I had few L's and F's, before I was granted Z in 2011. Z sponsor, Tianjin Middle School wanted HK as visa pick-up location, but Tianjin PSB required I apply for Z in country of origin, what is customary for Tianjin, Beijing, Guangdong, and few other PSBs.

In 2012, my Residence permit expired, and new School asked for 30 days L visa to complete all necessary documents for Z. HK Embassy granted only 15 days L. Reason given was: 'too many L's'.

35 days later, I was granted new Z, and I am currently milking it.

In general, the more visas you have had, no matter the type, the better your chances of a new one providing you complied (your record) with all regulations, and broke no law or regulation while in China.

This is why, for example with tourist (L) visa, the first ones are for 3 or 6 months duration, one or two entries, and 30 days.  If good behavior while in China, subsequent ones will show more latitude.  While you will not get a two years, multiple entry, 180 days stay on your first try, it may come to you down the line. 

Its never good to work on an F visa or L Visa.  People like me will rat you out.  Power to the Z Visa holders.

Don't be a fool ok?, If you have an F visa or L visa for a year or less, they will not give you a Z visa after March 1st 2013, New Policy in HK, I can't speaking for other short cut countries to get Chinese visa's.