You've had 2900 putts (or, attempts at putts). Lets assume that at least 2/3 of those were from under 5 feet away.
To increase your putts made from less than 5 feet by just 1%, you need to make 20 putts in a row from this distance. That means to get it over 50%, you need to make 160 putts in a row (well slightly more actually), assuming what you're saying is correct (that you make 90% of these putts), you'd actually make 160 putts, and miss about 16 putts in between
..meaning that almost 200 putts later, you've increased by about 7% (200 putts is about equivalent to 15-18 9 hole games depending on how good you are - 200 putts from 0-5 feet is equivalent to more like 20-25 9 hole games)
That meant that 20-25 9 hole games later (or about a week or two depending on activity) you'll increase by 7%
I've checked on a few of WGTs averages (driving accuracy, GIR) and they all ring true for me...never did analysis on putting averages yet but I'd be happy to do so if anyone wants me to...but fairly sure that'll ring true also
Rob