1995 Armenian Premier League Season

The navy dot is the actual value, the gold line and key are the model's reference where one applies, and the slate ticks are the cutoffs between read labels listed under each metric.

Home Edge

Share of matches won by the home team minus the share won by the away team.

No Edge: under 5% * Slight Edge: 5% to 10% * Clear Edge: 10% to 14% * Strong Edge: 14% and up.

Elo Value

Number of Elo rating points one goal is worth. A team this many Elo points better than another is expected to win by one goal on a neutral field.

Scoring Tilt

Average home goals minus average away goals per match. The gold line is the home goals edge implied by the scoring value of an Elo point and the home-field Elo bonus.

Road-Tilted: under -0.2 * Neutral: -0.2 to 0.5 * Home-Tilted: 0.5 to 1.2 * Strong Home: 1.2 and up.

The navy dot is the actual value, the gold line and key are the model's reference where one applies, and the slate ticks are the cutoffs between read labels listed under each metric.

Title-Race Openness

Effective number of teams with a live shot at finishing 1st, from the simulation. 1 means the favorite is a near-lock; larger means a wide-open race. Equal to 1 divided by the sum of squared title odds.

One-Team Race: under 2 * Top-Heavy: 2 to 3 * Open: 3 to 4 * Wide Open: 4 and up.

Title Margin

Points-per-game gap between the champion and the runner-up. Shown per game so it reads the same across long and short seasons. The gold line is the winning margin the model expected, so a dot to the right means a more one-sided race than projected. A title won on goal difference shows 0.00.

Photo Finish: under 0.07 * Tight Race: 0.07 to 0.19 * Comfortable: 0.19 to 0.27 * Runaway: 0.27 and up.

The navy dot is the actual value, the gold line and key are the model's reference where one applies, and the slate ticks are the cutoffs between read labels listed under each metric.

Luck Spread

Standard deviation of the gap between each team's actual points and their simulated average points. The gold line is the spread the model expected from chance alone.

As Expected: under 1.9 * Some Luck: 1.9 to 2.86 * Lucky: 2.86 to 3.81 * Wild Swing: 3.81 and up.

Average Finish Error

Average gap between where each team was projected to finish and where they actually finished in the table.

Pinpoint: under 1.54 * Close: 1.54 to 2.31 * Off: 2.31 to 3.08 * Way Off: 3.08 and up.

Biggest Overachiever

The team that finished highest inside its own range of simulated outcomes. The gold line is where the top team in a league of 12 typically lands.

Biggest Underachiever

The team that finished lowest inside its own range of simulated outcomes. The gold line is where the bottom team in a league of 12 typically lands.

Season Outliers

Number of teams that finished above the 95th or below the 5th percentile of their own simulated range. Even a well-calibrated model expects about 10% of teams in the extremes.

Minimal Outliers: under 12 * As Expected: 12 to 19.2 * Several Outliers: 19.2 to 26.4 * Many Outliers: 26.4 and up.

The navy dot is the actual value, the gold line and key are the model's reference where one applies, and the slate ticks are the cutoffs between read labels listed under each metric.

Gini Index

How evenly points were spread across the league. Lower means a tight, balanced table; higher means a few teams ran off with most of the points.

Balanced: under 0.2 * Even: 0.2 to 0.25 * Top-Heavy: 0.25 to 0.28 * Lopsided: 0.28 and up.

Noll-Scully

Take a league where every match is a coin flip and nobody is better than anybody. You would still get a table, with a leader and a bottom club, purely by luck, and you can work out how far apart that table would be. This is the real table measured against it. At 1.00 the season was no more spread out than pure chance; at 2.00 it was twice as spread out, which takes genuine differences in quality. Dividing by the luck figure is what makes seasons of different lengths comparable, because a short season spreads a table by luck alone far more than a long one does. Elo SD in the corner is the same question in rating points: how far apart the teams finished on the ratings.

Coin-Flip Parity: under 2.25 * Moderate Separation: 2.25 to 2.55 * Strong Separation: 2.55 to 2.8 * Wide Separation: 2.8 and up.

Interquartile Edge

Chance the team at the 75th percentile of Elo would beat the team at the 25th percentile on a neutral field. Higher means a bigger gap between the upper and lower half of the table.

Even: under 72.5% * Slight Edge: 72.5% to 85% * Clear Edge: 85% to 89% * Wide Edge: 89% and up.

Best vs. Worst

Chance the top-rated team would beat the bottom-rated team on a neutral field. The gold line is how large that gap tends to be in a league of this size; a dot to the right flags an unusually dominant or unusually weak team.

Even: under 93.5% * Clear Edge: 93.5% to 97.5% * Strong Edge: 97.5% to 99% * Dominant: 99% and up.

Close Games

Share of matches decided by 1 goal or fewer, draws included. The gold line is how many close games the matchups and the scoring value of an Elo point predict.

Few: under 47% * Some Drama: 47% to 56% * Frequent: 56% to 64.5% * Very Frequent: 64.5% and up.

Blowouts

Share of matches decided by 3 goals or more. The gold line is how many routs the matchups and the scoring model predict.

Rare: under 15% * Occasional: 15% to 20.5% * Frequent: 20.5% to 32% * Very Frequent: 32% and up.

The navy dot is the actual value, the gold line and key are the model's reference where one applies, and the slate ticks are the cutoffs between read labels listed under each metric.

Brier Score

How close the pregame probabilities landed to the actual result, averaged over the season. Confident, correct calls are rewarded most; confident misses are punished most. Lower is better; since draws are possible, a score under 0.66 beats guessing the base rate.

Highly Predictable: under 0.56 * Predictable: 0.56 to 0.62 * Hard to Predict: 0.62 to 0.66 * Coin-Flip: 0.66 and up.

Matchup Imbalance

How lopsided the matchups were on paper, averaging the gap between the two win probabilities over their sum. 0 means every match was a toss-up; 1 means every match was a heavy favorite against a big underdog.

Very Even: under 0.45 * Slight Separation: 0.45 to 0.51 * Notable Separation: 0.51 to 0.57 * Lopsided: 0.57 and up.

Strangeness

How wild the final table was versus what the model expected. A value of 1 means teams landed about one standard deviation from their projections on average. Above 1 is a stranger season; below 1 hugged the projections.

Very Predictable: under 0.8 * As Expected: 0.8 to 1.1 * Wilder Than Modeled: 1.1 to 1.4 * Chaotic: 1.4 and up.

Repeatability

How closely the final table order matched the preseason Elo order, by Spearman rank correlation. Higher means last season's ratings strongly predicted this season's finish. Shows N/A for an inaugural season.

Weak Carryover: under 0.37 * Some Carryover: 0.37 to 0.63 * Strong Carryover: 0.63 to 0.77 * Near-Lock: 0.77 and up.

Upset Rate

Share of matches the underdog won. The gold line is how often the model expected underdogs to win; a dot to the right means upsets ran hotter than expected.

Chalky: under 16% * As Expected: 16% to 19% * Upset-Prone: 19% to 23% * Very Upset-Prone: 23% and up.

Clear Favorite Upset Rate

Share of matches the underdog won, counting only games with a clear favorite (at least 60% likely to win once a draw is set aside). The gold line is how often the model expected these favorites to slip.

Solid Favorites: under 12.5% * As Expected: 12.5% to 15% * Shaky Favorites: 15% to 19% * Very Shaky: 19% and up.

The navy dot is the actual value, the gold line and key are the model's reference where one applies, and the slate ticks are the cutoffs between read labels listed under each metric.

Probability calibration

An all-in-one chi-square test of the model's probabilities. Matches are grouped by how confident the model was, and within each group the predicted and actual counts of home wins, draws, and away wins are compared. The p-value is plotted; above 0.05 means well-calibrated.

Miscalibrated: under 0.05 * Borderline: 0.05 to 0.1 * Well Calibrated: 0.1 to 0.5 * Excellent: 0.5 and up.

Calibration slope

Checks whether the spread of the probabilities is right. Each probability is turned into log-odds and a line is fit predicting the actual results. A slope of 1.00 is perfect; below 1 is overconfidence (favorites lost more than their odds implied); above 1 is under-confidence.

Overconfident: under 0.85 * Calibrated: 0.85 to 1.15 * Underconfident: 1.15 to 1.3 * Very Underconfident: 1.3 and up.

Calibration error (ECE)

The average gap between the model's stated chances and how often the predicted result actually happened. Smaller is better. The gold line is the noise ceiling, the error luck alone can produce even with perfect probabilities; below it, the model's error is no larger than chance.

Well Within Noise: under 0.21 * Near Noise Ceiling: 0.21 to 0.31 * Above Noise: 0.31 to 0.42 * Well Above Noise: 0.42 and up.