When a watch is run without getting it cleaned, the grit that is dust and old oil grinds away at pivots, making them egg-shaped. Eventually, the wheel will no longer sit straight, and the watch will stop. That must have happened here. Some repairer of old has punched the brass to close the hole, then reshaped it to be more round.
The rate the watch beats is one thing. How far the hands move with each beat is a function of normal gear ratios. The calculation is called "counting the train". We count the teeth on each wheel, and the leaves on each pinion, and plug the numbers into a formula that tell us how the watch will work.
Skipping the algebra, the formula we're interested in here takes this form...
(el * bph) / (ft * et * 2) = [4th wheel revolutions per hour]
the 4th wheel carries the second hand. So 4th wheel revolutions per hour should be 60, we hope.
el is escape wheel pinion leaves
bph is the beats per hour
ft is 4th wheel teeth
et is escape wheel teeth
and 2 is.... well 2. This is actually the "teeth" on the next thing in the train, which is the 2 pallet stones.
The watch we have is running at 18000 bph.
el is 7
et is 15
ft is 13
(7 * 18000) / (13 * 15 * 2) is 66.67
That's pretty fast, it works out to 160 minutes per 24 hours fast! But this is a grade 7 Elgin. The records say this design runs at 16200 bph, here:
(7 * 16200) / (13 * 15 * 2) is 60!
Conclusion: This watch has an incorrect hairspring, which acts as a simple pendulum, causing the escapement to cycle at 18000 beats per hour rather than 16200, which the train is geared for. This simply runs the hands too fast and the watch reads incorrectly, even though it is not actually running fast.
This watch is an Elgin grade 7, 18 size, 7 jewels, made about 1883