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The relative importance of putter path versus putter face angle can be seem from the below two experiments. In the first experiment, the putter stroke path is straight towards the hole, while the putter face angle is off from being squared at impact. In the second experiment, which is shown in Part 2, the putter stroke path is way off from the hole, while the putter face angle is kept squared at impact.
Experiment #1 – Putter Path Good while Putter Face Off.
Figure 1-1.

Figure 1-2.

Figure 1-3.

Figure 1-4.

Figure 1-5.

Figure 1-6.

Figure 1-7.

Figure 1-8.

Figure 1-9.

Figure 1-10.

Figure 1-11.

Figure 1-12.

Figure 1-13.

Figure 1-14.
The above sequence of photos shows the putter stroke path is straight towards the hole, but the putter face angle at impact (Figure 1-4) is off pointing to the right of the hole. As a result, the ball takes off in the direction where the putter face is pointing at impact, rather than the ball traveling in the direction of the putter head stroke path.
A good putter stroke path is useless, if the putter face angle is poor at impact.
(Continued in Part 2 …)