Set Score Modeling

Default data tool: AcesAPI (acesapi-tool). get_matches (2 credits per 100 matches) gives every set and tiebreak score for building distributions. get_surface_splits (3) and get_player_stats (3) give tiebreak and games-won rates. get_match (2) has the games_total and games_spread1 lines inside odds for the few books that post them.

You model the shape of a match: how likely a straight-sets win is, how many games to expect, how often tiebreaks occur. The standard tool for this, a point-by-point serve and return model, needs first-serve and break-point data that this dataset does not contain. So this skill builds from what scores give: games won share, hold-rate proxies and empirical set distributions. Say that out loud when presenting results.

When to Use

• "How likely is a straight-sets win?"
• "What is a reasonable total games line for this match?"
• "How often do ATP matches on grass go to a tiebreak?"
• "Convert a 70 percent match probability into set probabilities"
• "Is the market's games handicap consistent with its moneyline?"

When NOT to Use

• A pure win probability from ratings: see surface-elo
• Serve speed, aces, break points, player props: not in the data
• Deciding on a bet: see edge-detection

Commands Available

Commands That Do NOT Exist

From Match Probability to Set Probability

Let q be a player's probability of winning any one set (assumed constant and independent, which is an approximation). Then:

Best of three:  P(match) = q^2 (3 - 2q)
Best of five:   P(match) = q^3 (10 - 15q + 6q^2)

To go from a match probability P (from surface-elo or a no-vig close) back to q, solve by bisection. Real example: a no-vig match probability of 0.524 (Pinnacle close for Sinner in the 2025 Wimbledon final, best of five) corresponds to q = 0.5128; in best of three the same match probability needs q = 0.516. The format matters: the same set strength gives a more extreme match probability in best of five.

Set-score distribution, best of three, for player A with set probability q:

P(A wins 2-0) = q^2
P(A wins 2-1) = 2 q^2 (1 - q)
P(B wins 2-1) = 2 (1-q)^2 q
P(B wins 2-0) = (1-q)^2

At q = 0.6: 36 percent for 2-0, 28.8 percent for 2-1, and 64.8 percent match win. These are model outputs; compare them with the empirical shares from get_matches.

From Game Win Rate to Set Probability (without serve data)

Games-won share is available per player (games_won_pct in get_surface_splits, 0.58 for one top player over a career). Map two players' shares to a matchup game probability with a log5-style formula, then to a set probability with a hold model:

from functools import lru_cache

def set_win(hA, hB, first='A'):
    """P(A wins a set). hA, hB = probability each holds serve. Alternating serve."""
    @lru_cache(None)
    def go(a, b, srv):
        if a >= 6 and a - b >= 2: return 1.0
        if b >= 6 and b - a >= 2: return 0.0
        if a == 7: return 1.0
        if b == 7: return 0.0
        if a == 6 and b == 6:
            return 0.5 + 0.5 * (hA - hB)     # crude tiebreak: tilts with the hold gap
        nxt = 'B' if srv == 'A' else 'A'
        if srv == 'A':
            return hA * go(a + 1, b, nxt) + (1 - hA) * go(a, b + 1, nxt)
        return hB * go(a, b + 1, nxt) + (1 - hB) * go(a + 1, b, nxt)
    return go(0, 0, first)

Equal holds of 0.80 give exactly 0.5; holds of 0.85 and 0.80 give q = 0.591. The problem: hold rates are not in the data. You can only calibrate them: choose hA, hB so that the model reproduces the match win probability (from ratings or the market) and the total games the market expects. That is a fitted model, not an observation. Present it as "consistent with a hold gap of about X points", never as measured serve strength.

Total Games

Observed in get_match for a real final: stats.total_games 40 over four sets, no tiebreaks. The Pinnacle row carried games_total 41.5 and games_spread1 -0.5.

Build the expectation from data, not memory:

1. get_matches for a season, filtered to completed matches of one tour, one surface, one format.
2. Per match, total games = sum over sets[] of games1 + games2.
3. Take mean and standard deviation by surface and by format. Total games are right-skewed: a few five-set matches run long.
4. Adjust for the matchup. Two evenly matched players generate more games and more sets than a mismatch. The relation is roughly monotone in the rating gap, so regress total games on the absolute rating gap, surface and format on past matches (time-ordered, see walk-forward-validation).

Use the market's games_total as a benchmark where it exists, not as a fact: it is one book's line.

Tiebreak Frequency

Tiebreak share of sets is computable from get_surface_splits:

tiebreak_share = (tiebreaks_won + tiebreaks_lost) / (sets_won + sets_lost)

From a real call (one player's whole career): hard 92 of 545 sets (16.9 percent), clay 52 of 322 (16.1 percent), grass 21 of 128 (16.4 percent). The differences are inside sampling noise, which is a useful finding in itself. Do not claim grass produces more tiebreaks from one player's record; build the tour-level rate from get_matches.

Tiebreak outcomes are close to coin flips: keep the tiebreak model near 50 percent, tilted at most slightly by the hold gap or the rating gap, and shrink toward 0.5 when data is thin.

Pitfalls

• Independence. Sets are not independent: momentum, fatigue and tactics link them. The formulas above are a baseline. Check them against empirical 2-0 and 2-1 frequencies in get_matches and correct with a fitted adjustment.
• Format mixing. Men's Grand Slams are best of five; everything else, and all WTA matches, are best of three. Never pool them for totals or set distributions.
• Retirements. A retired match has an incomplete score. Exclude outcome != "completed" from distributions, or you bias total games down.
• Walkovers have empty sets.
• Survivorship in event totals. Early rounds have more mismatches than late rounds. Condition on round or on rating gap.
• Over-reading the line. games_total appears for only a few books (Pinnacle in the examples), and games_spread1 has the same limit. Do not call it "the market" without saying which book.

Credit Usage

Anti-patterns

Output Format

[A] vs [B], best of [3/5], [surface]
Match win: A [xx]% (from [source])
Set win: A [xx]%
Score distribution: 2-0 A [xx]%, 2-1 A [xx]%, 2-1 B [xx]%, 2-0 B [xx]%
Expected total games: [x] (empirical, [n] matches); market [y] at [book]
Model: set-level, no serve data; holds fitted, not observed.

What to Do Next