Forecasting Championship Results using Time Series and Nixtla

Introduction

In 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 Matches

To 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 Schedule

For 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 Series

Now 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 StatsForecast

Now 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 Results

The 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.

Conclusions

Let'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.

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