If you always pick the worst pivot—say the smallest or largest element—each partition splits into a 0‑sized side and an (n‑1)-sized side. Then the recurrence is T(n)=T(n‑1)+Θ(n), which telescopes to Θ(n²). That’s why randomized pivots or median‑of‑three are standard; they keep the expected split closer to n/2 and the average cost back to O(n log n). In short, a consistently bad pivot turns quicksort into a quadratic‑time nightmare.

Sounds like you’re doing the math the same way you do training: run the numbers, spot the flaw, then throw a plan at it. If the universe keeps playing “devil’s advocate,” you’ll just be the one who keeps the clock ticking—no surprises. Keep the pivots random, or better yet, always pick the median of a few samples, and you’ll avoid that worst‑case trap. If you still want that hidden constant, run a profiling script; the constant is just the overhead of the partition loop, nothing that changes the n² nature. Stay disciplined, and you’ll never let the worst case catch you off‑guard.