IntroductionIn the real world, we often face forecasting problems in environments where several teams, departments, or companies are competing and building up their performance over time. Think about how sales branches stack up revenue throughout the year, how factories compare production outputs, or how bids play out during a procurement cycle. In all these settings, we’re not just interested in the numbers themselves, but in how each competitor measures up against the rest as the results accumulate. Championship tournaments provide an excellent case study for this pattern. Unlike simple time series where we forecast a single variable in isolation, championship-style data creates unique challenges: Panel structure: Multiple entities (teams, plants, branches) tracked simultaneously Cumulative metrics: Performance compounds over time (points, sales, production) Fixed horizon: A predetermined endpoint where final rankings matter Historical patterns: Entities establish consistent performance trajectories These characteristics appear across industries. In manufacturing, production lines accumulate defect rates or output volumes over quarters. In finance, regional offices accumulate sales targets. In logistics, distribution centers accumulate delivery performance metrics. Understanding how to forecast these cumulative, competitive time series has broad applications beyond sports. In this blog post, we'll use a championship tournament as our example system to demonstrate how StatsForecast, a very powerful Nixtla's statistical forecasting library, can predict final outcomes by analyzing cumulative performance time series. The same methodology applies whenever you need to forecast how multiple entities will perform relative to each other over a defined period. To accomplish this, we'll follow a systematic approach: Prepare the Data: Generate a simulated championship with cumulative points time series for each team Hold Out Last N Matches: Keep final matches for evaluation Train Forecast Model: Fit the model on matches 1 to T−N using StatsForecast and AutoARIMA Predict Last N Outcomes: Generate forecasts for the remaining matches Evaluate and Visualize Results: Compare predictions with actual outcomes and assess forecast accuracy The setup is summarized in the following chart: It seems like we have a lot to cover. Let's get to it! 1. Setup Championship Teams and MatchesTo generate realistic championship data, we need to model teams with different strengths and simulate match outcomes. The key concepts are: Team strength parameters: Each team gets a strength value that influences their scoring ability Poisson match model: Goals are generated using a Poisson distribution based on team strengths Home advantage: Home teams get a slight boost in expected goals The core logic uses a Poisson process where expected goals depend on: Team strength differential Home advantage (typically ~0.3 goals) Base scoring rate (~1.35 goals per team) Match outcomes translate to points: Win = 3 points, Draw = 1 point, Loss = 0 points. 2. Generate Championship ScheduleFor a valid championship, each team must play every other team exactly twice (once home, once away). We use the circle method algorithm: First half of season: N-1 rounds with rotating pairings Second half: Mirror of first half (swap home/away) Validation: Each team plays N-1 home games and N-1 away games For 20 teams, this creates 38 matchdays with 380 total matches. Sample Output: Rounds: 38; Matches total: 380 (should be 38 & 380) Matchday 1 Team12 vs Team08 Team19 vs Team06 Team17 vs Team03 Team02 vs Team13 Team11 vs Team07 ... 3. Simulate Results and Build Time SeriesNow we put everything together: simulate matches, track cumulative statistics, and transform the data into a panel time series ready for forecasting. The key transformation is converting match-by-match results into a cumulative points time series for each team: Panel structure: unique_id (team), ds (matchday), y (cumulative points) Cumulative metrics: Points, goals for/against, wins/draws/losses accumulate over time Train/test split: Hold out final matchdays for evaluation This structure is exactly what Nixtla's forecasting libraries expect and is analogous to tracking cumulative sales across branches, production output across facilities, or any competitive metric across entities. Full implementation: For the complete code covering team setup, calendar generation, match simulation, and data transformation, see the championship_forecasting.ipynb notebook. Running the simulation: teams = [f"Team{i:02d}" for i in range(1, 21)] season = generate_calendar(teams, seed=2025, shuffle_rounds=True) strengths = make_tiered_strengths(teams) # 1) Full season → dataframes for plots + forecasting full_season_results = prepare_forecasting_data(teams, season, strengths, seed=777) matches_df = full_season_results["matches_df"] full_season_ts = full_season_results["ts_df"] # (unique_id, ds, y) ready for StatsForecast/TimeGPT standings_df = full_season_results["standings_df"] # 2) Train on first 35 matchdays, forecast remaining 3 train_data = prepare_forecasting_data(teams, season, strengths, seed=777, cutoff_matchday=35) train_ts = train_data["ts_df"] # ds ∈ [1..35] forecast_horizon = train_data["h"] # 3 matchdays remaining The following assumptions are made: We are considering 20 teams (so 38 matchdays per team, 380 matches total). We are training on the first 35 matchdays and predicting the last 3. Thanks to the structure of the output, we can train on part of the championship and predict the final championship results and standings. unique_id ds y pts opponent ha goals_for goals_against result cum_gf cum_ga cum_gd cum_w cum_d cum_l 0 Team01 1 3 3 Team20 H 6 0 W 6 0 6 1 0 0 20 Team01 2 6 3 Team09 H 4 1 W 10 1 9 2 0 0 40 Team01 3 9 3 Team11 H 5 1 W 15 2 13 3 0 0 60 Team01 4 10 1 Team07 H 0 0 D 15 2 13 3 1 0 80 Team01 5 13 3 Team12 H 5 3 W 20 5 15 4 1 0 117 Team01 6 16 3 Team19 A 7 1 W 27 6 21 5 1 0 120 Team01 7 16 0 Team10 H 1 2 L 28 8 20 5 1 1 140 Team01 8 19 3 Team14 H 3 1 W 31 9 22 6 1 1 160 Team01 9 22 3 Team04 H 5 2 W 36 11 25 7 1 1 180 Team01 10 25 3 Team05 H 2 1 W 38 12 26 8 1 1 200 Team01 11 28 3 Team13 H 4 1 W 42 13 29 9 1 1 220 Team01 12 31 3 Team06 H 6 0 W 48 13 35 10 1 1 240 Team01 13 34 3 Team17 H 6 0 W 54 13 41 11 1 1 273 Team01 14 37 3 Team16 A 5 0 W 59 13 46 12 1 1 280 Team01 15 40 3 Team03 H 3 1 W 62 14 48 13 1 1 315 Team01 16 43 3 Team18 A 4 1 W 66 15 51 14 1 1 320 Team01 17 46 3 Team02 H 2 0 W 68 15 53 15 1 1 347 Team01 18 47 1 Team08 A 0 0 D 68 15 53 15 2 1 373 Team01 19 50 3 Team15 A 3 0 W 71 15 56 16 2 1 380 Team01 20 53 3 Team08 H 2 1 W 73 16 57 17 2 1 415 Team01 21 56 3 Team12 A 1 0 W 74 16 58 18 2 1 439 Team01 22 59 3 Team20 A 5 1 W 79 17 62 19 2 1 447 Team01 23 62 3 Team06 A 2 1 W 81 18 63 20 2 1 ... | 637 | Team20 | 32 | 18 | 0 | Team14 | A | 1 | 4 | L | 26 | 91 | -65 | 4 | 6 | 22 | | 657 | Team20 | 33 | 18 | 0 | Team13 | A | 2 | 4 | L | 28 | 95 | -67 | 4 | 6 | 23 | | 678 | Team20 | 34 | 19 | 1 | Team15 | H | 0 | 0 | D | 28 | 95 | -67 | 4 | 7 | 23 | | 683 | Team20 | 35 | 19 | 0 | Team04 | A | 1 | 5 | L | 29 | 100 | -71 | 4 | 7 | 24 | 4. Predict and Forecast with StatsForecastNow that we have all the data, we can let StatsForecast do the magic. In particular, we will use the AutoARIMA feature to train and forecast the last three matches for the entire championship. The whole thing can be done in literally three lines of code: from statsforecast import StatsForecast from statsforecast.models import AutoARIMA sf = StatsForecast(models=[AutoARIMA()], freq=1) sf.fit(train_ts) forecast_raw = sf.predict(h=forecast_horizon, level=[95]) 5. Evaluate the ResultsThe championship forecast outputs are stored in forecast_raw. To properly evaluate and visualize our predictions, we need two key steps: Step 1: Round forecasts to valid integer points Since championship points can only be integers (0, 1, or 3 per match), we need to round all forecast values: def round_forecast_to_valid_points(forecast_df: pd.DataFrame) -> pd.DataFrame: """ Round forecast values to integers since points must be whole numbers. """ df = forecast_df.copy() for col in df.columns: if col not in ['unique_id', 'ds']: df[col] = df[col].round().astype(int) return df Step 2: Visualize forecasts with actual results For visualization, we'll use helper functions that plot cumulative points over time with prediction intervals. The plotting logic handles: Extracting team-specific data from panel forecasts Overlaying actual vs. predicted cumulative points Displaying 95% prediction intervals Marking the train/test split point Plotting utilities: For the complete plotting functions (plot_team_cumpoints_with_forecast and helpers), see the championship_forecasting.ipynb notebook. And display the results using the following block of code: # Round to valid integer points (football only allows 0, 1, or 3 points per match) forecast = round_forecast_to_valid_points(forecast_raw) # Add actual values to compare with predictions full_season_results = prepare_forecasting_data(teams, season, strengths, seed=777) full_season_ts = full_season_results["ts_df"][["unique_id", "ds", "y"]] # Merge actual values into the forecast dataframe forecast = forecast.merge( full_season_ts.rename(columns={"y": "actual"}), on=["unique_id", "ds"], how="left" ) plot_team_cumpoints_with_forecast( ts_df=full_season_results["ts_df"], # full actuals for context team="Team01", fcst_df=forecast, model_name="AutoARIMA", # tell the helper how to read the wide columns level=95 ) This is the output for Team01:

And this is how the predictions look (forecast for the full championship): unique_id ds AutoARIMA AutoARIMA-lo-95 AutoARIMA-hi-95 actual error abs_error squared_error 0 Team01 36 89 87 92 90 -1 1 1 1 Team01 37 92 89 95 93 -1 1 1 2 Team01 38 94 91 98 94 0 0 0 3 Team02 36 83 81 85 84 -1 1 1 4 Team02 37 86 83 89 87 -1 1 1 5 Team02 38 88 85 92 87 1 1 1 6 Team03 36 78 76 81 79 -1 1 1 7 Team03 37 81 77 84 82 -1 1 1 8 Team03 38 83 78 88 85 -2 2 4 9 Team04 36 85 83 88 86 -1 1 1 10 Team04 37 88 85 91 89 -1 1 1 11 Team04 38 90 86 94 90 0 0 0 12 Team05 36 72 69 75 70 2 2 4 13 Team05 37 75 70 79 73 2 2 4 14 Team05 38 78 72 84 76 2 2 4 15 Team06 36 67 64 70 68 -1 1 1 16 Team06 37 69 65 73 71 -2 2 4 17 Team06 38 71 66 75 74 -3 3 9 18 Team07 36 73 70 76 71 2 2 4 19 Team07 37 75 71 79 74 1 1 1 20 Team07 38 77 72 82 77 0 0 0 21 Team08 36 71 68 74 70 1 1 1 22 Team08 37 73 69 77 73 0 0 0 ... | 56 | Team19 | 38 | 23 | 19 | 27 | 21 | 2 | 2 | 4 | | 57 | Team20 | 36 | 20 | 18 | 21 | 19 | 1 | 1 | 1 | | 58 | Team20 | 37 | 20 | 17 | 23 | 19 | 1 | 1 | 1 | | 59 | Team20 | 38 | 21 | 17 | 24 | 19 | 2 | 2 | 4 | Thanks to the power of StatsForecast and AutoARIMA, we are able to predict the full championship in a few seconds, together with the prediction intervals and the average prediction for each team in the championship. ConclusionsLet's recap what we covered in this post: Forecast many entities at once with panel data structure: Instead of building separate models for each team, we organize our data so that all 20 teams are stacked together with shared columns (unique_id, ds, y). Tracked cumulative metrics which create predictable patterns: When performance accumulates over time (points, sales, production output), historical trajectories become informative for future outcomes. AutoARIMA automates model selection: Rather than manually tuning ARIMA parameters for each entity, StatsForecast's AutoARIMA automatically identifies the optimal model configuration per team. This automation is crucial when forecasting across many entities simultaneously, saving time while maintaining forecast accuracy. Prediction intervals quantify uncertainty: The 95% prediction intervals generated by our model provide not just point forecasts but also confidence ranges. This is essential for decision-making—knowing that a team will finish with 85-90 points is more actionable than a single-point estimate of 87 points. Historical holdout validation demonstrates practical performance: By training on matchdays 1-35 and predicting the final 3 matchdays, we simulated a realistic forecasting scenario, validating that this approach works when you need to forecast competitive outcomes before a period ends. This forecasting methodology extends beyond sports to any scenario where multiple entities compete on cumulative metrics over a fixed horizon: quarterly sales targets across regions, monthly production goals across facilities, or seasonal performance metrics across departments. The combination of panel data structure, cumulative metric tracking, and automated model selection with StatsForecast provides a powerful framework for forecasting competitive, multi-entity systems in any industry.