
hinken
to limp
To move unevenly and with difficulty because one leg is injured or shorter.
Seit seinem Skiunfall hinkt er auf dem linken Bein.
Since his skiing accident, he has been limping on his left leg.
to limp / lag
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to limp
To move unevenly and with difficulty because one leg is injured or shorter.
Seit seinem Skiunfall hinkt er auf dem linken Bein.
Since his skiing accident, he has been limping on his left leg.

to lag behind
Figuratively, to fall behind a development, performance level, or standard.
In der Digitalisierung hinkt die deutsche Verwaltung anderen Ländern hinterher.
In digitalization, the German administration lags behind other countries.

to be flawed
In the expression 'der Vergleich hinkt' (the comparison is flawed): to be inappropriate or not accurate.
Dein Vergleich hinkt, weil du zwei völlig unterschiedliche Situationen gleichsetzt.
Your comparison is flawed because you are equating two completely different situations.
Although 'hinken' (to limp) describes movement, the perfect tense is formed with 'haben' (to have) and not with 'sein' (to be). This is an important exception to the general rule for verbs of movement.
Nach seiner Knieoperation hat er wochenlang gehinkt.
After his knee operation, he limped for weeks.
To express which leg is affected, you use the preposition 'auf' followed by the dative. Alternatively, you can also use 'mit' and the dative.
Das alte Pferd hinkt auf dem linken Hinterbein.
The old horse is limping on its left hind leg.
In the figurative sense, 'hinken' (to lag) is often combined with the adverb 'hinterher' (behind). The expression 'hinterherhinken' means to lag behind compared to others.
Das Projekt hinkt dem Zeitplan deutlich hinterher.
The project is lagging well behind schedule.
The idiom 'der Vergleich hinkt' (the comparison is flawed) is very common. It expresses that a comparison is inappropriate or logically flawed.
Du kannst die Kosten nicht einfach so gegenüberstellen, der Vergleich hinkt.
You can't simply compare the costs like that; the comparison is flawed.
to stay behind / fall behind
Both verbs can express that a performance does not reach a benchmark. Zurückbleiben describes this neutrally and is usually used with “hinter.” Hinken is more figurative and, in this use, typically occurs with “hinterher” or also with “hinter.”

Die Leistung des Teams hinkte den Erwartungen hinterher.
The team's performance lagged behind expectations.
Die Leistung des Teams blieb hinter den Erwartungen zurück.
The team's performance fell short of expectations.