Predictions: Ensemble Workflow

One Poisson model per team, round by round

The ensemble workflow starts from the exact same per-team Poisson models as the naive workflow, then adds a player layer on top.

For each team we compute the average Elo of its four best attackers and compare it against the average Elo of the opponent’s defensive block (four best defenders, best midfielder and best goalkeeper). The ratio of the two, raised to a damping exponent ((atk/def) ** 2.5, tuned on the completed rounds - see model vs reality), multiplies the predicted goals: a team whose attack outclasses the opposing defense gets a boost, and a team facing a stronger defensive block gets discounted.

The point of running both workflows on identical fixtures is to answer one question: does player-level information actually improve the prediction, or is the team-level history enough?

1. Setup

All the heavy lifting lives in the project modules:

• fixtures.py holds the tournament calendar (this is the only file that changes between rounds),
• model_utils.py trains the per-team Poisson models,
• report_utils.py generates, stores and scores the predictions.

from model_utils import Workflow
from report_utils import predict_all_rounds, round_detail, scoreboard

2. Generating the predictions

One call predicts every round in the calendar. For each round, the model trains only on matches played before the round started, so these predictions are fully reproducible: re-running this notebook after the tournament produces the same numbers that were published in real time.

Each round is written to predictions/ensemble_<round>.csv, separate from the other workflow’s files, so the two approaches can always be compared side by side.

predictions = predict_all_rounds(Workflow.ATK_DEF, "ensemble")

3. Round by round

For every completed round we show the predicted score next to the real one. correct marks whether the predicted winner matched the actual result (a real draw counts as a miss, since the model virtually never predicts one).

3.1 Group stage - Matchday 1

Twenty-four matches, and the model’s first contact with reality. Group-stage matches allow draws, but a Poisson model almost never predicts identical expected goals for both sides, so every real draw counts against us here.

round_detail("ensemble", "first_round")

	team_1	team_2	predicted_score	real_score	winner_pred	winner_real	correct
0	Mexico	South Africa	3.3 - 0.23	2 - 0	Mexico	Mexico	True
1	South Korea	Czechia	1.8 - 1.31	2 - 1	South Korea	South Korea	True
2	Canada	Bosnia and Herzegovina	1.53 - 1.06	1 - 1	Canada	Draw	False
3	Qatar	Switzerland	0.21 - 7.41	1 - 1	Switzerland	Draw	False
4	Brazil	Morocco	1.99 - 0.98	1 - 1	Brazil	Draw	False
5	Haiti	Scotland	1.47 - 6.45	0 - 1	Scotland	Scotland	True
6	USA	Paraguay	4.09 - 0.75	4 - 1	USA	USA	True
7	Australia	Türkiye	0.54 - 2.66	2 - 0	Türkiye	Australia	False
8	Germany	Curaçao	19.67 - 0.2	7 - 1	Germany	Germany	True
9	Côte d'Ivoire	Ecuador	2.42 - 1.66	1 - 0	Côte d'Ivoire	Côte d'Ivoire	True
10	Netherlands	Japan	3.39 - 0.1	2 - 2	Netherlands	Draw	False
11	Sweden	Tunisia	1.18 - 0.4	5 - 1	Sweden	Sweden	True
12	Belgium	Egypt	1.37 - 0.26	1 - 1	Belgium	Draw	False
13	IR Iran	New Zealand	1.98 - 0.55	2 - 2	IR Iran	Draw	False
14	Spain	Cabo Verde	8.19 - 0.58	0 - 0	Spain	Draw	False
15	Saudi Arabia	Uruguay	0.22 - 9.01	1 - 1	Uruguay	Draw	False
16	France	Senegal	5.52 - 0.0	3 - 1	France	France	True
17	Iraq	Norway	0.0 - 0.89	1 - 4	Norway	Norway	True
18	Argentina	Algeria	2.27 - 4.07	3 - 0	Algeria	Argentina	False
19	Austria	Jordan	1.03 - 0.0	3 - 1	Austria	Austria	True
20	Portugal	Congo DR	31.55 - 0.0	1 - 1	Portugal	Draw	False
21	Uzbekistan	Colombia	0.44 - 1.9	1 - 3	Colombia	Colombia	True
22	Ghana	Panama	1.74 - 0.63	1 - 0	Ghana	Ghana	True
23	England	Croatia	11.39 - 1.77	4 - 2	England	England	True

3.2 Group stage - Matchday 2

By matchday 2 the favorites usually start separating from the rest of the group, which tends to make matches easier to call.

round_detail("ensemble", "second_round")

	team_1	team_2	predicted_score	real_score	winner_pred	winner_real	correct
0	Czechia	South Africa	1.52 - 0.01	1 - 1	Czechia	Draw	False
1	Mexico	South Korea	1.34 - 2.0	1 - 0	South Korea	Mexico	False
2	Switzerland	Bosnia and Herzegovina	1.56 - 1.49	4 - 1	Switzerland	Switzerland	True
3	Canada	Qatar	1.25 - 0.92	6 - 0	Canada	Canada	True
4	Brazil	Haiti	3.32 - 0.0	3 - 0	Brazil	Brazil	True
5	Scotland	Morocco	0.38 - 2.43	0 - 1	Morocco	Morocco	True
6	Türkiye	Paraguay	2.35 - 1.24	0 - 1	Türkiye	Paraguay	False
7	USA	Australia	2.75 - 0.31	2 - 0	USA	USA	True
8	Germany	Côte d'Ivoire	2.15 - 0.0	2 - 1	Germany	Germany	True
9	Ecuador	Curaçao	3.73 - 0.97	0 - 0	Ecuador	Draw	False
10	Netherlands	Sweden	4.81 - 0.85	5 - 1	Netherlands	Netherlands	True
11	Tunisia	Japan	0.15 - 8.75	0 - 4	Japan	Japan	True
12	Belgium	IR Iran	1.85 - 0.74	0 - 0	Belgium	Draw	False
13	New Zealand	Egypt	3.26 - 1.15	1 - 3	New Zealand	Egypt	False
14	Spain	Saudi Arabia	0.06 - 0.06	4 - 0	Spain	Spain	True
15	Uruguay	Cabo Verde	2.5 - 0.0	2 - 2	Uruguay	Draw	False
16	France	Iraq	7.17 - 0.49	3 - 0	France	France	True
17	Norway	Senegal	1.94 - 0.75	3 - 2	Norway	Norway	True
18	Argentina	Austria	2.92 - 2.38	2 - 0	Argentina	Argentina	True
19	Jordan	Algeria	0.39 - 0.21	1 - 2	Jordan	Algeria	False
20	Portugal	Uzbekistan	3.89 - 0.89	5 - 0	Portugal	Portugal	True
21	Colombia	Congo DR	1.95 - 0.0	1 - 0	Colombia	Colombia	True
22	England	Ghana	22.28 - 0.06	0 - 0	England	Draw	False
23	Panama	Croatia	0.0 - 4.37	0 - 1	Croatia	Croatia	True

3.3 Group stage - Matchday 3

The hardest matchday to predict: teams that already qualified rotate their squads, and teams that are already out play with nothing to lose. None of that appears in the training data.

round_detail("ensemble", "third_round")

	team_1	team_2	predicted_score	real_score	winner_pred	winner_real	correct
0	Czechia	Mexico	0.6 - 2.62	0 - 3	Mexico	Mexico	True
1	South Africa	South Korea	0.02 - 4.11	1 - 0	South Korea	South Africa	False
2	Switzerland	Canada	0.0 - 1.83	2 - 1	Canada	Switzerland	False
3	Bosnia and Herzegovina	Qatar	1.13 - 0.3	3 - 1	Bosnia and Herzegovina	Bosnia and Herzegovina	True
4	Scotland	Brazil	0.63 - 1.83	0 - 3	Brazil	Brazil	True
5	Morocco	Haiti	2.54 - 0.0	4 - 2	Morocco	Morocco	True
6	Türkiye	USA	0.01 - 2.18	3 - 2	USA	Türkiye	False
7	Paraguay	Australia	1.28 - 0.16	0 - 0	Paraguay	Draw	False
8	Curaçao	Côte d'Ivoire	0.28 - 1.26	0 - 2	Côte d'Ivoire	Côte d'Ivoire	True
9	Ecuador	Germany	0.17 - 7.33	2 - 1	Germany	Ecuador	False
10	Japan	Sweden	0.95 - 1.46	1 - 1	Sweden	Draw	False
11	Tunisia	Netherlands	0.17 - 11.95	1 - 3	Netherlands	Netherlands	True
12	Egypt	IR Iran	0.72 - 1.58	1 - 1	IR Iran	Draw	False
13	New Zealand	Belgium	1.43 - 1.61	1 - 5	Belgium	Belgium	True
14	Uruguay	Spain	0.17 - 5.75	0 - 1	Spain	Spain	True
15	Cabo Verde	Saudi Arabia	0.45 - 0.77	0 - 0	Saudi Arabia	Draw	False
16	Norway	France	5.36 - 2.95	1 - 4	Norway	France	False
17	Senegal	Iraq	2.3 - 1.24	5 - 0	Senegal	Senegal	True
18	Argentina	Jordan	4.34 - 0.26	3 - 1	Argentina	Argentina	True
19	Algeria	Austria	0.52 - 1.48	3 - 3	Austria	Draw	False
20	Colombia	Portugal	3.06 - 3.16	0 - 0	Portugal	Draw	False
21	Congo DR	Uzbekistan	1.19 - 0.0	3 - 1	Congo DR	Congo DR	True
22	Panama	England	0.69 - 12.11	0 - 2	England	England	True
23	Croatia	Ghana	3.49 - 0.04	2 - 1	Croatia	Croatia	True

3.4 Round of 32

First knockout round. A caveat on scoring: the match history records the score after 90 or 120 minutes, so a match decided on penalties is recorded as a draw and counts against the model even when its pick advanced.

round_detail("ensemble", "round_of_32")

	team_1	team_2	predicted_score	real_score	winner_pred	winner_real	correct
0	South Africa	Canada	0.19 - 2.79	0 - 1	Canada	Canada	True
1	Brazil	Japan	2.8 - 0.95	2 - 1	Brazil	Brazil	True
2	Germany	Paraguay	3.76 - 0.64	1 - 1	Germany	Draw	False
3	Netherlands	Morocco	4.88 - 2.7	1 - 1	Netherlands	Draw	False
4	Côte d'Ivoire	Norway	0.68 - 3.07	1 - 2	Norway	Norway	True
5	France	Sweden	3.19 - 0.38	3 - 0	France	France	True
6	Mexico	Ecuador	0.85 - 0.42	2 - 0	Mexico	Mexico	True
7	England	Congo DR	12.74 - 1.8	2 - 1	England	England	True
8	Belgium	Senegal	0.76 - 1.75	3 - 2	Senegal	Belgium	False
9	USA	Bosnia and Herzegovina	10.15 - 0.92	2 - 0	USA	USA	True
10	Spain	Austria	1.97 - 1.46	3 - 0	Spain	Spain	True
11	Portugal	Croatia	7.02 - 0.37	2 - 1	Portugal	Portugal	True
12	Switzerland	Algeria	0.0 - 0.84	2 - 0	Algeria	Switzerland	False
13	Australia	Egypt	0.2 - 0.6	1 - 1	Egypt	Draw	False
14	Argentina	Cabo Verde	4.18 - 0.39	3 - 2	Argentina	Argentina	True
15	Colombia	Ghana	0.53 - 0.08	1 - 0	Colombia	Colombia	True

3.5 Round of 16

Predictions for the current round. The evaluation below fills in automatically as matches are played and the ratings are re-scraped.

round_detail("ensemble", "round_of_16")

	team_1	team_2	predicted_score	predicted_winner
0	Morocco	Canada	3.53 - 0.44	Morocco
1	France	Paraguay	3.7 - 1.5	France
2	Brazil	Norway	2.54 - 2.33	Brazil
3	Mexico	England	1.23 - 2.19	England
4	Spain	Portugal	1.71 - 0.63	Spain
5	USA	Belgium	1.36 - 1.6	Belgium
6	Argentina	Egypt	3.39 - 0.18	Argentina
7	Colombia	Switzerland	0.44 - 1.92	Switzerland

4. Scoreboard

Winner accuracy and mean absolute goal error per round, over the matches played so far.

scoreboard(prefixes=("ensemble",))

	round	matches	ensemble_accuracy	ensemble_goal_mae
0	Group stage - Matchday 1	24	0.542	2.59
1	Group stage - Matchday 2	24	0.625	1.75
2	Group stage - Matchday 3	24	0.542	1.86
3	Round of 32	16	0.688	1.68

5. Discussion

Two patterns are worth calling out.

First, the deeper the tournament goes, the closer the expected goals of the two sides get. That is not a bug: the knockout bracket filters out weak teams, so the survivors are increasingly similar in strength, and the model’s honest answer is “this one is close to a coin flip”. Many of these matches will realistically be decided in extra time or on penalties, which no goals-based model can call.

Second, winner accuracy and goal error move in opposite directions as the stakes rise. Calling the winner gets harder (closer matchups), while the scores the model misses by grow because knockout football produces more extreme results than the friendlies and qualifiers it trained on.