Analysis: to figure out the average (mean) length of time a filmmaker will work until becoming a professional director. I was also interested in their career background before reaching a professional status since there seems to be little information on this elsewhere.

I collected data from the Internet Movie Database (IMDb.com) to complete a simple analysis of the queries noted above -- its resulting data is shown below. I defined "timespan" as the difference between a filmmaker's earliest credit on IMDb and their first professional directorial debut, and omitted timespans less than 3 years due to insufficient information. I defined "professional" by an amount of IMDb ratings (>50).

Findings: Although the number of entries is 184 directors, and therefor not statistically significant (it's time consuming doing this manually), it is still clear that a few patterns emerge: first, the average time to become a professional director is about 11.5 years. Second, the most common careers before becoming professional were: 

1) Actor

2) Short Film / Music Video Director

3) Assistant Director

With Producer next, and the rest roughly tying for fifth.

Conclusion: It's important to note these are likely conservative estimates since not everyone has their early careers ledgered accurately within IMDb. In any case, for anyone wishing to become a professional director it seems the most efficient manner of doing so is by creating short films and music videos (since this method has the highest percentage-to-time ratio, nearly 2:1).