Matt Anikiej

The NHL’s Lucky Charm

I’ve been wanting to explore which player is a “lucky charm” for their team. Not necessarily which player is getting lucky, but which player is causing his team to get lucky. Just how great players make their teammates better by setting them up beautifully, or scoring goals off any pass, lucky charm players make their teammates better by just being on the same team as them! “Puck luck” and “lucky bounces” are always talked about in hockey and it’s an intangible part of the game, but let’s try to quantify it anyway!

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

Exploring The Data

The data that I used for this is from MoneyPuck which is an incredible resource for any hockey stats nerd. This used the 2024-25 season’s data, but it should run with any season that you’d like to check.

season = "2024-25"

file_prefix = f"../data/{season}/"

skaters_file = file_prefix + "skaters.csv"

The data shows different statistics for different situations. This is a very important distinction to make in hockey, as the game is played completely differently in man-up vs even strength situations.

data = pd.read_csv(skaters_file)

data.head()
playerId season name team position situation games_played icetime shifts gameScore ... OffIce_F_xGoals OffIce_A_xGoals OffIce_F_shotAttempts OffIce_A_shotAttempts xGoalsForAfterShifts xGoalsAgainstAfterShifts corsiForAfterShifts corsiAgainstAfterShifts fenwickForAfterShifts fenwickAgainstAfterShifts
0 8478047 2024 Michael Bunting NSH L other 76 2237.0 37.0 26.19 ... 7.28 10.09 72.0 87.0 0.00 0.00 0.0 0.0 0.0 0.0
1 8478047 2024 Michael Bunting NSH L all 76 70819.0 1474.0 43.70 ... 161.54 187.75 3221.0 3522.0 0.00 0.00 0.0 0.0 0.0 0.0
2 8478047 2024 Michael Bunting NSH L 5on5 76 59813.0 1294.0 43.70 ... 112.73 122.08 2661.0 2707.0 0.71 1.71 19.0 43.0 16.0 31.0
3 8478047 2024 Michael Bunting NSH L 4on5 76 6.0 2.0 2.58 ... 0.20 0.17 4.0 11.0 0.00 0.00 0.0 0.0 0.0 0.0
4 8478047 2024 Michael Bunting NSH L 5on4 76 8763.0 141.0 36.88 ... 23.81 2.60 311.0 54.0 0.00 0.01 0.0 1.0 0.0 1.0

5 rows × 154 columns

Overall there were 920 unique players in the NHL in the 2024-25 season. However, we want to make sure to find someone who was consistently lucky, rather than someone who got lucky being lucky. There’s nothing more lucky than lucky number 7, so to make sure we have a good sample size, we’re going to only look at players who have played at least 77 games.

unique_players = len(data['playerId'].unique())

print(f"Number of players in the {season} NHL Season: {unique_players}")

Number of players in the 2024-25 NHL Season: 920

# get all players who have played at least 70 games
players_77 = data[data["games_played"] >= 77].copy()

unique_players_77 = len(players_77['playerId'].unique())

print(f"Number of players in the {season} NHL Season with at least 77 games played: {unique_players_77}")

Number of players in the 2024-25 NHL Season with at least 77 games played: 280

Current Puck Luck Stats

Right now, there’s already an advanced metric that we can use to sort of define “puck luck”, and that’s PDO (Personal Discouragement Outcomes). All PDO is, is the sum of a team’s shooting percentage plus a team’s save percentage. This averages out to 100.

With a big sample size, PDO can help see if a team is playing above or below expectations, and can help aid in understanding how a team might regress back to the mean. In small sample sizes, it can help show who is really hot or really cold. It is important to note that since PDO is measuring luck, and is very influenced by luck, it is not a good stat in isolation. It is extremely valuable in conjunction with other stats and showing a quick overview, but is not meant to be a sole stat used to inform a team’s or player’s performance.

So let’s use it for exactly that! I want to find the On Ice PDO of each player, rather than the team PDO or player’s individual PDO. This will help us see who’s teammates are getting lucky during their shifts as well, while ignoring the team’s performance while on the player is on the bench.

# calculate pdo based on shots and goals
shots_for = players_77["OnIce_F_shotsOnGoal"]
shots_against = players_77["OnIce_A_shotsOnGoal"]

players_77["OnIce_F_ShotPercentage"] = np.where(shots_for > 0,
                                    players_77["OnIce_F_goals"] / shots_for,
                                    np.nan)

players_77["OnIce_F_SavePercentage"] = np.where(shots_against > 0,
                                    1 - (players_77["OnIce_A_goals"] / shots_against),
                                    np.nan)

# PDO on 1.000 scale (typical analytics usage)
players_77["OnIce_PDO"] = players_77["OnIce_F_ShotPercentage"] + players_77["OnIce_F_SavePercentage"]

# PDO on ~100 scale (common media display)
players_77["OnIce_PDO_100"] = 100 * players_77["OnIce_PDO"]

pdo = players_77[["playerId", "name", "team", "position", "situation", "OnIce_F_ShotPercentage", "OnIce_F_SavePercentage", "OnIce_PDO", "OnIce_PDO_100"]]

pdo.head()
playerId name team position situation OnIce_F_ShotPercentage OnIce_F_SavePercentage OnIce_PDO OnIce_PDO_100
5 8480950 Ilya Lyubushkin DAL D other 1.000000 0.800000 1.800000 180.000000
6 8480950 Ilya Lyubushkin DAL D all 0.100000 0.902760 1.002760 100.275953
7 8480950 Ilya Lyubushkin DAL D 5on5 0.093306 0.920354 1.013660 101.366027
8 8480950 Ilya Lyubushkin DAL D 4on5 0.093750 0.866667 0.960417 96.041667
9 8480950 Ilya Lyubushkin DAL D 5on4 0.000000 NaN NaN NaN

If we look at the On Ice PDO in all situations, we see why it’s important that we’re going to make a distinction at only looking at 5 on 5 stats. In the 2024-25 season, the top 3 players are all on the Winnipeg Jets. That season, the Jets had the best power play in the entire NHL, and their goalie won both the Vezina and Hart trophies, and had the second highest save percentage (0.925) in the entire league. Only Anthony Stolarz had a higher save percentage with 0.926, but had 29 less games played (63 vs 34).

pdo_all = pdo[pdo["situation"] == "all"]

pdo_all.sort_values(by="OnIce_PDO_100", ascending=False).head(5)
playerId name team position situation OnIce_F_ShotPercentage OnIce_F_SavePercentage OnIce_PDO OnIce_PDO_100
2466 8478398 Kyle Connor WPG L all 0.147651 0.904762 1.052413 105.241291
956 8476460 Mark Scheifele WPG C all 0.145717 0.905055 1.050773 105.077295
1726 8475799 Nino Niederreiter WPG R all 0.112769 0.936508 1.049277 104.927742
2366 8474151 Ryan McDonagh TBL D all 0.138889 0.909624 1.048513 104.851330
2391 8478010 Brayden Point TBL C all 0.149286 0.898860 1.048147 104.814690

Elite special teams and goaltending is not lucky. If we change this to look at 5 on 5 only, we’ll get a much clearer picture on each player’s puck luck. We have more reasonable results like Kirill Marchenko who had an amazing breakout year, but a very high save percentage while he’s on the ice. This is no fault of his, in fact he’s directly influencing it by being great on the defensive end of the puck too! His goalie, Elvis Merzļikins, only had a 0.892 save percentage, which was the 41st ranked SV% and a far cry from the 0.931 with Kirill Marchenko on the ice.

Again, we run into similar issues as before, but at least our results are more reasonable. Adrian Kempe was great year, and Darcy Kuemper was phenomenal which isn’t lucky. Then we see Brayden Point’s entire line in the top 5, which makes sense since they’re backed by another Vezina winner, and have the 2024-25 Ted Lindsay winner on the wing, who’s known for his creative playmaking.

This shows the faults of isolating PDO. Especially since we know these players aren’t getting lucky, as they’ve been putting up good performances their entire careers. The 2024-25 season wasn’t even Adrian Kempe’s best year. Also, we don’t want to know which player is getting lucky, but who is making their team lucky. This On Ice PDO is going to help us understand at a glance who is getting slightly lucky, but we’re going to have to dive a little bit deeper.

pdo_5v5 = pdo[pdo["situation"] == "5on5"]

pdo_5v5.sort_values(by="OnIce_PDO_100", ascending=False).head(10)
playerId name team position situation OnIce_F_ShotPercentage OnIce_F_SavePercentage OnIce_PDO OnIce_PDO_100
1332 8477960 Adrian Kempe LAK R 5on5 0.117761 0.932790 1.050551 105.055084
2392 8478010 Brayden Point TBL C 5on5 0.124567 0.925566 1.050134 105.013382
767 8477404 Jake Guentzel TBL C 5on5 0.116694 0.931148 1.047841 104.784122
4537 8480893 Kirill Marchenko CBJ R 5on5 0.116641 0.930530 1.047171 104.717091
872 8476453 Nikita Kucherov TBL R 5on5 0.122754 0.922835 1.045589 104.558914
2012 8476902 Esa Lindell DAL D 5on5 0.108911 0.935438 1.044348 104.434848
1837 8479385 Jordan Kyrou STL R 5on5 0.114338 0.929577 1.043915 104.391503
4152 8478874 Adam Gaudette OTT R 5on5 0.101587 0.941358 1.042945 104.294533
2467 8478398 Kyle Connor WPG L 5on5 0.111675 0.930876 1.042551 104.255070
2367 8474151 Ryan McDonagh TBL D 5on5 0.111667 0.930769 1.042436 104.243590

What’s Luck?

To create a stat that is going to quantify luck, first we are going to have to define what it means to be lucky. We are going to incorporate 5 stats:

These metrics will be:

  1. On Ice PDO (defined above)
  2. Individual Point Percentage
  3. G - xG Difference
  4. Linemate G - Linemate xG Difference
  5. Low Danger Goals - Low Danger xG

Then we will build a composite z-score metric that will define luck. Using a composite z-score will allow us to combine these different stats on the same scale, and give us a clear picture of not only who is the luckiest charm, but how much more luck they bring than other players.

IPP (Individual Point Percentage)

IPP will help us see whose teammates are scoring goals without them needing to do anything. This doesn’t mean they’re freeloaders. They could be drawing defenders to them, screening the goalie, or otherwise letting their linemates get lucky and get to high danger areas more easily than they would’ve otherwise. This could even be something as lucky as a defender tripping over the blue line, and allowing a free lane for a player to have a free 1 on 1 with the opposing goalie.

# Calculate IPP (Individual Points Percentage)
# IPP = (Player's points on on-ice goals) / (Team goals while player is on ice)

on_ice_goals_for = players_77["OnIce_F_goals"]

players_77["IPP"] = np.where(on_ice_goals_for > 0,
                              players_77["I_F_points"] / on_ice_goals_for,
                              np.nan)

# IPP as percentage (0-100 scale)
players_77["IPP_percentage"] = 100 * players_77["IPP"]

# View IPP by situation
ipp_view = players_77[["playerId", "name", "team", "position", "situation", "I_F_points", "OnIce_F_goals", "IPP", "IPP_percentage"]]

There’s just one problem… Defenders are naturally going to have a significantly lower IPP as compared to forwards, since they don’t have the puck on their sticks as often in the offensive zone.

ipp_5v5 = ipp_view[ipp_view["situation"] == "5on5"]

ipp_5v5.sort_values(by="IPP_percentage", ascending=True).head(10)
playerId name team position situation I_F_points OnIce_F_goals IPP IPP_percentage
3522 8476885 Jacob Trouba ANA D 5on5 10.0 52.0 0.192308 19.230769
3562 8481122 Simon Benoit TOR D 5on5 9.0 44.0 0.204545 20.454545
1917 8470600 Ryan Suter STL D 5on5 13.0 58.0 0.224138 22.413793
1187 8475188 Brayden McNabb VGK D 5on5 16.0 68.0 0.235294 23.529412
942 8475279 Ben Chiarot DET D 5on5 12.0 51.0 0.235294 23.529412
2507 8478443 Brandon Carlo TOR D 5on5 11.0 46.0 0.239130 23.913043
3672 8477948 Travis Sanheim PHI D 5on5 17.0 69.0 0.246377 24.637681
3437 8475455 Brenden Dillon NJD D 5on5 14.0 56.0 0.250000 25.000000
2982 8476331 Dylan DeMelo WPG D 5on5 18.0 70.0 0.257143 25.714286
562 8481568 Alex Vlasic CHI D 5on5 16.0 61.0 0.262295 26.229508

Also, we’d expect IPP to be normally distributed, but there are clearly two humps in the histogram when we play the frequency of IPP.

plt.figure(figsize=(10, 6))
sns.histplot(ipp_5v5["IPP_percentage"], bins=30, kde=True)
plt.title("Historgram IPP 5on5")
plt.xlabel("IPP")
plt.show()

png

Not to worry though! Two humps most likely means that one of the distributions is for forwards, and the other for defense. If we look at the stats seperately for the positions, we see this to be true.

ipp_d = ipp_5v5[ipp_5v5["position"] == "D"]

ipp_d.describe()
playerId I_F_points OnIce_F_goals IPP IPP_percentage
count 7.400000e+01 74.000000 74.000000 74.000000 74.000000
mean 8.478267e+06 20.500000 57.864865 0.350878 35.087824
std 2.814328e+03 7.360111 11.622279 0.082019 8.201860
min 8.470600e+06 9.000000 29.000000 0.192308 19.230769
25% 8.476564e+06 15.250000 49.500000 0.289263 28.926282
50% 8.478020e+06 18.500000 57.500000 0.347319 34.731935
75% 8.480801e+06 24.000000 66.000000 0.411096 41.109626
max 8.483457e+06 48.000000 86.000000 0.575342 57.534247 
ipp_f = ipp_5v5[ipp_5v5["position"] != "D"]

ipp_f.describe()
playerId I_F_points OnIce_F_goals IPP IPP_percentage
count 2.060000e+02 206.000000 206.000000 206.000000 206.000000
mean 8.478728e+06 29.742718 44.660194 0.656910 65.690969
std 2.670904e+03 10.865332 13.580871 0.094020 9.401985
min 8.470621e+06 5.000000 12.000000 0.400000 40.000000
25% 8.476834e+06 22.250000 36.000000 0.600000 60.000000
50% 8.478460e+06 29.000000 44.000000 0.659545 65.954545
75% 8.480823e+06 36.000000 53.750000 0.713134 71.313364
max 8.484958e+06 66.000000 82.000000 0.916667 91.666667 
plt.figure(figsize=(10, 6))
sns.histplot(ipp_f["IPP_percentage"], bins=50, kde=True, label="Forwards")
sns.histplot(ipp_d["IPP_percentage"], bins=50, kde=True, label="Defensemen")
plt.title("Historgram Forward vs Defense IPP 5on5")
plt.xlabel("IPP")
plt.legend()
plt.show()

png

We can normalize the IPP by position, rather than as a whole. This way we get a mcuh clearer picture of who has the lowest IPP, since it’s going to be relative to the player’s position. When we do that, we can see that Jacob Trouba went from 1st place, to 9th in the lowest IPP.

# Filter to 5v5 only for clean analysis
luck_df = players_77[players_77['situation'] == '5on5'].copy()

# IPP Z-Score
# Calculate position-specific IPP means 
position_ipp_means = luck_df.groupby('position')['IPP'].transform('mean')
position_ipp_stds = luck_df.groupby('position')['IPP'].transform('std')

luck_df['ipp_deviation'] = (luck_df['IPP'] - position_ipp_means) / position_ipp_stds

# Z-score normalize the deviation (so it's on same scale as other components)
mean_ipp_dev = luck_df['ipp_deviation'].mean()
std_ipp_dev = luck_df['ipp_deviation'].std()
luck_df['component_ipp'] = (luck_df['ipp_deviation'] - mean_ipp_dev) / std_ipp_dev

print(f"\nTop 10 smallest IPP (relative to position):")
luck_df.nsmallest(10, 'component_ipp')[['name', 'position', 'team', 'IPP_percentage', 'I_F_points', 'OnIce_F_goals', 'component_ipp']]


Top 10 smallest IPP (relative to position):
name position team IPP_percentage I_F_points OnIce_F_goals component_ipp
1272 John Beecher C BOS 40.000000 8.0 20.0 -2.403228
3582 Luke Glendening C TBL 41.666667 5.0 12.0 -2.231466
2617 Isac Lundestrom C ANA 42.105263 8.0 19.0 -2.186266
3032 Alex Iafallo L WPG 50.000000 18.0 36.0 -2.144604
77 Barclay Goodrow C SJS 42.857143 6.0 14.0 -2.108779
597 Zemgus Girgensons C TBL 42.857143 6.0 14.0 -2.108779
2347 Martin Pospisil C CGY 43.181818 19.0 44.0 -2.075319
1727 Nino Niederreiter R WPG 51.162791 22.0 43.0 -1.988713
3522 Jacob Trouba D ANA 19.230769 10.0 52.0 -1.943827
2752 Lawson Crouse L UTA 51.612903 16.0 31.0 -1.942781

We already calculated the On Ice PDO earlier, so let’s get the z-score for it as well, and confirm it’s a normal distribution.

# PDO Z-Score 
# Calculate z-score normalization for OnIce_PDO_100 by situation
mean_pdo = luck_df.groupby('situation')['OnIce_PDO_100'].transform('mean')
std_pdo = luck_df.groupby('situation')['OnIce_PDO_100'].transform('std')
luck_df['OnIce_PDO_100_normalized'] = (luck_df['OnIce_PDO_100'] - mean_pdo) / std_pdo

# Use the normalized PDO for component calculation
luck_df['component_pdo'] = luck_df['OnIce_PDO_100_normalized']

plt.figure(figsize=(10, 6))
sns.histplot(luck_df['component_pdo'], bins=50, kde=True)
plt.title('PDO Z-Score Distribution')
plt.xlabel('Z-Score')
plt.ylabel('Frequency')
plt.show()

png

Another luck based metric we can use the difference in goals minus expected goals. This gives us an understanding of who is scoring at a higher rate than other players from the same location. We want to make sure we get the rate metric of this though, so we will get this difference per 60 minutes. Like I mentioned earlier, we want players who are consistently lucky, rather than lucky just once.

# Convert ice time to hours for per-60 calculations
luck_df['icetime_hours'] = luck_df['icetime'] / 3600

# Individual Goals vs xGoals per 60 minutes
luck_df['goals_minus_xgoals'] = luck_df['I_F_goals'] - luck_df['I_F_xGoals']
luck_df['goals_minus_xgoals_per60'] = (luck_df['goals_minus_xgoals'] / luck_df['icetime_hours']) * (60/60)

# Z-score normalize
mean_g_xg = luck_df['goals_minus_xgoals_per60'].mean()
std_g_xg = luck_df['goals_minus_xgoals_per60'].std()
luck_df['component_goals_xgoals'] = (luck_df['goals_minus_xgoals_per60'] - mean_g_xg) / std_g_xg

print(f"\nTop 5 luckiest finishers (goals above expected per 60):")
luck_df.nlargest(5, 'goals_minus_xgoals_per60')[['name', 'I_F_goals', 'I_F_xGoals', 'goals_minus_xgoals_per60']]


Top 5 luckiest finishers (goals above expected per 60):
name I_F_goals I_F_xGoals goals_minus_xgoals_per60
667 Adam Fantilli 25.0 11.23 0.673002
4152 Adam Gaudette 16.0 8.34 0.639607
1317 Artemi Panarin 25.0 12.75 0.588024
4537 Kirill Marchenko 24.0 12.78 0.558549
4177 Ryan Donato 23.0 13.07 0.539927

More importantly, we want to know who is getting their teammates lucky! We can use the same metric, but define it by the goals their teammates scored and their expected goals, without the current player’s goals and expected goals. This will give us a good sense of whose linemmates are scoring more than other players from the same location.

# Teammate Goals vs xGoals per 60 (linemate luck, excluding player's own goals)
# IMPORTANT: Subtract individual goals to avoid double-counting
# This isolates teammate/linemate luck separate from personal finishing luck
luck_df['teammate_goals'] = luck_df['OnIce_F_goals'] - luck_df['I_F_goals']
luck_df['teammate_xgoals'] = luck_df['OnIce_F_xGoals'] - luck_df['I_F_xGoals']
luck_df['teammate_goals_minus_xgoals'] = luck_df['teammate_goals'] - luck_df['teammate_xgoals']
luck_df['teammate_goals_minus_xgoals_per60'] = (luck_df['teammate_goals_minus_xgoals'] / luck_df['icetime_hours']) * (60/60)

# Z-score normalize
mean_tg_xg = luck_df['teammate_goals_minus_xgoals_per60'].mean()
std_tg_xg = luck_df['teammate_goals_minus_xgoals_per60'].std()
luck_df['component_teammate_goals_xgoals'] = (luck_df['teammate_goals_minus_xgoals_per60'] - mean_tg_xg) / std_tg_xg

print(f"\nTop 5 luckiest linemate performers (teammates scoring above expected):")
luck_df.nlargest(5, 'teammate_goals_minus_xgoals_per60')[['name', 'position', 'team', 'teammate_goals', 'teammate_xgoals', 'teammate_goals_minus_xgoals_per60']]

Top 5 luckiest linemate performers (teammates scoring above expected):
name position team teammate_goals teammate_xgoals teammate_goals_minus_xgoals_per60
4472 JJ Peterka R BUF 53.0 33.91 1.052580
1047 Pierre-Luc Dubois L WSH 60.0 44.03 0.819663
2347 Martin Pospisil C CGY 41.0 27.94 0.767997
4292 Jared McCann L SEA 40.0 27.33 0.763381
2132 Ryan McLeod C BUF 42.0 29.43 0.724357

Finally, scoring from low danger situations is a little bit lucky sometimes. While we want to know who is a lucky charm for their team, some of that luck has to rub off on yourself too right?

# Low Danger Goals Above Expected (shot quality luck)
luck_df['lowdanger_goals_minus_xgoals'] = luck_df['I_F_lowDangerGoals'] - luck_df['I_F_lowDangerxGoals']
luck_df['lowdanger_goals_minus_xgoals_per60'] = (luck_df['lowdanger_goals_minus_xgoals'] / luck_df['icetime_hours']) * (60/60)

# Z-score normalize
mean_ld = luck_df['lowdanger_goals_minus_xgoals_per60'].mean()
std_ld = luck_df['lowdanger_goals_minus_xgoals_per60'].std()
luck_df['component_lowdanger'] = (luck_df['lowdanger_goals_minus_xgoals_per60'] - mean_ld) / std_ld

print(f"\nTop 5 luckiest low danger scorers:")
luck_df.nlargest(5, 'lowdanger_goals_minus_xgoals_per60')[['name', 'position', 'team', 'I_F_lowDangerGoals', 'I_F_lowDangerxGoals', 'lowdanger_goals_minus_xgoals_per60']]

Top 5 luckiest low danger scorers:
name position team I_F_lowDangerGoals I_F_lowDangerxGoals lowdanger_goals_minus_xgoals_per60
4307 Kiefer Sherwood L VAN 11.0 4.16 0.428452
1737 Alex Tuch R BUF 12.0 4.20 0.421059
4537 Kirill Marchenko R CBJ 14.0 5.62 0.417169
1317 Artemi Panarin L NYR 15.0 6.88 0.389776
1837 Jordan Kyrou R STL 13.0 6.25 0.342896

Alright we have all our components! Now it’s time to bring them together. Not every stat should be weighted equally. Also, combining z-scores let’s us interpret and analyze new metrics as if they were normal z-scores. However, they are no longer in units of std, since the range can vary drasitcally. There are ways to bring it back, such as taking the average of all the metrics (same as having the same weight for each component), or making sure that our weights add up to 1.

Weights:

# Weighted combination of all components
luck_df['Luck_Score'] = (
    0.30 * luck_df['component_pdo'] +                    # PDO (team on-ice luck)
    -0.30 * luck_df['component_ipp'] +                   # Involvement luck
    0.20 * luck_df['component_teammate_goals_xgoals'] +  # Linemate/team luck
    0.10 * luck_df['component_goals_xgoals'] +           # Personal finishing luck
    0.10 * luck_df['component_lowdanger']                # Shot quality luck
)

plt.figure(figsize=(10, 6))
sns.histplot(luck_df['Luck_Score'], bins=30, kde=True)
plt.title('Luck Score Distribution')
plt.xlabel('Luck Score')
plt.ylabel('Frequency')
plt.show()

png

It worked! We have a normal distribution, so our math was correct! Our luckiest charm of the 2024-25 season was… (imagine there’s a corny drum roll here) JJ Peterka! JJ Peterka had an incredible breakout season last year, and was a bright spot on an otherwise dissappointing Buffalo Sabres Team. What really set him apart from other players was his huge Teammate Goals minus Expected Goals difference. Last year he became a much better playmaker and nearly doubled his career high assists total.

print("TOP 10 LUCKIEST PLAYERS IN THE NHL (2024 Season, 5v5)")

luck_df.nlargest(10, 'Luck_Score')[
    ['name', 'team', 'position', 'Luck_Score',
     'component_pdo', 'component_goals_xgoals', 'component_teammate_goals_xgoals',
     'component_ipp', 'component_lowdanger']
]


TOP 10 LUCKIEST PLAYERS IN THE NHL (2024 Season, 5v5)
name team position Luck_Score component_pdo component_goals_xgoals component_teammate_goals_xgoals component_ipp component_lowdanger
4472 JJ Peterka BUF R 1.754177 1.420772 1.816297 3.126413 -1.083948 1.958489
4537 Kirill Marchenko CBJ R 1.612333 2.127610 2.675489 0.771595 -0.837337 3.009810
2392 Brayden Point TBL C 1.448174 2.267434 1.661380 1.818725 -0.227574 1.697885
767 Jake Guentzel TBL C 1.269989 2.159243 0.371581 1.940786 -0.656979 -0.001933
3032 Alex Iafallo WPG L 1.242725 1.565437 -0.675543 0.942813 -2.144604 0.087045
1332 Adrian Kempe LAK R 1.180304 2.287114 1.068144 1.344476 0.013880 1.226245
3562 Simon Benoit TOR D 1.171758 1.458202 -0.031689 1.286739 -1.793812 -0.580253
2012 Esa Lindell DAL D 1.027736 1.994416 -0.065172 1.123149 -0.958009 -0.761040
1837 Jordan Kyrou STL R 1.027428 1.973960 2.303428 0.825344 0.664901 2.392991
732 Juraj Slafkovsk MTL L 1.011247 1.128212 -0.236128 2.095865 -0.606111 0.953893 
print("TOP 10 UNLUCKIEST PLAYERS IN THE NHL (2024 Season, 5v5)")
luck_df.nsmallest(10, 'Luck_Score')[
    ['name', 'team', 'position', 'Luck_Score', 
     'component_pdo', 'component_goals_xgoals', 'component_teammate_goals_xgoals',
     'component_ipp', 'component_lowdanger']
]



TOP 10 UNLUCKIEST PLAYERS IN THE NHL (2024 Season, 5v5)
name team position Luck_Score component_pdo component_goals_xgoals component_teammate_goals_xgoals component_ipp component_lowdanger
2127 Sam Steel DAL C -1.586776 -1.407685 -0.760224 -1.563049 2.491995 -0.282397
4182 Alexander Kerfoot UTA C -1.440901 -1.245025 -1.094082 -2.189002 1.375540 -1.075225
3037 Logan O'Connor COL R -1.285091 -1.548609 -0.065648 -1.725069 1.481691 -0.244229
2872 Conor Garland VAN R -1.283190 -0.867702 -0.628837 -1.329323 1.588155 -2.176852
1347 Travis Konecny PHI R -1.263194 -1.176164 -0.623230 -0.644318 2.309489 -0.263113
147 Scott Laughton TOR C -1.189860 -1.792731 -0.638392 -0.312881 1.525832 -0.678760
2262 Brady Skjei NSH D -1.152939 -1.660189 0.246818 -1.934162 0.713596 -0.786523
3802 Paul Cotter NJD C -1.123779 -2.194399 1.312482 -2.047127 1.108355 1.452247
577 Jake Sanderson OTT D -1.080926 -1.443615 0.224575 -1.889680 0.781548 -0.578983
1432 Brandon Tanev WPG L -1.071214 -1.302198 -0.779887 -1.255948 0.608273 -1.688938

We can get a better idea of how much more luck JJ Peterka brings to his team, if we plot all of the components, and where JJ Peterka lies along the historgram.

jj_peterka = luck_df[luck_df['name'] == 'JJ Peterka']

jj_peterka

fig, axes = plt.subplots(2, 3, figsize=(18, 10))
fig.suptitle('JJ Peterka Luck Score Components', fontsize=16, fontweight='bold')

# Component 1: PDO
axes[0, 0].hist(luck_df['component_pdo'], bins=30, edgecolor='black', alpha=0.7)
axes[0, 0].set_title('PDO Z-Score (30% weight)')
axes[0, 0].set_xlabel('Z-Score')
pdo_value = jj_peterka['component_pdo'].values[0]
axes[0, 0].axvline(pdo_value, color='red', linestyle='--', linewidth=2, label=f'JJ Peterka ({pdo_value:.2f})')
axes[0, 0].legend()

# Component 2: Goals vs xGoals
axes[0, 1].hist(luck_df['component_goals_xgoals'], bins=30, edgecolor='black', alpha=0.7)
axes[0, 1].set_title('Goals vs xGoals per 60 (10% weight)')
axes[0, 1].set_xlabel('Z-Score')
goals_xgoals_value = jj_peterka['component_goals_xgoals'].values[0]
axes[0, 1].axvline(goals_xgoals_value, color='red', linestyle='--', linewidth=2, label=f'JJ Peterka ({goals_xgoals_value:.2f})')
axes[0, 1].legend()

# Component 3: Teammate Goals vs xGoals (linemate luck)
axes[0, 2].hist(luck_df['component_teammate_goals_xgoals'], bins=30, edgecolor='black', alpha=0.7)
axes[0, 2].set_title('Teammate Goals vs xGoals per 60 (20% weight)')
axes[0, 2].set_xlabel('Z-Score (Linemate Luck)')
onice_goals_xgoals_value = jj_peterka['component_teammate_goals_xgoals'].values[0]
axes[0, 2].axvline(onice_goals_xgoals_value, color='red', linestyle='--', linewidth=2, label=f'JJ Peterka ({onice_goals_xgoals_value:.2f})')
axes[0, 2].legend()

# Component 4: IPP
axes[1, 0].hist(luck_df['component_ipp'], bins=30, edgecolor='black', alpha=0.7)
axes[1, 0].set_title('IPP Deviation (10% weight)')
axes[1, 0].set_xlabel('Z-Score')
ipp_value = jj_peterka['component_ipp'].values[0]
axes[1, 0].axvline(ipp_value, color='red', linestyle='--', linewidth=2, label=f'JJ Peterka ({ipp_value:.2f})')
axes[1, 0].legend()

# Component 5: Low Danger
axes[1, 1].hist(luck_df['component_lowdanger'], bins=30, edgecolor='black', alpha=0.7)
axes[1, 1].set_title('Low Danger Goals vs xGoals (20% weight)')
axes[1, 1].set_xlabel('Z-Score')
lowdanger_value = jj_peterka['component_lowdanger'].values[0]
axes[1, 1].axvline(lowdanger_value, color='red', linestyle='--', linewidth=2, label=f'JJ Peterka ({lowdanger_value:.2f})')
axes[1, 1].legend()

# Final Luck Score
axes[1, 2].hist(luck_df['Luck_Score'], bins=30, edgecolor='black', alpha=0.7, color='purple')
axes[1, 2].set_title('FINAL LUCK SCORE', fontweight='bold')
axes[1, 2].set_xlabel('Luck Score')
luck_score_value = jj_peterka['Luck_Score'].values[0]
axes[1, 2].axvline(luck_score_value, color='red', linestyle='--', linewidth=2, label=f'JJ Peterka ({luck_score_value:.2f})')
axes[1, 2].legend()

plt.tight_layout()
plt.show()

png

Interpreting Luck

Ok so here’s where we get a little hand wavy, but stick with me! Let’s try to make something fun out of this score. I want to know how many goals does 1 luck translate into for a team.

What we’re going to do is:

(On Ice Goals - On Ice xG) / luck

for each player, and then get the average of the On Ice Goals above expected per luck per player, we can see how many goals 1 luck is worth over a season.

# calculate how many goals each team scored with the player on the ice
onice_f_g = luck_df['OnIce_F_goals']
onice_f_xg = luck_df['OnIce_F_xGoals']

luck_score = luck_df['Luck_Score']

goals_minus_xgoals = onice_f_g - onice_f_xg

# divide goals above expected by luck score to get a sense of how many goals per luck score
goals_per_luck_score = goals_minus_xgoals / luck_score

goals_per_luck_score_mean = np.mean(goals_per_luck_score)

print(f"Goals per Luck Score: {goals_per_luck_score_mean:.3f}")

Goals per Luck Score: 8.876

So, JJ Peterka is good for 15.57 lucky goals from his team when he is on the ice, over the course of a whole season. If we agree that scoring 5 goals (waving our hand so often we have jazz hands), then JJ Peterka is good for 3 lucky wins on the season.

luck_df['lucky_goals'] = luck_df['Luck_Score'] * goals_per_luck_score_mean

luck_df[
    ['name', 'team', 'position', 
     'OnIce_PDO_100', 'I_F_goals', 'I_F_xGoals', 
     'IPP_percentage', 'Luck_Score', 'lucky_goals']
     ].sort_values(by='lucky_goals', ascending=False).head(10)
name team position OnIce_PDO_100 I_F_goals I_F_xGoals IPP_percentage Luck_Score lucky_goals
4472 JJ Peterka BUF R 103.219283 18.0 11.20 59.154930 1.754177 15.570500
4537 Kirill Marchenko CBJ R 104.717091 24.0 12.78 61.333333 1.612333 14.311460
2392 Brayden Point TBL C 105.013382 21.0 14.34 61.111111 1.448174 12.854343
767 Jake Guentzel TBL C 104.784122 19.0 17.64 56.944444 1.269989 11.272727
3032 Alex Iafallo WPG L 103.525832 8.0 10.15 50.000000 1.242725 11.030730
1332 Adrian Kempe LAK R 105.055084 21.0 16.92 68.852459 1.180304 10.476666
3562 Simon Benoit TOR D 103.298599 1.0 1.37 20.454545 1.171758 10.400804
2012 Esa Lindell DAL D 104.434848 3.0 3.64 27.272727 1.027736 9.122433
1837 Jordan Kyrou STL R 104.391503 25.0 15.57 74.603175 1.027428 9.119703
732 Juraj Slafkovsk MTL L 102.599342 13.0 14.16 62.295082 1.011247 8.976070

Just Luck?

So is JJ Peterka not good, is he just lucky? NO!!! JJ Peterka is not good because he’s lucky, he’s lucky because he is good. And besides, we weren’t measuring how lucky JJ Peterka is, but how lucky he is making his team! That’s a very important distinction to understand.

We even see that the highest value component for him, was how many goals his teammates scored. While he had a lower IPP than average, it’s not significantly lower, just 1 std. He also became a much better playmaker in the 2024-25 season than he ever was before, which is shown in in his assists nearly doubling from 22 to 41. The low IPP can be explained by dry stretches that every young player goes through. Even still, he has improved his consistency tremendously which is what led to his career best points and assists.

This season so far, he’s already put up 7 points in his first 8 games. He’s now part of a new team, new franchise, and one that just got a new logo and is in a market that’s hungry for hockey. We’ve seen what Vegas accomplished in their first few seasons compared to Seattle. Well, one of those cities is world famous for their luck. Maybe it’s not such a bad idea to take a bet on bringing in a lucky charm for a few clutch goals.

Thanks for reading!

Thanks For Reading!

Hey everyone, thanks for reading (I know I said it 3 times in a row, sorry)! I wanted to add in this little note here since it’s my first article ever on Medium. I want to try to write some fun articles on some cool anomalies, or making silly stats like this one. Hockey stats lag significantly far behind other sports like baseball and basketball, and I’d love to try to add to the community and try to make them more accessible. I’m not one who believes stats are the end all - be all, and capture everything, but they can bring interesting insights and can help inform a lot about the game.

I’ve also started a YouTube channel, which I hope to be more digestible, and these blogs will be more in depth. This is the link to this topic’s video.

Let me know if you enjoyed, and what your thoughts were on this!