A Note on Degrees of Freedom
We are using the sample to estimate the standard deviation, which recall measures how widely the data is scattered.
You cannot get information about how widely data is scattered if you have only one data value.
So, the general idea is that the first data value gives no information and the remaining n - 1 values, the number of degrees of freedom,
gives an estimate of the standard deviation.
If you think this is a rotten explanation: Sorry, do Nike math and just do it.