Wald–Wolfowitz runs test, permutation
Are clubs streaky?
A runs test on every club's win-loss sequence, and two thousand shuffled seasons to see how long a streak chance alone produces.
Computed on request from the record book (Oct 13, 2026) and 720 finals in the game log.
The finding
Run the Wald–Wolfowitz test on each club's sequence of wins and losses and none of the 10 comes out streakier than chance at the 5% level — about 0.5 would by luck alone. The most clumped sequence belongs to Hanwha (z = −1.86, p = 0.06), the most alternating to Doosan (z = +0.46). Pooled across the league, z = −2.03 (p = 0.04): a faint league-wide lean toward clumping, though the cause could as easily be the schedule as momentum.
SSG's 13-game losing streak is the season's longest. Shuffle the same 65–74 record 2,000 times and a streak at least that long turns up in 1% of them. That one is genuinely rare for a single club — though across ten clubs, the chance that at least one produces a streak this unlikely is about 12%. Most long streaks are ordinary: in a typical shuffled season, a club's longest run is about 7 games.
Streaky at 5%
0 / 10
0.5 expected by luck
League, combined z
−2.03
p = 0.04
Longest streak
13
SSG, losses
Shuffled seasons that long
1%
of 2,000
Every club's season, game by game
Wins above the line, losses below, in the order they were played; ties are left out. The rule above and below marks each club's longest winning and losing streak.
Runs test, club by club
Each club's z-score: negative means fewer runs of wins and losses than chance expects, so the results came in clumps. The bar is the range chance produces 95% of the time.
| Club | W–L | Runs | Expected | z | Longest W | Longest L | Shuffled ≥ |
|---|---|---|---|---|---|---|---|
| Hanwha | 57–83 | 58 | 68.6 | −1.86 | 5 | 11 | 14% |
| Samsung | 83–58 | 63 | 69.3 | −1.10 | 8 | 7 | 60% |
| NC | 64–78 | 65 | 71.3 | −1.07 | 7 | 8 | 44% |
| SSG | 65–74 | 64 | 70.2 | −1.06 | 5 | 13 | 1% |
| KIA | 79–63 | 66 | 71.1 | −0.87 | 8 | 5 | 43% |
| Lotte | 64–77 | 67 | 70.9 | −0.67 | 7 | 7 | 70% |
| LG | 78–65 | 69 | 71.9 | −0.49 | 8 | 8 | 45% |
| KT | 90–49 | 65 | 64.5 | +0.10 | 10 | 3 | 46% |
| Kiwoom | 50–90 | 66 | 65.3 | +0.13 | 5 | 10 | 45% |
| Doosan | 73–66 | 73 | 70.3 | +0.46 | 4 | 5 | 99% |
Method
A run is an unbroken stretch of wins or of losses. With n₁ wins and n₂ losses in random order, the number of runs R has a known mean and variance; a z-score below zero means fewer, longer runs than chance — streakiness.
E[R] = 2n₁n₂ ÷ n + 1 · Var[R] = 2n₁n₂(2n₁n₂ − n) ÷ (n²(n − 1)) · z = (R − E[R]) ÷ √Var[R]
The streak-length check shuffles each club's own results 2,000 times on a fixed seed, keeping its win and loss totals, and counts how often the longest streak of either kind is at least as long as the real one. The league figure combines the ten z-scores by Stouffer's method, z = Σzᵢ ÷ √k.
Ten tests on one page: at the 5% level, the chance at least one clears by luck is about 40%. A club's quality also genuinely changes within a season — injuries, call-ups, a run of games against the top of the table — and that produces clumping the runs test cannot tell from momentum. The test only sees order, not margins, and it drops ties.