Teams, Luck & the Title Sim

Why the #1 team still loses 7 times out of 8

This is the whole point of the page. The model spits out a single chip% per team. That number is easy to distrust — so let's take it apart into pieces you can check by hand. A title requires clearing three single-elimination games: a conference semfinal (1v4 / 2v3), a conference final, and the grand final. So:

chip% = P(make playoff) × P(win conference | in) × P(win grand final | in final)

The two right-hand pieces are derived columns — we compute them straight from the model's own outputs:

• P(win conf | in) = reach_final% ÷ make_playoff% — of the times you make the bracket, how often you come out of your conference.
• P(win GF | in final) = chip% ÷ reach_final% — of the times you reach the grand final, how often you win it.

Read the last column first. Every single team's P(win GF | in final) lands between 47% and 53%. That is not a coincidence and it is not the model being lazy — it's the grand final being a coin flip for everyone, favorite or underdog. The middle-derived column, P(win conf | in), clusters near 22–27% — because winning your conference means clearing two single-elim games, and 0.5 × 0.5 = 0.25.

Why each game is ≈50/50 — and how we know it's not just the model

The sim rates teams from the combine, but the combine explains only ~6% of the variance in a game's final margin. Put differently: 94% of what decides a science-bowl game is stuff no pre-game rating can see. Collapse a rating edge that small into a win/loss and you get something very close to a coin toss.

Crucially, this is corroborated by data that has nothing to do with our model. The league's internal prediction market — real people, real stakes, setting pre-game prices on 60 games — finished the season calling those games at a 50/50 clip. A room full of motivated forecasters could not beat a coin flip on individual games. When an outside signal and our sim independently land on "it's a coin flip," that's the number being discovered, not invented. SOLID

Worked example — mingle/Yunyi, the best regular-season team

Mingle is the cleanest case because their playoff berth is already locked, so their title math is just the three playoff coin flips with no "do they even make it" discount:

• Make playoff = 100.0%. They're in. No qualifier.
• Reach final = 25.2%. That's two wins (semi + conf final): 0.5 × 0.5 = 25.0%. The sim says 25.2%. Basically 0.5².
• Chip = 12.2%. That's three wins: 0.5 × 0.5 × 0.5 = 12.5%. The sim says 12.2%. Basically 0.5³.
• And the derived third flip: chip ÷ reach_final = 12.2 ÷ 25.2 = 48.4% — the grand-final coin flip, right on ½.

So the model's headline "mingle 12.2% to win it all" isn't a black-box guess. It's 0.5³ ≈ 12.5%, three coin flips stacked, reproduced by hand from two ratios. The mild shortfall vs. a pure 12.5% is the small rating edges nudging matchups a hair off 50/50 in both directions.

Method: make_playoff%, reach_final%, chip% are direct sim outputs (season_sim_odds.csv, 30k trials). The two rightmost columns are exact ratios of those, computed here — no new modeling. The 47–53% band on the final column is the model's honest statement that the grand final is a toss-up for every finalist.

Chip odds & seed distributions — both conferences

The complete sim output. Seed 1–4% is how often the team lands on each playoff line; Miss% is how often they're out. Rows sum across the seed/miss columns to 100%. SOLID as a model — with the top-4 caveat below.

The top four is a dead heat, and we can prove it. cryo 13.9 / sumin 13.8 / James W 13.6 / mingle 12.2 all sit within ~2× the Monte-Carlo standard error (±0.2pp at 30k trials). Calling cryo "the favorite" over sumin is reading noise. TINY n — the ratings underneath are 4–5 games old.

Two structural reads that the seed columns justify

• Dark horse — ChessFun. Only 61.5% to make the bracket (the biggest bubble in the field — see its 38.5% Miss), yet 7.9% to win it all. Its P(win GF|final) of 51.0% and P(win conf|in) of 25.2% (top of Section A's decomposition) are contender-grade — the only thing holding its chip% down is getting in. SOLID
• West cannibalism. cryo and James W are both title-caliber but share a conference, so one must eliminate the other before the grand final. That's visible in the board: the West's two best can't both reach the final, which caps the conference's combined chip odds. Good "why the bracket matters" beat. COLOR

Pythagorean wins — who the scoreboard has been kind to

Baseball's oldest sabermetric: from a team's points for and points against, how many wins did they "deserve"? expected_wins = PF^k / (PF^k + PA^k) × games, with the exponent k pinned at 2.37 (the documented cross-sport default). Luck = actual − expected. TINY n (4–5 games).

DANK is the luckiest team in the league — 3 wins on a −74 point differential. By the points they've deserved 1.4 wins; they've banked 3. Ponnor St. Germain (Connor Chang) is the unluckiest — a positive +22 differential and just 1 win, when the math says ~2.1. The best team by raw points, robbed by the scoreboard. TINY n

Method / honesty box: k=2.37 is the documented default, not a fit. We tried fitting k freely, but on 4–5 games it collapses to k≈1.1 and just chases noise — so we pin the default. Reassuringly, the luck ordering is stable across k=1.1–3.0, so the "who's lucky / who's unlucky" ranking isn't an artifact of the exponent. Still a small sample — directional.

Who's had it easy, who's run a gauntlet

SoS(played) = average strength of opponents faced, relative to league average. More negative = easier slate; more positive = harder. Rank 1 = easiest played schedule. COLOR (opponent strength itself rests on 4–5 games).

dan.k.memes has run the hardest gauntlet in the league (+9.3) — and is still 3rd in the East at 3-1. That's the most impressive record-relative-to-schedule on the board, and it pairs with the luck note above: their record survives both the toughest slate and a negative point differential. anurag has the easiest slate (−6.6) and sits 7th — no schedule alibi for that record. COLOR

Method: "own strength" is the team's own rating (context for why their slate rates as it does — a strong team makes everyone else's schedule look harder, and vice-versa). PADDED / GAUNTLET flags mark the extreme quartiles. Still Weeks 1–5, so opponent ratings will move.

One-man teams vs. true teams

HHI (Herfindahl index) of scoring share: sum of each scorer's squared share of team points. High HHI = concentrated (one carry); low HHI = balanced. SOLID as color — it's a descriptive split of who scored, not a projection.

Most one-man team — Ponnor St. Germain: 58.1% of all points come from Kian D alone (HHI 0.417). CZZ is close behind (59.5% from vishnu m). At the other pole, Fez_Keyreb is the most balanced true team (HHI 0.219) — five scorers, top gun Chris W at just 25%. SOLID

Method: shares computed on scored points only across Weeks 1–5; a no-show week naturally inflates the concentration for teams that lean on one player. The single-carry read (Ponnor / CZZ) also connects to the luck note — thin, top-heavy rosters are exactly the ones whose results swing hardest game to game.

Fattens up on the weak, shrinks against the good

Split each team's average margin into games vs. contenders (top-4-by-rating per conference) and vs. bottom teams. bully_gap = margin_vs_bottom − margin_vs_contender. A big positive gap = pads stats against weak teams but disappears against real ones; a negative gap = raises its level in big games. TINY n — 1–4 games per bucket; a single blowout can make a gap.

mingle/Yunyi is the flat-track bully — +111 vs. bottom teams but −19 vs. contenders (gap +130). Their gaudy point differential is built on beating up the weak; against the field's best they've actually been outscored. That's the honest asterisk on "best regular-season team." The mirror image: GidTheKid2 is the big-game riser — +19 vs. contenders, −112 vs. bottom (gap −131). They shrink against bad teams and rise against good ones. TINY n

Method / honesty box: buckets are tiny (see the game counts in-cell). Connor Chang's league-leading +151 gap is one −108 blowout vs. a contender — noise, not a trend, which is why we lead with mingle (2g/2g, cleaner split). Directional only; a big gap is usually one game.

What if everyone had shown up?

We re-ran the season giving every team its full-strength roster (no no-shows) and compared to reality. The counter-intuitive result — and it's the same mechanism as the whole page: because games are near coin-flips, no-shows barely move the WIN column. Full-strength win probabilities span only 0.46–0.54, so pulling a star swings a game's odds by a few points, not from a win to a loss. The biggest phantom swing anywhere is ~0.1 wins. SOLID (self-labeled razor-thin).

The story isn't lost wins — it's points left on the table. xpoes leaked the most: +19.3 points of margin to their own no-shows (Rohan G missing two games is the single biggest individual line, ~10 pts). But that converts to only +0.09 phantom wins — not enough to change a single playoff berth on its own. The one seed flip in the whole table is cosmetic: at full strength (Stitch)² would edge into the West top-4 (seed 5→4) and ChessFun would drop out (4→5) — but on a +0.08 / +0.03 win margin, i.e. a point-differential tiebreak shuffle, not a real gap. SOLID

Method: phantom = re-sim with full rosters, win prob = Φ(margin / 56). The seed 4↔5 flip is explicitly razor-thin (a tiebreak shuffle worth <0.1 wins) and should be framed as such, not as "attendance decides the bracket." Attendance is a real lever for point margins; it just doesn't cash into wins in a coin-flip league.