buttype == quickfix plus WinEnter

I would like to set the (unfortunately global) scrolloff option dynamically.
To accomplish that, I use the following construct (simplified):

autocmd BufEnter * call SetScrollOff()

function SetScrollOff()
let &scrolloff = &buftype == "quickfix" ? 3 : 5
endfunc

This approach works fine for non-quickfix windows.
However, when entering the quickfix window *for the first time* with e.g. :qf, scrolloff is not getting set.
When entering the quickfix window the next time, the approach works as intended.

Do I use the wrong
a) event,
b) comparison?

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