Dynamic ticket pricing with a human in the loop

Forecast ticket demand at every candidate price, pick the revenue-maximizing one, and let a pricing analyst approve it in one click. The engine was deployed at a European football club in 2023; this repository is a reimplementation on synthetic data, written up in the paper Human-in-the-Loop Dynamic Pricing for Football Tickets.

+6%	+4%	86%	7×
revenue per match	sell-through rate	of proposals approved	faster price updates

_{Analyst control panel (mockup), filled with the model's proposals for one synthetic match ten days before kick-off.}

The problem

Before	After
Prices set once per season in fixed categories (A++, A, B), revised weekly or monthly	A price proposal per match and seating zone, every day
Data pulled by hand from several systems	Sales, web analytics and context data in one store
No way to test a price before setting it	What-if simulation of revenue and sales at any price
Approved prices typed into the ticketing platform	One-click approval pushes the price to the live platform

How it works

1. Forecast. One Prophet model per (match, zone) series captures the sales curve over the selling window. One XGBoost model, pooled across series, fits Prophet's residuals from price, demand signals and external factors: final = max(0, prophet + residual). A second XGBoost, trained directly on sales, serves matches with no history yet.
2. Optimize. A grid search in €5 steps returns the price with the highest price × predicted sales, searching only between the 5th and 95th percentile of prices each zone was actually sold at.
3. Approve. The analyst sees the proposal, its revenue curve and a what-if simulator, then approves or rejects it. Approved prices go to the ticketing platform; new sales feed the next forecast.

Deployed architecture

Design choices

Choice	Why
Prophet + XGBoost on residuals	Prophet handles time to kick-off and weekly patterns; XGBoost learns the non-linear effects of price and context Prophet cannot.
Pooled XGBoost fallback	A match that just went on sale has no Prophet model; without the fallback its forecast is the residual alone.
Search only observed prices	Trees predict flat sales above the highest training price, so revenue looks unbounded and an unconstrained search picks the cap.
Grid search, not Bayesian optimization	Guarantees the best price within the search space, for one prediction batch per match and zone.
No web_conversion_rate feature	It is sales / web_visits, so it leaks the target at decision time and breaks the price response.

Results

Deployment (2023)

Segment-based A/B tests: a subset of seating zones was priced by the engine, the rest kept the static price list, across matches of varying importance.

Outcome	Result
Revenue per match (treatment vs. control)	+6%
Sell-through rate	+4%
Price update cadence	weekly → daily (7×)
Proposals approved by analysts	86%

Revenue and sell-through rose together, so the gain came from better prices, not only higher ones. These figures come from confidential club data and cannot be reproduced from this repository.

Reimplementation on synthetic data

The true demand curve of the synthetic data is known, so every recommendation is scored by the share of the best achievable revenue it earns, not only by forecast error. Holdout: the last 14 days of each series; all models are retrained on the first 77.

Model	WAPE	R²	MAE	RMSE	MAE vs. naive
Ensemble (Prophet + XGBoost)	26.4%	0.729	6.2	11.7	0.71
Prophet only	41.8%	0.483	9.8	16.2	1.12
XGBoost only (on sales)	22.6%	0.717	5.3	12.0	0.60
Naive: last 7 days per series	37.4%	0.544	8.7	15.2	1.00
Naive: global mean	79.7%	−0.428	18.6	27.0	2.13

• Recommendations earn 95% of the best achievable revenue (91% in VIP to 98% in the corners).
• Searching beyond observed prices drops that to 26%: no training row is priced above 1.9× base, and 72% of recommendations land at the 2.5× cap.
• The median recommendation is 1.52× base against a true optimum of 1.25×; 19% sit at the band's upper edge.
• Unseen matches: the pooled fallback cuts median WAPE from 89.8% to 12.5%, and its recommendations earn 94%.

Forecasts and cold start per match

make sanity fails the model if predicted sales don't move with price or if more than 40% of optimal prices sit at the band's upper edge.

Quickstart

pip install -r requirements-dev.txt   # Python 3.12, pinned versions
make all       # synthetic data, train, holdout evaluation, sanity check
make test      # unit tests: optimizer bounds, cold start, save/load
make app       # human-in-the-loop Streamlit page, locally

CI runs make all and make test on every push. To rebuild the paper and its figures, install Typst and run make figures.

Data

data/03_synthetic/synthetic_match_data.csv is generated from a fixed seed: 10 matches of varied importance, 91 days of daily sales each, up to 5 seating zones, 37 series and 3,367 zone-days. A single match excitement factor (opponent, league position, injuries, holidays, weekday) drives both demand signals and price levels, and prices also vary with promotions and discounts, so the price effect is identifiable from history. Demand falls linearly with price, so revenue peaks at 1.25× the zone's base price.

Feature schema

Group	Features
Match	days_until_match, is_weekday, opponent_tier, ea_opponent_strength, is_international
Team status	team_position, top_player_injured, league_winner_known
Ticket & zone	seat_zone, ticket_price, ticket_availability_pct, zone_seats_availability
Demand signals	internal_search_trends, google_trends_index, social_media_sentiment, web_visits
External	is_holiday, popular_concert_in_city, competitor_avg_price, flights_to_barcelona_index, weather_forecast

Target: zone_historical_sales, tickets sold per zone and day.

Repository

├── app.py                    # Streamlit human-in-the-loop page
├── src/
│   ├── data/                 # synthetic data generator (seeded)
│   ├── features/             # feature pipeline
│   ├── models/               # train, predict, evaluate, sanity check
│   └── decision_engine/      # grid-search optimizer and what-if simulation
├── tests/                    # unit tests
├── paper/                    # paper source (Typst), figures script, PDF
└── assets/                   # README figures, exported from the paper

License

MIT