Monte Carlo Engine

Tennis Tournament Simulations

For every live ATP tournament we simulate the entire remaining bracket 20,000 times on our Elo & Glicko-2 player ratings. Completed matches are locked in, every match still to play is sampled from its win probability — what comes out is each player's chance of reaching every round and lifting the trophy.

Updated Jul 25, 08:08 20,000 simulations / draw Calibrated probabilities How it works Past title races

Estoril 2026

ATP 250 clay Semifinals in play
20,000 simulations
draw updated Jul 25, 08:01
4 players still in the running
Luciano DarderiDarderi 38.4% title chance
Alexander BlockxBlockx 35.9% title chance
Hugo GastonGaston 15.6% title chance

Title race

how the forecast moved · daily runs Jul 20 to Jul 25

Coloured lines: players who entered the daily top 5 of title probability at least once. A line ending in ✕ is an elimination. Grey lines are the best of the rest. Tap a player to isolate their line.

Data table: title probability by day
Player Jul 20Jul 22Jul 23Jul 24Jul 25
Luciano Darderi 14.7% 16.0% 10.3% 15.3% 38.4%
Alexander Blockx 15.8% 13.1% 22.1% 17.5% 35.9%
Hugo Gaston 0.7% 1.3% 4.1% 4.7% 15.6%
Luca Van Assche 0.5% 0.7% 0.7% 1.9% 10.1%
Andrey Rublev 18.1% 23.3% 27.8% 38.4% out
Jaime Faria 6.8% 10.6% 10.9% 11.5% out
Tiago Torres 4.5% 2.0% 8.4% 4.8% out
Pablo Carreno Busta 4.5% 7.3% 7.3% out
Nuno Borges 4.8% 6.6% out
Roman Andres Burruchaga 1.9% 2.3% 5.3% 5.8% out
Projected draw our pick to lift the trophy: Darderi

Each box is the player most likely to reach that round from that part of the draw, with the chance they get there. Orange traces our projected champion's path; solid boxes are already decided. swipe to follow the draw to the title

R16
1 Rublev
Skatov
Van Assche
8 Carreno Busta
3 Tabilo
Torres
Gaston
Droguet
5 Borges
Andres Burruchaga
Jacquet
4 Blockx
Faria
Bueno
Martinez
2 Darderi
QF
1 Rublev
Van Assche
Torres
Gaston
Andres Burruchaga
4 Blockx
Faria
2 Darderi
SF
Van Assche
Gaston
4 Blockx
2 Darderi
F
Gaston 59.7%
or Van Assche 40.3%
2 Darderi 52.5%
or Blockx 47.5%
Champion
2 Darderi 38.4%
or Blockx 35.9%
R16 QF SF F 52.5% Title 38.4% E[wins] 3.91 Elo 1772 Seed 2 Country ITA
R16 QF SF F 47.5% Title 35.9% E[wins] 3.83 Elo 1821 Seed 4 Country BEL
R16 QF SF F 59.7% Title 15.6% E[wins] 3.75 Elo 1625 Country FRA
R16 QF SF F 40.3% Title 10.1% E[wins] 3.50 Elo 1556 Country FRA
Eliminated (24)
Andrey Rublev · out in QF Jaime Faria · out in QF Roman Andres Burruchaga · out in QF Tiago Torres · out in QF Alejandro Tabilo · out in R16 Gonzalo Bueno · out in R16 Kyrian Jacquet · out in R16 Nuno Borges · out in R16 Pablo Carreno Busta · out in R16 Pedro Martinez · out in R16 Timofey Skatov · out in R16 Titouan Droguet · out in R16 Botic Van De Zandschulp · out in R32 Camilo Ugo Carabelli · out in R32 Damir Dzumhur · out in R32 Daniel Merida · out in R32 Frederico Ferreira Silva · out in R32 Henrique Rocha · out in R32 Jesper De Jong · out in R32 Nikoloz Basilashvili · out in R32 Orlando Luz · out in R32 Stan Wawrinka · out in R32 Tiago Pereira · out in R32 Vilius Gaubas · out in R32
Elo + Glicko-2 rating model · per-simulation skill uncertainty sampling · played results locked in · qualifiers priced with field-average ratings

Kitzbuhel 2026

ATP 250 clay Final in play
20,000 simulations
draw updated Jul 25, 08:01
2 players still in the running

Title race

how the forecast moved · daily runs Jul 20 to Jul 25

Coloured lines: players who entered the daily top 5 of title probability at least once. A line ending in ✕ is an elimination. Grey lines are the best of the rest. Tap a player to isolate their line.

Data table: title probability by day
Player Jul 20Jul 22Jul 23Jul 24Jul 25
Alexander Bublik 15.0% 15.4% 22.2% 31.4% 58.7%
Quentin Halys 2.4% 1.8% 11.1% 22.7% 41.3%
Yannick Hanfmann 3.6% 3.2% 13.8% 23.9% out
Tomas Martin Etcheverry 5.7% 5.8% 9.3% 22.0% out
Valentin Vacherot 17.4% 18.3% out
Mariano Navone 4.1% 4.5% 15.6% out
Ignacio Buse 3.6% 4.0% 12.1% out
Juan Manuel Cerundolo 9.5% 8.1% out
Arthur Rinderknech 5.9% 6.4% out
Raphael Collignon 5.8% 5.0% out
Projected draw our pick to lift the trophy: Bublik

Each box is the player most likely to reach that round from that part of the draw, with the chance they get there. Orange traces our projected champion's path; solid boxes are already decided. swipe to follow the draw to the title

R16
1 Bublik
Diaz Acosta
Molcan
Altmaier
4 Martin Etcheverry
Rodionov
Feldbausch
5 Buse
Trungelliti
Hanfmann
Baez
3 Rinderknech
6 Lennard Struff
Navone
Halys
2 Vacherot
QF
1 Bublik
Molcan
4 Martin Etcheverry
5 Buse
Hanfmann
Baez
Navone
Halys
SF
1 Bublik
4 Martin Etcheverry
Hanfmann
Halys
F
1 Bublik
Halys
Champion
1 Bublik 58.7%
or Halys 41.3%
R16 QF SF F Title 58.7% E[wins] 4.59 Elo 1760 Seed 1 Country KAZ
R16 QF SF F Title 41.3% E[wins] 4.41 Elo 1700 Country FRA
Eliminated (26)
Tomas Martin Etcheverry · out in SF Yannick Hanfmann · out in SF Alex Molcan · out in QF Ignacio Buse · out in QF Mariano Navone · out in QF Sebastian Baez · out in QF Arthur Rinderknech · out in R16 Daniel Altmaier · out in R16 Facundo Diaz Acosta · out in R16 Jan Lennard Struff · out in R16 Jurij Rodionov · out in R16 Kilian Feldbausch · out in R16 Marco Trungelliti · out in R16 Valentin Vacherot · out in R16 Adolfo Daniel Vallejo · out in R32 Aleksandr Shevchenko · out in R32 Alexandre Muller · out in R32 Federico Cina · out in R32 Joel Schwaerzler · out in R32 Juan Manuel Cerundolo · out in R32 Laslo Djere · out in R32 Lukas Neumayer · out in R32 Miomir Kecmanovic · out in R32 Raphael Collignon · out in R32 Sebastian Ofner · out in R32 Vit Kopriva · out in R32
Elo + Glicko-2 rating model · per-simulation skill uncertainty sampling · played results locked in · qualifiers priced with field-average ratings

Track record — tested against history, no hindsight

Before going live, the engine was made to re-forecast 30 historical ATP tournaments (2023–2025) from each one's opening day — with the model trained only on data through 2022, so it could never peek at the answers. These are the results, straight from that test.

33% champions named
pre-tournament (top pick)
67% champions in our
top 5 picks
100% top-5 hit rate
at Grand Slams
21% for comparison: just
picking the #1 seed

By tournament tier

TiernTop-1Top-5
Grand Slams1242%100%
Masters 10001030%50%
ATP 500520%40%
ATP 250333%33%

Do the probabilities mean what they say?

When we predicted…It happenedn
0–1% (avg 0.2%)0.1%6,650
1–2% (avg 1.5%)0.7%1,347
2–5% (avg 3.3%)3.0%1,985
5–10% (avg 7.2%)6.9%1,641
10–20% (avg 14.4%)13.8%1,721
20–30% (avg 24.5%)23.9%961
30–50% (avg 40.4%)42.0%1,597
50–70% (avg 58.8%)59.6%1,379
70–90% (avg 78.5%)79.4%528
90–100% (avg 98.7%)98.9%379

Every round-reach probability from the test, grouped into bands and compared with what actually happened — predicted and observed match within about a point in every band. That's what makes a 30% title chance a number you can act on, not a vibe.

Backtest generated Jun 09, 23:41 · 20,000 simulations per tournament · methodology in how the simulations work · more model audits on model transparency.

How the simulations work

Where do these probabilities come from?

Every player carries Elo, Glicko-2 and surface-specific strength ratings rebuilt from 39,000+ ATP matches. A calibrated model turns any rating gap into a match win probability, and we then play out the entire remaining bracket 20,000 times — sampling every not-yet-played match from its probability. A player's title chance is simply the share of those 20,000 tournaments he wins.

Why simulate instead of just picking the favourite?

Because the draw matters. Two equally strong players can have very different title chances if one has byes and qualifiers ahead while the other faces seeds from the second round. Simulation prices the whole path — including the matches your rivals might lose for you — which a single head-to-head number can't capture.

How accurate are these forecasts?

Backtested on 30 historical ATP tournaments (2023–2025): the pre-tournament favourite by our model won 33% of events and the champion came from our top 5 in 67% (100% at Grand Slams). More importantly, the probabilities are calibrated: when we say a player has a 40% chance of reaching a round, it happens about 40% of the time. See model transparency.

When do the forecasts update?

On every daily prediction run while a tournament is live: finished matches are locked in, ratings refresh, and the remaining bracket is re-simulated — so the odds sharpen round by round until the final.

1 · Rate

Every player carries continuously updated Elo, Glicko-2 and surface-specific strength ratings, rebuilt from 39,000+ ATP matches since 2015.

2 · Simulate

The remaining bracket is played out 20,000 times. Each hypothetical match is sampled from the rating model's win probability; rating uncertainty is resampled per simulation so volatile players get honest long shots.

3 · Verify

Backtested on 30 historical tournaments: round-reach probabilities are calibrated within a point of observed frequencies. See model transparency.

Reuse this data — CC BY 4.0

The ATP tournament title odds dataset is free to reuse, including commercially, under CC BY 4.0 — attribution with a link is the only requirement. Copy-paste credit:

Data: <a href="https://www.predixsport.com/tennis_atp_tournament_simulations">ATP tournament title odds by Predixsport</a> (CC BY 4.0)

Or embed the live, self-updating widget (the credit link is built in):

<iframe src="https://www.predixsport.com/embed/bracket/tennis"
        style="width:100%;min-width:320px;height:660px;border:0;border-radius:10px" loading="lazy"
        title="ATP tournament title odds — Predixsport"></iframe>
<a href="https://www.predixsport.com/tennis_atp_tournament_simulations">ATP tournament title odds by Predixsport</a>
Preview widget All widgets

2 tournaments are live — by default the widget shows the highest-tier one. Pin a specific tournament by appending ?t=<tournament> to the iframe URL: ?t=estoril (Estoril) · ?t=kitzbuhel (Kitzbuhel)