Assuming a 385 day maleh leap year in Diaspora and no Torah portions doubled which would yield 54 Shabbatot.
Every day of the year has, Ma'ariv, Shacahrit and Mincha. Including both silent & repetitions you get 5 Amidot per day.
385 * 5 = 1,1925
Add an extra 2 for the days of Musaph:
54 Shabbatot + 20 days Rosh Hodesh + 22 Yom Tov = 96 days * 2 Amidot = 192
Total 1,925 + 192 + 2 = 2,119.
However, within this count, 2 of the Shabbatot occur during a Yom Tov, and I've included that in the Yom Tov count, so, I'm subtracting 2 Musaphim.
So, your total is 2,117. If I have calculated incorrectly, please update.
This is for a year with such configuration and only in Diaspora. In Israel, the count is less, regular years would be at least 30 days less (depends on year type), and of course, the kevi'ah will influence how many Shabatot there are in the year.
(DoubleAA wasn't that far off!)