Onset putters are a little hard to come by, but can make a big difference to your putting. The definition of onset is that the shaft attaches into the head in such a way that the face of the putter is "ahead" (i.e. closer to the target of your putt) than the leading edge of the shaft.
There are two major why you might want to choose an onset design:
1. You can see the whole of the top edge of the putter blade without your vision being obscured by the shaft.
2. Your aiming may improve by using an onset design. Although this is not always the case, the majority of people aim further right with an onset putter and further left with an offset putter.
Unless you invest in a fitting with a well trained putter fitter who can measure how accurately you aim a variety of putters with offset and onset, your best option is going to be to try out the putters you like from short range (say 2-3 feet) and see how consistently you can get the ball going right into the middle of the hole.
If you're sneaking too many in at the sides of the hole from this range, it's likely that you're not aiming the putter very well. If that's the case from 2-3 feet you're almost never going to succeed from 10 or 20 feet.
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