server response time gtmetrix vs ping

The definition of Time To First Byte (by gtmetrix) is: "Redirect duration" + "Connection duration" + "Backend duration"

Thus, a ping is obviously irrelevant in this measurement. Your 1.6 seconds is a combination of the above three durations, probably most of that is the Backend, which is usually the longest delay.

edit

I just run gtmetrix on one of the e-shops I've built, it comes up with:

PageSpeed A (99%)

YSlow A (90%)

Fully Loaded Time 2.4s

Total Page Size 400KB

Requests 16

Fully Loaded Time is derived from:

Redirect 0ms

Connect 321ms

Backend 220ms

TTFB 0.5s <– This is my Time To First Byte

First paint 1.0s

DOM int. 1.5s

DOM loaded 1.5s (1ms)

Onload 1.6s (9ms)

(gtmetrix server at Vancouver Canada, my server at Frankfurt Germany)