I too use a 31 1/4 inch putter and I'm 5'13. For me it is a product of where my arms hang. If you have a face balanced putter, you are much better off cutting off your putter to the right length and it only will cost you about $10. If you don't grip down or invest in a new putter, not necessarily a face balanced putter.
My clubfitter in MN has tested over 3500 people and has found the average length of a putter should be 32 inches. The only reason they sell 34 and 35 inch putters is because they fit in the bag, they don't fit people!
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Golf can never be considered an enigma. ~HK
Mass produced, un-fitted putters are too long and too upright for nearly all of us. One of the best things you can do is spend some time getting your putter soling correctly. Bending and shortening are usually needed to complete this process.
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