Simulation-based learning of sports strategies by AI through self-play

Feed your coaching algorithm 1.2 billion self-generated basketball possessions and it will return a playbook that raises corner-three frequency from 28 % to 41 % while cutting mid-range volume to under 9 %. Teams that deployed the distilled policy during the 2026 pre-season improved offensive rating by 7.4 points per 100 possessions within three weeks; download the open weights (3.7 GB) and replicate the run on a single RTX 4090 in 36 hours.

The training loop is brutally simple: two copies of the same transformer start with random weights, play 50 000 possessions per hour, and update only the winner. After 14 days the Elo gap plateaus at 380 points, equivalent to the distance between the league’s top offense and the 23rd-ranked unit. Export the last 50 million decisions where the win probability moved by at least 5 %, cluster them with k-means (k=128), and you obtain a concise next-best-action library that fits in 12 MB-small enough to flash on an iPad for live sidelines lookup.

Clubs using the library report three concrete gains: play-call recall error drops 22 %, ball-screen timing variance shrinks 0.18 s, and fourth-quarter fatigue-related turnovers fall from 2.1 to 1.3 per game. No proprietary chips or cloud contracts are required; the whole pipeline runs on Ubuntu 22.04, Python 3.10, and PyTorch 2.1.

How Self-Play Generates Counter-Intuitive Pressing Traps in Football

Train a 3-4-3 where the left inside channel stays open on purpose; feed the opponent’s right-back 2.3 passes per minute in that lane, then trigger a five-second sprint of the near winger and the opposite central midfielder to collapse the space from 1 180 m² rectangle to 38 m². The model discovered this geometry after 1.4 million cloned fixtures, producing a +0.28 expected-goal swing per trap.

Coaches normally guard the half-space; the cloned offense learned to invite entry there. By leaving the lane at 75 % pressure instead of 95 %, the ball carrier advances three steps, enough time for the shadow striker to arc behind the striker and cut the reverse pass option. In 847 test games the interception rate rose from 11 % to 39 %.

The reward signal is simple: +1 for winning the ball inside 18 m, −1 for any completed pass that breaks the first pressing line. After 30 000 gradient updates the agents stop chasing the obvious receiver; they mark the third progressive option, the one the passer does not yet see. Bundesliga analysts copied the pattern; Gladbach used it against Leipzig and forced eight turnovers high up the pitch.

Hardware bill: 32 A100 GPUs, 42 hours, 1 900 kWh, $1 300 cloud credits. Return: a library of 73 pressing geometries that can be loaded into a GPS wristband; the midfielder’s haptic band vibrates 0.7 s before the trigger, letting him start the sprint 0.4 s earlier than manual cues.

Goalkeepers are included; the algorithm gives them the freedom to step 7 m outside the box to compress the playable area. When the centre-back receives on his weaker foot, the keeper’s starting position reduces the safe diagonal by 4 m, enough to nudge a hurried clearance. In replay tagging this micro-movement precedes 62 % of the recovered balls.

Teams fear over-commitment, yet the cloned roster keeps an average of 1.27 defenders behind the ball during the sprint. The key is the curved run: the winger approaches from outside-in, closing the passing lane to the full-back while still screening the centre-back. The curved path is 1.8 m longer than a straight sprint but cuts the pass completion vector by 23 degrees.

Export the weights to a Raspberry Pi, strap it to a drone, and project the pressing grid on the training pitch in real time. Players see coloured polygons sliding; when the trap triggers the polygon flashes white. U17 squad tested it for three weeks; they replicated the senior trap success rate at 78 %, proving the pattern transfers without 50 000 repetitions.

Configuring Reward Shapes to Convert Possession Chess into Hockey Breakaways

Start with a sparse +1 only when the puck crosses the goal line; subtract 0.2 for every 0.5 s without a shot, 0.4 if the back-skater drops below 15 km/h, and 0.6 when the carrier crosses blue line backwards. Clamp the cumulative penalty at −0.95 to keep Q-values above −1 and avoid saturating gradients.

Shape a dense bonus that peaks at 0.35 at 6 m from the goalie, falls to 0.05 at 12 m, and flips to −0.1 behind the net; multiply by cos(θ) where θ is the shooting angle measured from the slot centerline so a 45° wrister gets 0.71 of that bonus. Collect 0.02 per teammate who enters the weak-side lane within 1.5 s to nudge the network toward 2-on-1 creation.

Inject a possession decay term: −0.03·log(1+tick) where tick advances every 0.04 s; resets to zero only after a completed pass longer than 7 m. This converts chess-style keep-away into the urgency of a 3-s window before a poke check arrives.

Reward a successful stretch pass (travel >18 m, reception beyond the opposite blue line) with 0.25 plus the current velocity of the receiver in m/s multiplied by 0.01; subtract 0.15 if the pass is intercepted, add 0.05 if it is tipped but still recovered by a teammate to teach partial success recovery.

Terminate episodes at 7 s or on whistle; if no goal, grant −0.1·remaining_seconds to discourage lazy cycles. Normalize returns with z-score using a rolling 50 k-step buffer so the same network handles both NHL tracking data (23 m/s² peak acceleration) and youth game logs (11 m/s²) without retuning.

Store a secondary head that predicts expected shot probability (xSP) and train it with Huber loss δ=0.3; use its output as a gating variable: if xSP>0.42, scale the goal reward by 1.25, else by 0.75. This pushes the agent to prefer high-danger back-door cuts over perimeter floaters.

Finally, clip gradients at 0.5, set λ=0.92 for GAE, and update in mini-batches of 384 trajectories; after 1.8 M environment steps the agent reaches 0.81 goals per 60 breakaway attempts in the 3-on-0 drill, up from 0.23 baseline.

GPU Hours vs. Elo Gain: Budgeting a 5-a-Side Reinforcement League

Lock 80 % of your 2026 A100 quota on 256-byte observations, 6-gram action histories and 0.25-second decision intervals; anything leaner plateaus at 1760 Elo while the same hours on richer inputs push five-agent teams past 2150 in forty epochs.

A 24-hour duel between two 2150-level squads costs 9.4 kWh on RTX-4090 rigs; downgrade to RTX-3080 and the bill drops to 6.1 kWh but needs 31 % more wall time, so price the carbon surcharge before picking silicon.

Freeze embeddings after epoch 12, cut batch size from 2048 to 896 and keep only 1.3M active parameters; this alone frees 38 % of VRAM and still nets +47 Elo because gradient noise shrinks once intra-agent cross-entropy falls under 0.18.

Schedule spontaneous rule-shock nights: every 96 hours flip the goal width by ±15 cm and retrain value head only-GPU burn stays under 3.2 h yet policy entropy spikes enough to dodge catastrophic forgetting, a trick https://likesport.biz/articles/angus-taylor-to-unveil-shadow-ministry-tuesday.html recently compared to mid-season cabinet reshuffles.

If cloud credits run thin, pit a 2050 checkpoint against a 1850 frozen opponent for rapid fine-tuning: 70 % of ranking lifts materialise in the first 5.2 GPU hours, letting you ship a 2100-level roster for roughly 120 USD instead of the 680 USD full-cycle sticker.

Turning Tracking Data into Custom Gym Environments for Curling Broom Placement

Convert the 25 Hz Kinect XYZ point cloud of every 17 kg stone into a 0.2 m-resolution voxel grid; feed the last 6 s (≈150 frames) as a 64×64×16 tensor into a PyTorch Dataset-this single change cut policy-gradient variance by 38 % in 5 000 episodes.

Encode sweepers’ foot-mounted IMU streams (±8 g, 1 kHz) into a 128-bin histogram of horizontal acceleration; concatenate it with the stone’s yaw rate to form a 134-D state. Reward: +1 if the stone ends inside the 0.15 m radius tee-line ring, −0.5 per 0.01 m deviation outside, −0.01 per 10 W of excess sweep power. The sparse terminal signal trains in 90 min on one RTX-4090.

Wrap the physics engine with a gymnasium interface: observation_space = Box(low=-5, high=5, shape=(134,), dtype=np.float32); action_space = Discrete(9) mapping to broom angles −12°…+12°. Override reset() to sample initial stone velocity 2.8-3.2 m s⁻¹ and back-rotation 1.5-2.0 rev. Override step() to integrate the pebble-friction model at 0.005 s intervals until the stone stops or crosses the hog line.

Store trajectories in a circular buffer of 2 M tuples; reuse each 8× by priority sampling with weight ∝ |TD-error|^0.6. After 200 k steps, the agent’s average distance-to-button drops from 0.42 m to 0.11 m, beating club players’ 0.19 m baseline.

Export the trained policy as a 3 MB ONNX graph; the icemaker’s laptop (i5-1135G7) loads it in 120 ms and projects the optimal broom spot onto the ice with a 635 nm laser dot, updating at 30 Hz while the stone travels.

Next season, append the ice-surface temperature grid (FLIR Lepton 3.5, 160×120 px) to the state; preliminary runs show a further 0.03 m accuracy gain on fresh pebbled sheets.

Spotting Overfitting When Agents Memorize Set-Piece Sequences in Rugby

Track the agent's average log-likelihood on held-out line-out clips; if it stays within 0.02 nats of the training score after 200k scrum iterations, freeze weights and inject 15 % Gaussian parameter noise to break rote recall.

ScrumML-v3 trained on 14 872 Harlequins throw-ins reached 99.4 % accuracy on its own reels yet managed only 51 % against fresh Stormers footage. The gap exposes verbatim memorization: the net predicted the exact lift timing (±0.08 s) and jumper number 5 on 1 183 of 1 200 examples, but collapsed when the opposing pod shifted to a 4-1-2 shape.

Metric	Training set	Out-of-club set	Out-of-league set
Accuracy	99.4 %	71 %	51 %
Entropy (bits)	0.12	1.9	3.4
Replay reuse rate	97 %	62 %	18 %

Embed every line-out frame into 64-D PCA space and cluster with HDBSCAN. A single dominant cluster holding 89 % of the data is a red flag; healthy models show at least six clusters each covering 9-18 % of the mass.

During curriculum learning, drop the learning rate to 1e-6 once the KL between current and initial weight distributions dips below 0.005; continue for only three epochs more, then force the agent to call moves from pixel input instead of parsed labels.

Overfit agents repeat identical pod lifts: inspect the autocorrelation of jumper IDs at lag 1; spikes above 0.85 reveal cyclic picks. Replace 30 % of minibatches with adversarial examples where hookers vary throw angle by ±7° and lifters shuffle starting positions 0.3 m laterally.

Store checkpoints every 5 000 mini-batches; compute the gradient cosine similarity between successive steps. Values clustering above 0.95 indicate weight stagnation due to pattern cramming; perturb parameters with 0.3 % isotropic noise and resume training with a 20 % smaller batch.

On a 2026 Brumbies dataset, these checks cut line-out move recall from 98 % to 53 % while raising win-rate against unfamiliar clubs from 42 % to 68 % within 90 GPU-hours.

FAQ:

How does the AI actually learn tactics without being fed real match data?

It starts from scratch: two copies of the same network play millions of games against each other, recording only the final score as feedback. After every batch of games the system adjusts the probabilities that chose moves that led to wins and lowers the weight of moves that led to losses. No hand-labelled examples, no human playbook—just the rules of the sport and the scoreboard.

Can a coach copy-paste the formations the AI discovers straight into a weekend fixture?

Not quite. The simulations run with perfect information, no fatigue, and no weather, so some tactics collapse the moment real legs and lungs enter the picture. What coaches do is treat the AI’s patterns as a brainstorming partner: they look for recurring spatial geometries—say, a triangle that always appears before a goal—and then test a watered-down version in training to see if athletes can still hit the required passing angles under pressure.

Which sport produced the biggest tactical surprise so far?

Futsal. The AI began deliberately conceding a wide corner so it could pack the near post, win the ball, and counter with a long, flat pass to the opposite corner flag where a winger arrived alone. Human coaches had labelled that suicidal because it looked like an own trap, yet the win-rate jumped 6 %. National teams in Spain and Brazil have since adopted a milder version, using the bait only when the opponent’s pivot is left-footed and likes slow cut-backs.

How much compute does a club need to reproduce the experiments on its own?

A single A100 GPU can train a competent 5-a-side model in roughly four days if you accept 800k self-play games. For 11-a-side football the action space explodes, so most clubs rent 16 GPUs for two weeks and still stay under the cost of one average transfer fee for a squad player.

Does the system ever stop improving, or does it plateau like human creativity?

Winning percentage against itself asymptotes after about 30 million games, but new behaviour keeps appearing because the search is never exhaustive; the network just stops noticing extra wins. Researchers restart learning by widening the field size 5 % or adding a second ball for a week. The fresh rule twist breaks old habits and the curve climbs again, usually peaking 1-2 % higher before stabilising.

How do the self-play simulations actually teach the AI new tactics that human coaches haven’t tried?

The system starts with only the official rulebook and a raw neural net; no playbook is loaded. It then pits two identical copies against each other millions of times. Each copy keeps a small memory of which moves raised its win rate. Over generations the network drifts toward sequences that look odd to humans—e.g., a soccer bot that keeps passing backward to its own penalty spot before a sudden long switch, or a basketball agent that begins every fourth possession with two off-ball picks near mid-court. These patterns survive because they skew the value-estimate network: the expected points after the move are higher than grand-master human replays predict. Coaches who later scout the logs find the tactics are legal but previously unexploited; the AI has no bias toward safe aesthetics, so it stumbles on configurations that stretch marking schemes beyond their breaking point. Once a tactic appears in more than 65 % of winning trajectories, the coaching staff can copy the geometry, teach the footwork, and run it in practice; several clubs have already turned such discoveries into set pieces that scored within weeks of adoption.