15th)
2007 - 15 total

Note that the bulk of these active seasons were during the current level of higher activity that started in 1995.
Cheers,
ED