erfahrungsgemäss
as experience shows
Based on previous experience; as experience has shown.
Erfahrungsgemäß ist um diese Uhrzeit immer viel Verkehr auf der Autobahn.
As experience shows, there is always a lot of traffic on the highway at this time.

as experience shows
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as experience shows
Based on previous experience; as experience has shown.
Erfahrungsgemäß ist um diese Uhrzeit immer viel Verkehr auf der Autobahn.
As experience shows, there is always a lot of traffic on the highway at this time.

The word is made up of 'Erfahrung' (experience), the linking -s, and 'gemäß' (according to / in accordance with). 'Gemäß' means 'entsprechend' (corresponding to) or 'laut' (according to). So the word literally means 'in accordance with experience'.
Vorsicht, diese Kurve ist erfahrungsgemäß sehr rutschig bei Regen.
Be careful; as experience shows, this curve is very slippery in the rain.
As an adverb, 'erfahrungsgemäß' (as experience shows) can stand in different positions in the sentence. If it is in position 1, the verb follows directly after it (inversion). It can also stand after the verb.
Erfahrungsgemäß dauert die Lieferung zwischen drei und fünf Tagen.
As experience shows, delivery takes between three and five days.
'Erfahrungsgemäß' (as experience shows) is often used in factual, more formal, or explanatory contexts. It signals that a statement is based on repeated observations and not just on a one-time opinion.
Die Züge sind auf dieser Strecke erfahrungsgemäß oft verspätet.
The trains on this route are often delayed, as experience shows.
normally
'normalerweise' and 'erfahrungsgemäss' can both say that something is often the case. 'normalerweise' simply describes the normal or usual case. 'erfahrungsgemäss' emphasizes that you know this from past experience. It sounds as if you have experienced similar situations several times before. If you are only describing a habit, 'normalerweise' is more natural. If you are expressing an expectation based on experience, 'erfahrungsgemäss' is more precise.

Erfahrungsgemäss ist der Zug am Freitagabend sehr voll.
As experience shows, the train is very crowded on Friday evenings.
Nach der Arbeit gehen wir normalerweise noch kurz einkaufen.
After work, we normally go shopping briefly.