On ave4rage,how many comets are discovered each year?

Around a dozen "new" comets are discovered each year. Short-period comets are more predictable because they take less than 200 years to orbit the Sun. Most come from a region of icy bodies beyond the orbit of Neptune. These icy bodies are variously called Kuiper Belt Objects, Edgeworth-Kuiper Belt Objects, or trans-Neptunian objects. Less predictable are long-period comets, many of which arrive from a distant region called the Oort cloud about 100,000 astronomical units (that is, 100,000 times the mean distance between Earth and the Sun) from the Sun. These comets can take as long as 30 million years to complete one trip around the Sun. (It takes Earth only 1 year to orbit the Sun.) As many as a trillion comets may reside in the Oort cloud, orbiting the Sun near the edge of the Sun's gravitational influence.

Congratulations to Robert Cardinal

Here's a list of the comet designations assigned in the past year

http://www.cfa.harvard.edu/iau/lists/LastYear.html

By my count that's 225.