Originally a classical military term — 败绩 in 《左传》 and other early texts described the catastrophic rout of an army. It now mostly survives in two contexts: war/history writing (a major military defeat) and sports commentary (an undefeated record described as 没有败绩).
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Written/literary. In casual speech you'd just say 输 (lose) or 输了几场 (lost a few games). 败绩 carries weight — it implies a recorded, total defeat, not a minor setback.
