Simulating today’s hockey games

Run monte carlo simulations using the expected goals model to predict the winners of today’s games

Intro

Use the chickenstats library to scrape play-by-play data, aggregate to the team level, then run monte carlo simulations to predict the winners of today’s games.

Parts of this tutorial are optional and will be clearly marked as such. For help, or any questions, please don’t hesitate to reach out to chicken@chickenandstats.com or @chickenandstats.com on Blue Sky.

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Housekeeping

Import dependencies

Import the dependencies we’ll need for the guide

import matplotlib.pyplot as plt
import seaborn as sns

import polars as pl

from pathlib import Path
import datetime as dt


from chickenstats.chicken_nhl import Scraper, Season
from chickenstats.chicken_nhl._helpers import charts_directory
from chickenstats.chicken_nhl.team import NHL_COLORS

from monte_carlo import (
    aggregate_strength_states,
    prep_nhl_stats,
    prep_team_stats,
    prep_todays_games,
    simulate_game,
    predict_game,
    predict_games,
    process_winners,
    assess_predictions,
)

Polars options

Set different polars options. This cell is optional

pl.Config.set_tbl_cols(-1)

polars.config.Config

Folder structure

charts_directory()

Chickenstats matplotlib style

chickenstats.utilities includes a custom style package - this activates it. This cell is also optional

plt.style.use("chickenstats")

---

Scrape data

Schedule

Scrape the schedule using the Season object

season = Season(2025, backend="polars")

schedule = season.schedule()

Standings and team names

Scrape the standings and create team name dictionaries to use later

standings = season.standings

standings.head(5)

shape: (5, 57)

season	date	team	team_name	conference	division	games_played	points	points_pct	wins	regulation_wins	shootout_wins	losses	ot_losses	shootout_losses	ties	win_pct	regulation_win_pct	streak_code	streak_count	goals_for	goals_against	goals_for_pct	goal_differential	goal_differential_pct	home_games_played	home_points	home_goals_for	home_goals_against	home_goal_differential	home_wins	home_losses	home_ot_losses	home_ties	home_regulation_wins	road_games_played	road_points	road_goals_for	road_goals_against	road_goal_differential	road_wins	road_losses	road_ot_losses	road_ties	road_regulation_wins	l10_points	l10_goals_for	l10_goals_against	l10_goal_differential	l10_wins	l10_losses	l10_ot_losses	l10_ties	l10_regulation_wins	team_logo	wildcard_sequence	waivers_sequence
i64	str	str	str	str	str	i64	i64	f64	i64	i64	i64	i64	i64	i64	i64	f64	f64	str	i64	i64	i64	f64	i64	f64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	str	i64	i64
20252026	"2026-02-05"	"COL"	"Colorado Avalanche"	"Western"	"Central"	55	83	0.754545	37	34	1	9	9	null	0	0.672727	0.618182	"W"	1	212	138	3.854545	74	1.345455	28	46	117	66	51	21	3	4	0	21	27	37	95	72	23	16	6	5	0	13	9	30	35	-5	4	5	1	0	4	"https://assets.nhle.com/logos/…	0	32
20252026	"2026-02-05"	"CAR"	"Carolina Hurricanes"	"Eastern"	"Metropolitan"	57	78	0.684211	36	26	4	15	6	null	0	0.631579	0.45614	"W"	3	197	163	3.45614	34	0.596491	31	44	118	94	24	21	8	2	0	15	26	34	79	69	10	15	7	4	0	11	18	39	21	18	8	0	2	0	7	"https://assets.nhle.com/logos/…	0	30
20252026	"2026-02-05"	"MIN"	"Minnesota Wild"	"Western"	"Central"	58	78	0.672414	34	21	4	14	10	null	0	0.586207	0.362069	"W"	5	196	169	3.37931	27	0.465517	30	41	97	91	6	17	6	7	0	9	28	37	99	78	21	17	8	3	0	12	17	46	33	13	8	1	1	0	3	"https://assets.nhle.com/logos/…	0	28
20252026	"2026-02-05"	"DAL"	"Dallas Stars"	"Western"	"Central"	57	77	0.675439	34	28	4	14	9	null	0	0.596491	0.491228	"W"	6	193	160	3.385965	33	0.578947	26	35	85	72	13	16	7	3	0	13	31	42	108	88	20	18	7	6	0	15	14	32	27	5	7	3	0	0	5	"https://assets.nhle.com/logos/…	0	29
20252026	"2026-02-05"	"TBL"	"Tampa Bay Lightning"	"Eastern"	"Atlantic"	54	76	0.703704	36	27	4	14	4	null	0	0.666667	0.5	"W"	4	193	139	3.574074	54	1.0	26	34	85	70	15	17	9	0	0	11	28	42	108	69	39	19	5	4	0	16	17	35	24	11	8	1	1	0	4	"https://assets.nhle.com/logos/…	0	31

team_names = standings.sort(by="team_name")["team_name"].str.to_uppercase().to_list()
team_codes = standings.sort(by="team_name")["team"].str.to_uppercase().to_list()
team_names_dict = dict(zip(team_codes, team_names, strict=False))

home_teams = dict(zip(schedule["game_id"].to_list(), schedule["home_team"].to_list(), strict=False))

Game IDs

Create a list of game IDs to scrape

conds = pl.col("game_state") == "OFF"

game_ids = schedule.filter(conds)["game_id"].unique().to_list()

Latest date

Important! If you don’t set this, it will just pull from the last completed game

conds = pl.col("game_state") == "OFF"

dt_format = "%Y-%m-%d"
latest_date_dt = schedule.filter(conds)["game_date"].str.to_datetime(format=dt_format).max()  # In YYYY-MM-DD format
latest_date = latest_date_dt.strftime(dt_format)

latest_date = "2026-01-24"
latest_date_dt = dt.date(year=int(latest_date[:4]), month=int(latest_date[5:7]), day=int(latest_date[8:10]))

Checking to see if you’ve already scraped the data

Check to see if you’ve already scraped, so you’re only getting the game_ids that you need

data_directory = Path.cwd() / "data"
stats_file = data_directory / "team_stats.csv"

if not data_directory.exists():
    data_directory.mkdir()

if stats_file.exists():
    team_stats = pl.read_csv(source=stats_file, infer_schema_length=2000)

    saved_game_ids = team_stats["game_id"].to_list()
    game_ids = [x for x in game_ids if x not in saved_game_ids]

if game_ids:
    scraper = Scraper(game_ids, backend="polars")

    pbp = scraper.play_by_play
    scraped_team_stats = scraper.team_stats

Combine scraped and saved data

Combine the scraped data and the saved data, then save the new file, but only if there are game_ids

if game_ids:
    team_stats = pl.concat(
        [team_stats.with_columns(pl.col("bsf_adj_percent").cast(pl.Float64)), scraped_team_stats], strict=False
    )  # Quick, don't ask
    team_stats.write_csv(stats_file)

team_stats.head(5)

shape: (5, 141)

season	session	game_id	game_date	team	opp_team	strength_state	toi	gf	ga	gf_adj	ga_adj	hdgf	hdga	xgf	xga	xgf_adj	xga_adj	sf	sa	sf_adj	sa_adj	hdsf	hdsa	ff	fa	ff_adj	fa_adj	hdff	hdfa	cf	ca	cf_adj	ca_adj	bsf	bsa	bsf_adj	bsa_adj	msf	msa	msf_adj	msa_adj	hdmsf	hdmsa	teammate_block	hf	ht	give	take	ozf	nzf	dzf	fow	fol	ozfw	ozfl	nzfw	nzfl	dzfw	dzfl	pent0	pent2	pent4	pent5	pent10	pend0	pend2	pend4	pend5	pend10	gf_p60	ga_p60	gf_adj_p60	ga_adj_p60	hdgf_p60	hdga_p60	xgf_p60	xga_p60	xgf_adj_p60	xga_adj_p60	sf_p60	sa_p60	sf_adj_p60	sa_adj_p60	hdsf_p60	hdsa_p60	ff_p60	fa_p60	ff_adj_p60	fa_adj_p60	hdff_p60	hdfa_p60	cf_p60	ca_p60	cf_adj_p60	ca_adj_p60	bsf_p60	bsa_p60	bsf_adj_p60	bsa_adj_p60	msf_p60	msa_p60	msf_adj_p60	msa_adj_p60	hdmsf_p60	hdmsa_p60	teammate_block_p60	hf_p60	ht_p60	give_p60	take_p60	pent0_p60	pent2_p60	pent4_p60	pent5_p60	pent10_p60	pend0_p60	pend2_p60	pend4_p60	pend5_p60	pend10_p60	gf_percent	gf_adj_percent	hdgf_percent	xgf_percent	xgf_adj_percent	sf_percent	sf_adj_percent	hdsf_percent	ff_percent	ff_adj_percent	hdff_percent	cf_percent	cf_adj_percent	bsf_percent	bsf_adj_percent	msf_percent	msf_adj_percent	hdmsf_percent	hf_percent	take_percent
i64	str	i64	str	str	str	str	f64	i64	i64	f64	f64	i64	i64	f64	f64	f64	f64	i64	i64	f64	f64	i64	i64	i64	i64	f64	f64	i64	i64	i64	i64	f64	f64	i64	i64	f64	f64	i64	i64	f64	f64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
20252026	"R"	2025020813	"2026-01-24"	"CAR"	"OTT"	"5v4"	5.5	0	0	0.0	0.0	0	0	0.266756	0.175814	0.311799	0.153621	1	1	1.200956	1.200956	1	0	1	2	1.205802	2.411605	1	0	1	2	1.205802	2.411605	0	0	0.0	0.0	0	1	0.0	0.854207	0	0	0	1	0	1	0	0	2	3	0	5	0	0	0	2	0	3	0	0	0	0	0	0	1	0	0	0	0.0	0.0	0.0	0.0	0.0	0.0	2.910065	1.917967	3.40144	1.67587	10.909091	10.909091	13.101342	13.101342	10.909091	0.0	10.909091	21.818182	13.154208	26.308416	10.909091	0.0	10.909091	21.818182	13.154208	26.308416	0.0	0.0	0.0	0.0	0.0	10.909091	0.0	9.31862	0.0	0.0	0.0	10.909091	0.0	10.909091	0.0	0.0	0.0	0.0	0.0	0.0	0.0	10.909091	0.0	0.0	0.0	NaN	NaN	NaN	0.602743	0.66993	0.5	0.5	1.0	0.333333	0.333333	1.0	0.333333	0.333333	NaN	NaN	0.0	0.0	NaN	1.0	0.0
20252026	"R"	2025020103	"2025-10-21"	"FLA"	"BOS"	"4v5"	9.3	0	1	0.0	0.868644	0	1	0.337972	0.40907	0.388038	0.357434	2	3	1.78708	2.569967	0	1	3	6	2.6342	5.125241	0	2	3	9	2.6342	5.125241	0	3	0.0	0.0	1	3	1.205802	2.56262	0	1	0	3	1	1	0	5	1	3	3	6	0	5	0	1	3	0	0	0	0	0	0	0	0	0	0	0	0.0	6.451613	0.0	5.604155	0.0	6.451613	2.180462	2.639159	2.503471	2.306027	12.903226	19.354839	11.529549	16.580431	0.0	6.451613	19.354839	38.709677	16.994839	33.066069	0.0	12.903226	19.354839	58.064516	16.994839	33.066069	0.0	19.354839	0.0	0.0	6.451613	19.354839	7.77937	16.533035	0.0	6.451613	0.0	19.354839	6.451613	6.451613	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.452414	0.520526	0.4	0.410159	0.0	0.333333	0.339483	0.0	0.25	0.339483	0.0	NaN	0.25	0.319975	0.0	0.75	0.0
20252026	"R"	2025020849	"2026-01-29"	"NYR"	"NYI"	"5v4"	5.366667	1	0	0.868644	0.0	0	0	0.217852	0.0	0.190353	0.0	2	0	1.713311	0.0	0	0	2	0	1.708414	0.0	0	0	4	0	1.708414	0.0	2	0	0.0	0.0	0	0	0.0	0.0	0	0	0	0	3	2	0	2	1	4	3	4	2	0	1	0	0	4	0	0	0	0	0	0	0	0	0	0	11.180124	0.0	9.711549	0.0	0.0	0.0	2.435613	0.0	2.128175	0.0	22.360248	0.0	19.155032	0.0	0.0	0.0	22.360248	0.0	19.100276	0.0	0.0	0.0	44.720497	0.0	19.100276	0.0	22.360248	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	33.540373	22.360248	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	1.0	NaN	1.0	1.0	1.0	1.0	NaN	1.0	1.0	NaN	1.0	1.0	1.0	NaN	NaN	NaN	NaN	0.0	0.0
20252026	"R"	2025020247	"2025-11-09"	"OTT"	"UTA"	"5vE"	2.766667	0	0	0.0	0.0	0	0	0.594731	0.609058	0.594731	0.609058	0	4	0.0	4.0	0	3	1	8	1.0	8.0	0	3	2	9	1.0	8.0	1	1	0.0	0.0	1	4	1.0	4.0	0	0	0	0	1	0	0	2	0	2	2	2	0	2	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0.0	0.0	0.0	0.0	0.0	0.0	12.897772	13.208493	12.897772	13.208493	0.0	86.746988	0.0	86.746988	0.0	65.060241	21.686747	173.493976	21.686747	173.493976	0.0	65.060241	43.373494	195.180723	21.686747	173.493976	21.686747	21.686747	0.0	0.0	21.686747	86.746988	21.686747	86.746988	0.0	0.0	0.0	0.0	21.686747	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	NaN	NaN	NaN	0.494049	0.494049	0.0	0.0	0.0	0.111111	0.111111	0.0	0.181818	0.111111	0.5	NaN	0.2	0.2	NaN	0.0	NaN
20252026	"R"	2025020092	"2025-10-19"	"UTA"	"BOS"	"5vE"	1.183333	0	0	0.0	0.0	0	0	0.0	0.0	0.0	0.0	0	0	0.0	0.0	0	0	0	0	0.0	0.0	0	0	2	1	0.0	0.0	2	1	0.0	0.0	0	0	0.0	0.0	0	0	0	1	0	0	0	1	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	101.408451	50.704225	0.0	0.0	101.408451	50.704225	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	50.704225	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0.666667	NaN	0.666667	NaN	NaN	NaN	NaN	1.0	NaN

---

Munge the data

Cleaning the data and prepping for analysis

Add Home games to the data set

Check to see if team is the home team, adding a dummy column

home_map = dict(zip(schedule["game_id"], schedule["home_team"], strict=False))

team_stats = team_stats.with_columns(
    is_home=pl.when(pl.col("game_id").replace_strict(home_map, return_dtype=str) == pl.col("team"))
    .then(pl.lit(1))
    .otherwise(pl.lit(0))
)

Aggregate strength state

Add a column to aggregate strength states (e.g., powerplay for 5v4, 5v3, and 4v3)

team_stats = aggregate_strength_states(team_stats)

Prep overall NHL stats

Function to calculate the goals scored and allowed above the expected goals model, at the overall NHL season level, adjusted for score and venue

nhl_stats = prep_nhl_stats(team_stats)

nhl_stats.head(5)

shape: (5, 81)

season	session	is_home	strength_state2	toi	gf	ga	gf_adj	ga_adj	hdgf	hdga	xgf	xga	xgf_adj	xga_adj	sf	sa	sf_adj	sa_adj	hdsf	hdsa	ff	fa	ff_adj	fa_adj	hdff	hdfa	cf	ca	cf_adj	ca_adj	bsf	bsa	bsf_adj	bsa_adj	msf	msa	msf_adj	msa_adj	hdmsf	hdmsa	teammate_block	hf	ht	give	take	ozf	nzf	dzf	fow	fol	ozfw	ozfl	nzfw	nzfl	dzfw	dzfl	pent0	pent2	pent4	pent5	pent10	pend0	pend2	pend4	pend5	pend10	game_id	g_score_ax	g_save_ax	toi_gp	gf_p60	ga_p60	gf_adj_p60	ga_adj_p60	xgf_p60	xga_p60	xgf_adj_p60	xga_adj_p60	g_score_ax_p60	g_save_ax_p60
i64	str	i32	str	f64	i64	i64	f64	f64	i64	i64	f64	f64	f64	f64	i64	i64	f64	f64	i64	i64	i64	i64	f64	f64	i64	i64	i64	i64	f64	f64	i64	i64	f64	f64	i64	i64	f64	f64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	u32	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
20252026	"R"	0	"Ev5"	536.35	57	166	57.0	166.0	20	37	69.020614	179.961909	69.020614	179.961909	494	166	494.0	166.0	159	37	794	307	794.0	306.0	228	37	1150	418	794.0	306.0	318	111	0.0	0.0	300	141	300.0	140.0	69	0	38	67	94	109	24	262	29	211	274	228	262	0	12	17	0	211	0	23	0	3	6	0	332	4	2	2	483	-12.020614	13.961909	1.110455	6.376433	18.569964	6.376433	18.569964	7.721146	20.131844	7.721146	20.131844	-1.344713	1.56188
20252026	"R"	0	"3vE"	2.5	0	0	0.0	0.0	0	0	0.0	1.110907	0.0	1.110907	0	6	0.0	6.0	0	2	0	8	0.0	8.0	0	2	0	9	0.0	8.0	0	1	0.0	0.0	0	2	0.0	2.0	0	0	0	0	0	0	0	1	0	2	2	1	0	1	0	0	2	0	0	6	0	0	0	0	0	0	0	0	9	0.0	1.110907	0.277778	0.0	0.0	0.0	0.0	0.0	26.661775	0.0	26.661775	0.0	26.661775
20252026	"R"	0	"Ev4"	40.0	9	10	9.0	10.0	3	2	8.10169	7.612753	8.10169	7.612753	45	10	45.0	10.0	7	2	78	15	78.0	15.0	12	2	111	22	78.0	15.0	28	7	0.0	0.0	33	5	33.0	5.0	5	0	5	1	4	5	2	34	1	13	34	14	34	0	0	1	0	13	0	2	0	0	0	0	8	0	0	0	53	0.89831	-2.387247	0.754717	13.5	15.0	13.5	15.0	12.152535	11.419129	12.152535	11.419129	1.347465	-3.580871
20252026	"R"	0	"powerplay"	4105.033333	514	49	555.923431	51.608182	222	26	632.442075	50.900359	685.593593	47.745515	3541	625	3757.638052	659.030873	1103	119	5362	793	5728.852631	842.420465	1592	150	6988	891	5728.852631	842.420465	1463	98	0.0	0.0	1821	168	1945.086182	158.628621	489	31	163	179	517	823	174	1943	624	1732	2334	1965	1888	55	347	277	99	1633	4	154	0	2	1	0	87	4	2	1	883	-129.670162	-3.862667	4.648962	7.512728	0.716194	8.12549	0.754316	9.243902	0.74397	10.020775	0.697858	-1.895285	-0.056458
20252026	"R"	1	"ILLEGAL"	1.9	0	0	0.0	0.0	0	0	0.0	0.0	0.0	0.0	0	2	0.0	0.0	0	0	0	2	0.0	0.0	0	0	0	2	0.0	0.0	0	0	0.0	0.0	0	0	0.0	0.0	0	0	0	2	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	4	0	0	0	0	13	0	0	0	19	0.0	0.0	0.1	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

Prep team stats

Function to prep and aggregate team stats to match up with the schedule for predicting the game’s values

team_stats_agg = prep_team_stats(team_stats=team_stats, nhl_stats=nhl_stats, latest_date=latest_date)

team_stats_agg.head(5)

shape: (5, 98)

season	session	team	is_home	strength_state2	toi	gf	ga	gf_adj	ga_adj	hdgf	hdga	xgf	xga	xgf_adj	xga_adj	sf	sa	sf_adj	sa_adj	hdsf	hdsa	ff	fa	ff_adj	fa_adj	hdff	hdfa	cf	ca	cf_adj	ca_adj	bsf	bsa	bsf_adj	bsa_adj	msf	msa	msf_adj	msa_adj	hdmsf	hdmsa	teammate_block	hf	ht	give	take	ozf	nzf	dzf	fow	fol	ozfw	ozfl	nzfw	nzfl	dzfw	dzfl	pent0	pent2	pent4	pent5	pent10	pend0	pend2	pend4	pend5	pend10	game_id	g_score_ax	g_save_ax	toi_gp	gf_p60	ga_p60	gf_adj_p60	ga_adj_p60	xgf_p60	xga_p60	xgf_adj_p60	xga_adj_p60	g_score_ax_p60	g_save_ax_p60	mean_xgf_p60	mean_xga_p60	mean_xgf_adj_p60	mean_xga_adj_p60	mean_gf_p60	mean_ga_p60	mean_gf_adj_p60	mean_ga_adj_p60	mean_g_score_ax_p60	mean_g_save_ax_p60	mean_toi_gp	off_strength	def_strength	toi_comparison	scoring_strength	goalie_strength
i64	str	str	i32	str	f64	i64	i64	f64	f64	i64	i64	f64	f64	f64	f64	i64	i64	f64	f64	i64	i64	i64	i64	f64	f64	i64	i64	i64	i64	f64	f64	i64	i64	f64	f64	i64	i64	f64	f64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	u32	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
20252026	"R"	"CBJ"	1	"4vE"	0.866667	1	0	1.0	0.0	0	0	0.61581	0.049193	0.61581	0.049193	1	1	1.0	1.0	0	0	1	1	1.0	1.0	0	0	1	1	1.0	1.0	0	0	0.0	0.0	0	0	0.0	0.0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0.38419	0.049193	0.866667	69.230769	0.0	69.230769	0.0	42.63297	3.405685	42.63297	3.405685	26.5978	3.405685	11.419129	12.152535	11.419129	12.152535	15.0	13.5	15.0	13.5	3.580871	-1.347465	0.754717	3.733469	0.280245	1.148333	7.427746	-2.527476
20252026	"R"	"NSH"	1	"4vE"	1.766667	0	1	0.0	1.0	0	0	0.0	0.13276	0.0	0.13276	0	2	0.0	2.0	0	0	0	4	0.0	4.0	0	0	0	4	0.0	4.0	0	0	0.0	0.0	0	2	0.0	2.0	0	0	0	0	0	0	0	2	0	0	0	2	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0.0	-0.86724	0.883333	0.0	33.962264	0.0	33.962264	0.0	4.508823	0.0	4.508823	0.0	-29.453441	11.419129	12.152535	11.419129	12.152535	15.0	13.5	15.0	13.5	3.580871	-1.347465	0.754717	0.0	0.371019	1.170417	0.0	21.858415
20252026	"R"	"DAL"	0	"ILLEGAL"	0.383333	0	0	0.0	0.0	0	0	0.0	0.0	0.0	0.0	0	0	0.0	0.0	0	0	0	0	0.0	0.0	0	0	0	0	0.0	0.0	0	0	0.0	0.0	0	0	0.0	0.0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	3	0.0	0.0	0.127778	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.1	NaN	NaN	1.277778	NaN	NaN
20252026	"R"	"PHI"	0	"ILLEGAL"	0.083333	0	0	0.0	0.0	0	0	0.0	0.0	0.0	0.0	1	0	0.0	0.0	0	0	1	0	0.0	0.0	0	0	1	0	0.0	0.0	0	0	0.0	0.0	0	0	0.0	0.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0.0	0.0	0.083333	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.1	NaN	NaN	0.833333	NaN	NaN
20252026	"R"	"NJD"	0	"shorthanded"	120.933333	2	16	1.737288	15.06796	0	6	1.977491	20.020203	2.213706	18.863242	17	116	16.053371	110.466815	6	33	24	171	22.643352	162.09692	6	52	27	213	22.643352	162.09692	3	42	0.0	0.0	7	55	7.463236	52.44747	0	19	0	13	7	19	11	73	18	58	64	85	2	71	6	12	56	2	0	5	0	0	0	0	6	0	0	0	26	-0.476418	3.795282	4.651282	0.992282	7.938258	0.86194	7.475834	0.981115	9.932846	1.098311	9.35883	-0.236371	1.882996	0.755118	9.38011	0.826901	8.675806	0.892854	7.649225	0.836282	7.069986	0.009381	1.60582	5.064586	1.328225	1.078727	0.918393	-25.197613	1.172607

Prep today’s games

Function to prepare today’s games

todays_games = prep_todays_games(schedule=schedule, team_stats=team_stats, nhl_stats=nhl_stats, latest_date=latest_date)

todays_games.head(5)

shape: (5, 128)

season	session	game_id	game_date	start_time	game_state	home_team	home_team_id	home_score	away_team	away_team_id	away_score	venue	venue_timezone	neutral_site	game_date_dt_utc	tv_broadcasts	home_logo	home_logo_dark	away_logo	away_logo_dark	home_5v5_off_strength	home_5v5_def_strength	home_5v5_scoring_strength	home_5v5_goalie_strength	home_5v5_toi_comparison	home_powerplay_off_strength	home_powerplay_scoring_strength	home_powerplay_toi_comparison	home_shorthanded_def_strength	home_shorthanded_goalie_strength	home_shorthanded_toi_comparison	away_5v5_off_strength	away_5v5_def_strength	away_5v5_scoring_strength	away_5v5_goalie_strength	away_5v5_toi_comparison	away_powerplay_off_strength	away_powerplay_scoring_strength	away_powerplay_toi_comparison	away_shorthanded_def_strength	away_shorthanded_goalie_strength	away_shorthanded_toi_comparison	mean_home_5v5_xgf_p60	mean_home_5v5_xga_p60	mean_home_5v5_xgf_adj_p60	mean_home_5v5_xga_adj_p60	mean_home_5v5_gf_p60	mean_home_5v5_ga_p60	mean_home_5v5_gf_adj_p60	mean_home_5v5_ga_adj_p60	mean_home_5v5_g_score_ax_p60	mean_home_5v5_g_save_ax_p60	mean_home_5v5_toi_gp	mean_home_powerplay_xgf_p60	mean_home_powerplay_xga_p60	mean_home_powerplay_xgf_adj_p60	mean_home_powerplay_xga_adj_p60	mean_home_powerplay_gf_p60	mean_home_powerplay_ga_p60	mean_home_powerplay_gf_adj_p60	mean_home_powerplay_ga_adj_p60	mean_home_powerplay_g_score_ax_p60	mean_home_powerplay_g_save_ax_p60	mean_home_powerplay_toi_gp	mean_home_shorthanded_xgf_p60	mean_home_shorthanded_xga_p60	mean_home_shorthanded_xgf_adj_p60	mean_home_shorthanded_xga_adj_p60	mean_home_shorthanded_gf_p60	mean_home_shorthanded_ga_p60	mean_home_shorthanded_gf_adj_p60	mean_home_shorthanded_ga_adj_p60	mean_home_shorthanded_g_score_ax_p60	mean_home_shorthanded_g_save_ax_p60	mean_home_shorthanded_toi_gp	mean_away_5v5_xgf_p60	mean_away_5v5_xga_p60	mean_away_5v5_xgf_adj_p60	mean_away_5v5_xga_adj_p60	mean_away_5v5_gf_p60	mean_away_5v5_ga_p60	mean_away_5v5_gf_adj_p60	mean_away_5v5_ga_adj_p60	mean_away_5v5_g_score_ax_p60	mean_away_5v5_g_save_ax_p60	mean_away_5v5_toi_gp	mean_away_powerplay_xgf_p60	mean_away_powerplay_xga_p60	mean_away_powerplay_xgf_adj_p60	mean_away_powerplay_xga_adj_p60	mean_away_powerplay_gf_p60	mean_away_powerplay_ga_p60	mean_away_powerplay_gf_adj_p60	mean_away_powerplay_ga_adj_p60	mean_away_powerplay_g_score_ax_p60	mean_away_powerplay_g_save_ax_p60	mean_away_powerplay_toi_gp	mean_away_shorthanded_xgf_p60	mean_away_shorthanded_xga_p60	mean_away_shorthanded_xgf_adj_p60	mean_away_shorthanded_xga_adj_p60	mean_away_shorthanded_gf_p60	mean_away_shorthanded_ga_p60	mean_away_shorthanded_gf_adj_p60	mean_away_shorthanded_ga_adj_p60	mean_away_shorthanded_g_score_ax_p60	mean_away_shorthanded_g_save_ax_p60	mean_away_shorthanded_toi_gp	predicted_home_5v5_toi	predicted_home_powerplay_toi	predicted_home_shorthanded_toi	predicted_home_5v5_xgf_p60	predicted_home_5v5_xga_p60	predicted_home_5v5_gf_p60	predicted_home_5v5_ga_p60	predicted_home_powerplay_xgf_p60	predicted_home_powerplay_gf_p60	predicted_home_shorthanded_xga_p60	predicted_home_shorthanded_ga_p60	predicted_away_5v5_xgf_p60	predicted_away_5v5_xga_p60	predicted_away_5v5_gf_p60	predicted_away_5v5_ga_p60	predicted_away_powerplay_xgf_p60	predicted_away_powerplay_gf_p60	predicted_away_shorthanded_xga_p60	predicted_away_shorthanded_ga_p60
i64	i64	i64	str	str	str	str	i64	i64	str	i64	i64	str	str	i64	datetime[μs, UTC]	list[struct[5]]	str	str	str	str	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
20252026	2	2025020810	"2026-01-24"	"13:00"	"OFF"	"NYI"	2	0	"BUF"	7	5	"UBS ARENA"	"America/New_York"	0	2026-01-24 18:00:00 UTC	[{282,"N","CA","SN",107}, {28,"A","US","MSG-B",392}, {409,"H","US","MSGSN",411}]	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	1.032099	1.098022	1.215772	2.5018	0.998547	1.019476	1.519422	1.078344	1.166022	2.812028	0.972322	1.013831	0.959593	1.192254	0.226348	1.002412	1.015596	2.379345	1.059298	0.962996	1.663244	0.847453	2.941164	2.728581	2.816787	2.851487	2.533148	2.485146	2.43756	2.566546	-0.379227	0.28494	48.501035	9.38011	0.755118	8.675806	0.826901	7.649225	0.892854	7.069986	0.836282	-1.60582	-0.009381	5.064586	0.74397	9.243902	0.697858	10.020775	0.686962	7.512728	0.754316	8.12549	0.056458	1.895285	4.648962	2.728581	2.941164	2.851487	2.816787	2.483774	2.535891	2.566546	2.43756	-0.28494	0.379227	48.501035	9.243902	0.74397	10.020775	0.697858	7.512728	0.716194	8.12549	0.754316	-1.895285	-0.056458	4.648962	0.755118	9.38011	0.826901	8.675806	0.892854	7.649225	0.836282	7.069986	0.009381	1.60582	5.064586	48.547351	4.628251	4.788336	2.789734	3.174302	0.664344	8.522113	8.51749	17.541011	11.866671	64.38049	3.174302	2.789734	8.522113	0.664344	11.866671	64.38049	8.51749	17.541011
20252026	2	2025020811	"2026-01-24"	"12:30"	"OFF"	"NSH"	18	2	"UTA"	68	5	"BRIDGESTONE ARENA"	"US/Central"	0	2026-01-24 18:30:00 UTC	[{282,"N","CA","SN",107}, {284,"N","CA","SN1",113}, … {558,"A","US","Utah16",381}]	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	1.029662	0.983516	2.188479	-0.431273	0.978291	0.817146	0.418178	0.987613	0.86872	2.024623	1.145351	1.072654	0.912573	1.046681	0.277726	1.004538	0.78517	0.944735	1.00629	0.908922	1.070264	1.009018	2.941164	2.728581	2.816787	2.851487	2.533148	2.485146	2.43756	2.566546	-0.379227	0.28494	48.501035	9.38011	0.755118	8.675806	0.826901	7.649225	0.892854	7.069986	0.836282	-1.60582	-0.009381	5.064586	0.74397	9.243902	0.697858	10.020775	0.686962	7.512728	0.754316	8.12549	0.056458	1.895285	4.648962	2.728581	2.941164	2.851487	2.816787	2.483774	2.535891	2.566546	2.43756	-0.28494	0.379227	48.501035	9.243902	0.74397	10.020775	0.697858	7.512728	0.716194	8.12549	0.754316	-1.895285	-0.056458	4.648962	0.755118	9.38011	0.826901	8.675806	0.892854	7.649225	0.836282	7.069986	0.009381	1.60582	5.064586	47.663489	5.046957	5.358185	2.646771	3.008242	1.392119	-1.22224	6.443714	2.350161	6.835096	10.601006	3.008242	2.646771	-1.22224	1.392119	6.835096	10.601006	6.443714	2.350161
20252026	2	2025020812	"2026-01-24"	"19:00"	"OFF"	"BOS"	6	4	"MTL"	8	3	"TD GARDEN"	"US/Eastern"	0	2026-01-25 00:00:00 UTC	[{287,"N","CA","SNE",30}, {288,"N","CA","SNO",31}, … {31,"H","US","NESN",405}]	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	0.985353	1.063828	0.149162	2.623023	0.977731	0.945022	-0.130636	1.008577	1.088831	1.718694	1.165002	0.888426	0.943972	-0.718902	1.236217	0.976611	1.072128	-0.141762	1.132869	1.026001	0.702074	1.108745	2.941164	2.728581	2.816787	2.851487	2.533148	2.485146	2.43756	2.566546	-0.379227	0.28494	48.501035	9.38011	0.755118	8.675806	0.826901	7.649225	0.892854	7.069986	0.836282	-1.60582	-0.009381	5.064586	0.74397	9.243902	0.697858	10.020775	0.686962	7.512728	0.754316	8.12549	0.056458	1.895285	4.648962	2.728581	2.941164	2.851487	2.816787	2.483774	2.535891	2.566546	2.43756	-0.28494	0.379227	48.501035	9.243902	0.74397	10.020775	0.697858	7.512728	0.716194	8.12549	0.754316	-1.895285	-0.056458	4.648962	0.755118	9.38011	0.826901	8.675806	0.892854	7.649225	0.836282	7.069986	0.009381	1.60582	5.064586	46.31188	5.663496	6.135677	2.620023	2.695034	0.418081	-4.574184	8.412006	-0.628717	11.697909	-2.311086	2.695034	2.620023	-4.574184	0.418081	11.697909	-2.311086	8.412006	-0.628717
20252026	2	2025020813	"2026-01-24"	"19:00"	"OFF"	"OTT"	9	1	"CAR"	12	4	"CANADIAN TIRE CENTRE"	"US/Eastern"	0	2026-01-25 00:00:00 UTC	[{284,"N","CA","SN1",113}, {286,"N","CA","CITY",137}, {561,"A","US","FDSNSO",202}]	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	0.991645	0.818598	1.545365	-0.907254	0.968379	0.89586	-0.503662	1.15124	0.725061	-0.22982	1.058032	1.198828	0.966861	2.877418	1.415492	0.993524	0.968843	1.812915	1.140039	0.713705	0.434465	1.074454	2.941164	2.728581	2.816787	2.851487	2.533148	2.485146	2.43756	2.566546	-0.379227	0.28494	48.501035	9.38011	0.755118	8.675806	0.826901	7.649225	0.892854	7.069986	0.836282	-1.60582	-0.009381	5.064586	0.74397	9.243902	0.697858	10.020775	0.686962	7.512728	0.754316	8.12549	0.056458	1.895285	4.648962	2.728581	2.941164	2.851487	2.816787	2.483774	2.535891	2.566546	2.43756	-0.28494	0.379227	48.501035	9.243902	0.74397	10.020775	0.697858	7.512728	0.716194	8.12549	0.754316	-1.895285	-0.056458	4.648962	0.755118	9.38011	0.826901	8.675806	0.892854	7.649225	0.836282	7.069986	0.009381	1.60582	5.064586	46.663215	6.264666	5.607569	2.700687	2.798327	5.112274	-6.57519	5.547136	-0.989171	7.039295	-2.378168	2.798327	2.700687	-6.57519	5.112274	7.039295	-2.378168	5.547136	-0.989171
20252026	2	2025020814	"2026-01-24"	"19:00"	"OFF"	"CBJ"	29	8	"TBL"	14	5	"NATIONWIDE ARENA"	"US/Eastern"	0	2026-01-25 00:00:00 UTC	[{581,"A","US","The Spot",211}, {565,"H","US","FDSNOH",286}]	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	"https://assets.nhle.com/logos/…	1.010127	1.054735	0.755682	2.576822	1.030619	1.068771	2.476875	0.822706	1.036681	-0.315558	0.956388	1.185417	0.853779	0.201814	1.910094	0.965921	0.948375	0.145274	1.09516	0.959875	2.335107	1.097917	2.941164	2.728581	2.816787	2.851487	2.533148	2.485146	2.43756	2.566546	-0.379227	0.28494	48.501035	9.38011	0.755118	8.675806	0.826901	7.649225	0.892854	7.069986	0.836282	-1.60582	-0.009381	5.064586	0.74397	9.243902	0.697858	10.020775	0.686962	7.512728	0.754316	8.12549	0.056458	1.895285	4.648962	2.728581	2.941164	2.851487	2.816787	2.483774	2.535891	2.566546	2.43756	-0.28494	0.379227	48.501035	9.243902	0.74397	10.020775	0.697858	7.512728	0.716194	8.12549	0.754316	-1.895285	-0.056458	4.648962	0.755118	9.38011	0.826901	8.675806	0.892854	7.649225	0.836282	7.069986	0.009381	1.60582	5.064586	48.282614	4.574653	4.869315	2.429269	3.565215	3.034386	1.668781	8.900392	41.949684	9.852042	-0.36622	3.565215	2.429269	1.668781	3.034386	9.852042	-0.36622	8.900392	41.949684

---

Simulating the actual games

Functions to simulate the games

Random float

Generate a random floating number between 0 and 1

def random_float() -> float: “““Generate a random floating number between 0 and 1.”“” random_generator = np.random.default_rng()

# return random_generator.triangular(left=0.0, mode=0.5, right=1.0)
return random_generator.random()

Simulating an individual game

Predicts various game values, based on a poissoin distribution

game = todays_games.filter((pl.col("away_team") == "NSH") | (pl.col("home_team") == "NSH")).to_dicts()[0]

pl.DataFrame(simulate_game(game))  # Showing it as a dataframe just to make it easy

shape: (1, 26)

game_id	home_team	away_team	predicted_home_5v5_toi	predicted_home_powerplay_toi	predicted_home_shorthanded_toi	predicted_away_5v5_toi	predicted_away_powerplay_toi	predicted_away_shorthanded_toi	predicted_home_5v5_gf_p60	predicted_home_5v5_xgf_p60	predicted_home_powerplay_gf_p60	predicted_home_powerplay_xgf_p60	predicted_home_5v5_goals	predicted_home_powerplay_goals	predicted_home_total_goals	predicted_away_5v5_gf_p60	predicted_away_5v5_xgf_p60	predicted_away_powerplay_gf_p60	predicted_away_powerplay_xgf_p60	predicted_away_5v5_goals	predicted_away_powerplay_goals	predicted_away_total_goals	home_win	away_win	draw
i64	str	str	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	i64	i64	i64
2025020811	"NSH"	"UTA"	43.0	2.0	8.0	43.0	8.0	2.0	3.0	3.0	1.0	13.0	2.15	0.433333	2.583333	NaN	1.0	18.0	5.0	0.716667	0.666667	1.383333	1	0	0

Predict an entire game

Predict an entire game based on n number of simulations

predicted_game = predict_game(game, 100)

predicted_game.head(5)

shape: (5, 26)

game_id	home_team	away_team	predicted_home_5v5_toi	predicted_home_powerplay_toi	predicted_home_shorthanded_toi	predicted_away_5v5_toi	predicted_away_powerplay_toi	predicted_away_shorthanded_toi	predicted_home_5v5_gf_p60	predicted_home_5v5_xgf_p60	predicted_home_powerplay_gf_p60	predicted_home_powerplay_xgf_p60	predicted_home_5v5_goals	predicted_home_powerplay_goals	predicted_home_total_goals	predicted_away_5v5_gf_p60	predicted_away_5v5_xgf_p60	predicted_away_powerplay_gf_p60	predicted_away_powerplay_xgf_p60	predicted_away_5v5_goals	predicted_away_powerplay_goals	predicted_away_total_goals	home_win	away_win	draw
i64	str	str	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	i64	i64	i64
2025020811	"NSH"	"UTA"	49.6	4.0	6.4	49.6	6.4	4.0	0.0	3.0	2.0	8.0	2.48	0.533333	3.013333	NaN	1.0	14.0	4.0	0.826667	0.426667	1.253333	1	0	0
2025020811	"NSH"	"UTA"	36.0	3.0	4.0	36.0	4.0	3.0	2.0	1.0	1.0	4.0	0.6	0.2	0.8	NaN	2.0	13.0	6.0	1.2	0.4	1.6	0	1	0
2025020811	"NSH"	"UTA"	44.262295	7.868852	7.868852	44.262295	7.868852	7.868852	1.0	1.0	2.0	9.0	0.737705	1.180328	1.918033	NaN	5.0	12.0	1.0	3.688525	0.131148	3.819672	0	1	0
2025020811	"NSH"	"UTA"	49.52381	5.714286	4.761905	49.52381	4.761905	5.714286	1.0	3.0	1.0	6.0	2.47619	0.571429	3.047619	NaN	5.0	10.0	8.0	4.126984	0.634921	4.761905	0	1	0
2025020811	"NSH"	"UTA"	44.0	6.0	9.0	44.0	9.0	6.0	0.0	1.0	4.0	9.0	0.733333	0.9	1.633333	NaN	6.0	11.0	4.0	4.4	0.6	5.0	0	1	0

Simulating multiple games

Simulating multiple games at once

predictions = predict_games(predict_game, todays_games, total_simulations=1_000, n_workers=1, disable_progress_bar=True)

predictions.head(5)

shape: (5, 26)

game_id	home_team	away_team	predicted_home_5v5_toi	predicted_home_powerplay_toi	predicted_home_shorthanded_toi	predicted_away_5v5_toi	predicted_away_powerplay_toi	predicted_away_shorthanded_toi	predicted_home_5v5_gf_p60	predicted_home_5v5_xgf_p60	predicted_home_powerplay_gf_p60	predicted_home_powerplay_xgf_p60	predicted_home_5v5_goals	predicted_home_powerplay_goals	predicted_home_total_goals	predicted_away_5v5_gf_p60	predicted_away_5v5_xgf_p60	predicted_away_powerplay_gf_p60	predicted_away_powerplay_xgf_p60	predicted_away_5v5_goals	predicted_away_powerplay_goals	predicted_away_total_goals	home_win	away_win	draw
i64	str	str	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	i64	i64	i64
2025020810	"NYI"	"BUF"	52.5	2.5	5.0	52.5	5.0	2.5	0.0	2.0	16.0	12.0	1.75	0.5	2.25	7.0	4.0	55.0	12.0	3.5	1.0	4.5	0	1	0
2025020810	"NYI"	"BUF"	52.131148	1.967213	5.901639	52.131148	5.901639	1.967213	0.0	3.0	22.0	10.0	2.606557	0.327869	2.934426	9.0	4.0	59.0	6.0	3.47541	0.590164	4.065574	0	1	0
2025020810	"NYI"	"BUF"	52.5	4.6875	2.8125	52.5	2.8125	4.6875	0.0	5.0	19.0	9.0	4.375	0.703125	5.078125	9.0	5.0	59.0	15.0	4.375	0.703125	5.078125	0	0	1
2025020810	"NYI"	"BUF"	33.0	10.0	2.0	33.0	2.0	10.0	0.0	1.0	22.0	13.0	0.55	2.166667	2.716667	9.0	3.0	66.0	20.0	1.65	0.666667	2.316667	1	0	0
2025020810	"NYI"	"BUF"	40.0	1.0	0.0	40.0	0.0	1.0	1.0	4.0	11.0	5.0	2.666667	0.083333	2.75	8.0	5.0	59.0	16.0	3.333333	0.0	3.333333	0	1	0

---

Assessing results

Check to see if the simulation is accurate

Process winners

Aggregate the predictions to “predict” a winner

predicted_winners = process_winners(predictions)

predicted_winners

shape: (9, 26)

game_id	home_team	away_team	predicted_winner	predicted_home_win	predicted_away_win	predicted_draw	predicted_home_win_percent	predicted_away_win_percent	predicted_draw_percent	predicted_home_5v5_goals_mean	predicted_home_powerplay_goals_mean	predicted_home_total_goals_mean	predicted_home_5v5_xgf_p60_mean	predicted_home_powerplay_xgf_p60_mean	predicted_home_5v5_toi_mean	predicted_home_powerplay_toi_mean	predicted_home_shorthanded_toi_mean	predicted_away_5v5_goals_mean	predicted_away_powerplay_goals_mean	predicted_away_total_goals_mean	predicted_away_5v5_xgf_p60_mean	predicted_away_powerplay_xgf_p60_mean	predicted_away_5v5_toi_mean	predicted_away_powerplay_toi_mean	predicted_away_shorthanded_toi_mean
i64	str	str	str	i64	i64	i64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
2025020817	"MIN"	"FLA"	"FLA"	461	536	3	0.461	0.536	0.003	2.075311	0.739172	2.814484	2.773	6.988	44.898838	6.308386	4.402776	2.113866	0.868102	2.981968	2.826	11.836	44.898838	4.402776	6.308386
2025020814	"CBJ"	"TBL"	"TBL"	306	690	4	0.306	0.69	0.004	1.906553	0.669293	2.575845	2.45	9.007	46.679519	4.449252	4.628229	2.824785	0.760766	3.585551	3.629	9.881	46.679519	4.628229	4.449252
2025020813	"OTT"	"CAR"	"CAR"	459	537	4	0.459	0.537	0.004	1.976862	0.557561	2.534423	2.65	5.609	44.872112	5.927584	5.440304	2.062832	0.643848	2.70668	2.756	7.065	44.872112	5.440304	5.927584
2025020812	"BOS"	"MTL"	"MTL"	397	600	3	0.397	0.6	0.003	1.894879	0.762433	2.657312	2.557	8.452	44.568994	5.414241	6.037765	1.968763	1.177527	3.14629	2.643	11.672	44.568994	6.037765	5.414241
2025020811	"NSH"	"UTA"	"UTA"	433	564	3	0.433	0.564	0.003	2.00005	0.517972	2.518022	2.606	6.436	46.140582	4.837774	5.105645	2.318929	0.587029	2.905959	3.018	6.945	46.140582	5.105645	4.837774
2025020810	"NYI"	"BUF"	"BUF"	372	623	5	0.372	0.623	0.005	2.113746	0.624885	2.738631	2.711	8.495	46.857121	4.435936	4.562943	2.491938	0.903787	3.395725	3.19	11.983	46.857121	4.562943	4.435936
2025020818	"EDM"	"WSH"	"EDM"	500	499	1	0.5	0.499	0.001	2.303046	1.020846	3.323892	2.984	12.598	46.357211	4.832619	4.49217	2.356921	0.908569	3.265491	3.058	12.179	46.357211	4.49217	4.832619
2025020816	"STL"	"LAK"	"LAK"	378	613	9	0.378	0.613	0.009	1.787255	0.412386	2.199641	2.244	5.351	47.567413	4.592821	4.259765	1.969469	0.647448	2.616917	2.494	9.101	47.567413	4.259765	4.592821
2025020815	"WPG"	"DET"	"DET"	361	633	6	0.361	0.633	0.006	2.177507	0.577372	2.754879	2.81	8.746	46.495734	3.938766	5.2035	2.535959	0.955715	3.491675	3.274	11.014	46.495734	5.2035	3.938766

Assessing predictions

Checking to see if the predictions were correct

assessed_predictions = assess_predictions(predicted_winners, schedule)

assessed_predictions

shape: (9, 28)

game_id	home_team	away_team	predicted_winner	actual_winner	prediction_correct	predicted_home_win	predicted_away_win	predicted_draw	predicted_home_win_percent	predicted_away_win_percent	predicted_draw_percent	predicted_home_5v5_goals_mean	predicted_home_powerplay_goals_mean	predicted_home_total_goals_mean	predicted_home_5v5_xgf_p60_mean	predicted_home_powerplay_xgf_p60_mean	predicted_home_5v5_toi_mean	predicted_home_powerplay_toi_mean	predicted_home_shorthanded_toi_mean	predicted_away_5v5_goals_mean	predicted_away_powerplay_goals_mean	predicted_away_total_goals_mean	predicted_away_5v5_xgf_p60_mean	predicted_away_powerplay_xgf_p60_mean	predicted_away_5v5_toi_mean	predicted_away_powerplay_toi_mean	predicted_away_shorthanded_toi_mean
i64	str	str	str	str	i32	i64	i64	i64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
2025020817	"MIN"	"FLA"	"FLA"	"FLA"	1	461	536	3	0.461	0.536	0.003	2.075311	0.739172	2.814484	2.773	6.988	44.898838	6.308386	4.402776	2.113866	0.868102	2.981968	2.826	11.836	44.898838	4.402776	6.308386
2025020814	"CBJ"	"TBL"	"TBL"	"CBJ"	0	306	690	4	0.306	0.69	0.004	1.906553	0.669293	2.575845	2.45	9.007	46.679519	4.449252	4.628229	2.824785	0.760766	3.585551	3.629	9.881	46.679519	4.628229	4.449252
2025020813	"OTT"	"CAR"	"CAR"	"CAR"	1	459	537	4	0.459	0.537	0.004	1.976862	0.557561	2.534423	2.65	5.609	44.872112	5.927584	5.440304	2.062832	0.643848	2.70668	2.756	7.065	44.872112	5.440304	5.927584
2025020812	"BOS"	"MTL"	"MTL"	"BOS"	0	397	600	3	0.397	0.6	0.003	1.894879	0.762433	2.657312	2.557	8.452	44.568994	5.414241	6.037765	1.968763	1.177527	3.14629	2.643	11.672	44.568994	6.037765	5.414241
2025020811	"NSH"	"UTA"	"UTA"	"UTA"	1	433	564	3	0.433	0.564	0.003	2.00005	0.517972	2.518022	2.606	6.436	46.140582	4.837774	5.105645	2.318929	0.587029	2.905959	3.018	6.945	46.140582	5.105645	4.837774
2025020810	"NYI"	"BUF"	"BUF"	"BUF"	1	372	623	5	0.372	0.623	0.005	2.113746	0.624885	2.738631	2.711	8.495	46.857121	4.435936	4.562943	2.491938	0.903787	3.395725	3.19	11.983	46.857121	4.562943	4.435936
2025020818	"EDM"	"WSH"	"EDM"	"EDM"	1	500	499	1	0.5	0.499	0.001	2.303046	1.020846	3.323892	2.984	12.598	46.357211	4.832619	4.49217	2.356921	0.908569	3.265491	3.058	12.179	46.357211	4.49217	4.832619
2025020816	"STL"	"LAK"	"LAK"	"LAK"	1	378	613	9	0.378	0.613	0.009	1.787255	0.412386	2.199641	2.244	5.351	47.567413	4.592821	4.259765	1.969469	0.647448	2.616917	2.494	9.101	47.567413	4.259765	4.592821
2025020815	"WPG"	"DET"	"DET"	"DET"	1	361	633	6	0.361	0.633	0.006	2.177507	0.577372	2.754879	2.81	8.746	46.495734	3.938766	5.2035	2.535959	0.955715	3.491675	3.274	11.014	46.495734	5.2035	3.938766

---

Charts

Plotting the results of your simulations

Color dictionary

Taking the NHL colors and making a dictionary out of them

color_dict = {
    key: (value["GOAL"] if value["GOAL"] != "#FFFFFF" else value["SHOT"]) for key, value in NHL_COLORS.items()
}

Plotting a single game

Plotting the results for a single game

dpi = 650
figsize = (8, 5)
nrows = 1  # len(assessed_predictions["home_team"].to_list())
ncols = 1

fig, ax = plt.subplots(nrows=nrows, ncols=ncols, figsize=figsize, dpi=dpi, sharex=True, sharey=True)

for idx, game in enumerate(
    assessed_predictions.filter((pl.col("away_team") == "NSH") | (pl.col("home_team") == "NSH"))
    .sort("predicted_away_total_goals_mean")
    .to_dicts()
):
    # ax = axs[idx]

    plot_predictions = predictions.filter(pl.col("game_id") == game["game_id"])

    venues = ["away", "home"]

    for venue in venues:
        sns.kdeplot(
            data=plot_predictions,
            x=plot_predictions[f"predicted_{venue}_total_goals"],
            bw_adjust=0.5,
            clip_on=False,
            fill=True,
            alpha=0.1,
            linewidth=1.5,
            hue=plot_predictions[f"{venue}_team"],
            palette=color_dict,
            legend=False,
            ax=ax,
        )

    sns.despine(left=True)

    ax.set(yticks=[], ylabel="", xlabel="predicted total goals")

    if idx != (nrows - 1):
        ax.set(xticks=[])

    # else:
    #     ax.set(xlabel="predicted total goals")

    ax.set_title(f"{game['home_team']} vs. {game['away_team']}")

fig.savefig(f"./charts/{latest_date}_NSH.png", dpi=650, bbox_inches="tight", facecolor="white")

Plotting today’s games

Plotting the predicted goals for all of today’s games

dpi = 500
figsize = (4, 12)
nrows = len(assessed_predictions["home_team"].to_list())
ncols = 1

fig, axs = plt.subplots(nrows=nrows, ncols=ncols, figsize=figsize, dpi=dpi, sharex=True, sharey=True)

for idx, game in enumerate(assessed_predictions.sort("predicted_home_total_goals_mean").to_dicts()):
    ax = axs[idx]

    plot_predictions = predictions.filter(pl.col("game_id") == game["game_id"])

    venues = ["away", "home"]

    for venue in venues:
        sns.kdeplot(
            data=plot_predictions,
            x=plot_predictions[f"predicted_{venue}_total_goals"],
            bw_adjust=0.5,
            clip_on=False,
            fill=True,
            alpha=0.1,
            linewidth=1.5,
            hue=plot_predictions[f"{venue}_team"],
            palette=color_dict,
            legend=False,
            ax=ax,
        )

    sns.despine(left=True)

    ax.set(yticks=[], ylabel="")

    if idx != (nrows - 1):
        ax.set(xticks=[])

    # else:
    #     ax.set(xlabel="predicted total goals")

    ax.set_title(f"{game['home_team']} vs. {game['away_team']}", y=0.8)

fig.savefig(f"./charts/{latest_date}.png", dpi=650, bbox_inches="tight", facecolor="white")

Assessing predictions

Seeing how the season long predictions have been playing

Downloading the data from GitHub

Downloading the data from the chickenstats repository on GitHub

csv_url = "https://raw.githubusercontent.com/chickenandstats/chickenstats-blog/refs/heads/main/nbs/blog/posts/tutorials/monte_carlo/results/predicted_winners.csv"

season_predictions = pl.read_csv(csv_url)

season_predictions.head(10)

shape: (10, 28)

game_id	home_team	away_team	predicted_winner	actual_winner	prediction_correct	predicted_home_win	predicted_away_win	predicted_draw	predicted_home_win_percent	predicted_away_win_percent	predicted_draw_percent	predicted_home_5v5_goals_mean	predicted_home_powerplay_goals_mean	predicted_home_total_goals_mean	predicted_home_5v5_xgf_p60_mean	predicted_home_powerplay_xgf_p60_mean	predicted_home_5v5_toi_mean	predicted_home_powerplay_toi_mean	predicted_home_shorthanded_toi_mean	predicted_away_5v5_goals_mean	predicted_away_powerplay_goals_mean	predicted_away_total_goals_mean	predicted_away_5v5_xgf_p60_mean	predicted_away_powerplay_xgf_p60_mean	predicted_away_5v5_toi_mean	predicted_away_powerplay_toi_mean	predicted_away_shorthanded_toi_mean
i64	str	str	str	str	i64	i64	i64	i64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64
2025020695	"WPG"	"LAK"	"LAK"	"WPG"	0	4060	5892	48	0.406	0.5892	0.0048	1.956666	0.641295	2.597961	2.5485	7.1324	46.105153	5.400488	4.396158	2.202071	0.824131	3.026202	2.8657	11.2256	46.105153	4.396158	5.400488
2025020530	"DET"	"UTA"	"UTA"	"UTA"	1	4511	5435	54	0.4511	0.5435	0.0054	2.187779	0.527668	2.715447	2.7515	6.9293	47.688887	4.564279	3.723834	2.512217	0.435366	2.947583	3.1607	7.008	47.688887	3.723834	4.564279
2025020148	"PIT"	"STL"	"STL"	"PIT"	0	2056	7903	41	0.2056	0.7903	0.0041	1.962572	1.252185	3.214757	2.782	9.6232	42.352182	7.806185	6.377632	3.922311	1.086998	5.00931	5.5547	10.2336	42.352182	6.377632	7.806185
2025020593	"CAR"	"DET"	"DET"	"CAR"	0	4917	5037	46	0.4917	0.5037	0.0046	2.486878	0.699148	3.186026	3.1919	9.9487	46.735572	4.217244	4.457284	2.362811	0.840152	3.202963	3.0351	11.309	46.735572	4.457284	4.217244
2025020427	"OTT"	"NYR"	"NYR"	"NYR"	1	3814	6144	42	0.3814	0.6144	0.0042	1.583031	0.48285	2.065881	1.9963	6.3484	47.649183	4.570142	3.926674	1.909994	0.669286	2.57928	2.4068	10.228	47.649183	3.926674	4.570142
2025020712	"BOS"	"PIT"	"PIT"	"BOS"	0	3955	5997	48	0.3955	0.5997	0.0048	2.251294	0.423561	2.674854	2.82	5.8083	47.907743	4.377982	3.811276	2.579232	0.621881	3.201113	3.2312	9.8068	47.907743	3.811276	4.377982
2025020329	"ANA"	"OTT"	"OTT"	"OTT"	1	3673	6274	53	0.3673	0.6274	0.0053	1.782043	0.533371	2.315414	2.3281	8.1117	45.880385	3.939515	5.5705	2.322641	0.583617	2.906258	3.0382	6.2758	45.880385	5.5705	3.939515
2025020478	"UTA"	"FLA"	"UTA"	"FLA"	0	5255	4681	64	0.5255	0.4681	0.0064	2.160342	0.722947	2.883289	3.0104	7.2158	43.032919	5.999608	6.071273	1.920013	0.8197	2.739713	2.6752	8.1008	43.032919	6.071273	5.999608
2025020665	"CGY"	"SEA"	"CGY"	"SEA"	0	6768	3177	55	0.6768	0.3177	0.0055	2.404052	0.712321	3.116374	3.0099	9.7929	47.894337	4.372837	3.531827	1.704213	0.540618	2.244831	2.1322	9.1522	47.894337	3.531827	4.372837
2025020319	"TOR"	"CBJ"	"CBJ"	"CBJ"	1	2905	7062	33	0.2905	0.7062	0.0033	1.959842	0.663825	2.623667	2.431	10.4463	48.388112	3.816683	3.615505	2.558635	1.188494	3.747129	3.1704	19.7096	48.388112	3.615505	3.816683

Checking the results

Let’s see how the simulation does

season_predictions.select(
    pl.col("prediction_correct").sum().alias("correct_predictions"),
    pl.col("game_id").n_unique().alias("total games"),
    (pl.col("prediction_correct").sum() / pl.col("game_id").n_unique()).alias("correct_prediction_percent"),
)

# Kind of meh, TBH

shape: (1, 3)

correct_predictions	total games	correct_prediction_percent
i64	u32	f64
414	796	0.520101