Introduction

This report uses the 2021-2022 season (excluding playoffs) for comparing bet results vs. the markets. The win/loss models and the xG models are tuned separately as minor parameter changes will push the model toward better performance on different metrics.

Win/Loss Model

Model Performance

Win/Loss Model performance:

## Log Loss: 0.65301

## Accuracy: 62.31%

## AUC: 0.6605

This model was trained by reducing Log Loss

NOTE Previous editions of this had a minor issue in the model code, incorrectly normalizing the prediction of tied games.

Basic Market Calculations:

Not using market lines with vigs as percent win/loss (instead adding 0.02 to the database odds). Calculating American odds from the percents given, with rounding (toward zero) any decimal -> so if calculated american odds were +225.4, then using +225, and if -142.9 then using -142.

Presuming we place a bet if our predictions for the winner differ by 5%, the bet results from the whole season are as follows:

HomeBets	95.00
AwayBets	185.00
HomeBetResults	-1659.00
AwayBetResults	2856.00
HomeUnits	-17.46
AwayUnits	15.44
TotalBets	280.00
TotalResults	1197.00
TotalUnits	4.28

Detailed Breakdowns

Team Breakdown (Click to expand)

The results of betting broken down by each team we would have bet on:

BetTeam	Number_of_Bets	Total_Bet_Result
Anaheim Ducks	6	-604
Arizona Coyotes	61	73
Boston Bruins	13	-171
Buffalo Sabres	13	42
Carolina Hurricanes	9	685
Colorado Avalanche	4	-55
Columbus Blue Jackets	9	197
Dallas Stars	1	-100
Detroit Red Wings	1	-100
Edmonton Oilers	10	368
Florida Panthers	3	62
Los Angeles Kings	1	214
Minnesota Wild	1	124
Montreal Canadiens	19	721
Nashville Predators	11	-238
New Jersey Devils	11	518
New York Islanders	10	-553
New York Rangers	3	137
Ottawa Senators	33	661
Philadelphia Flyers	3	-300
Pittsburgh Penguins	11	-397
San Jose Sharks	2	180
Seattle Kraken	10	-788
St. Louis Blues	7	-92
Tampa Bay Lightning	9	154
Vancouver Canucks	5	319
Vegas Golden Knights	8	223
Washington Capitals	3	-46
Winnipeg Jets	3	-37

Favourite/Underdog Breakdown (Click to expand)

The results of betting broken down by whether we bet on favourites or underdogs:

Check if we would make more money betting with or against the favourite (based on + 100 or < -100 we bet with favourite).

FavBet	Number_of_Bets	Total_Bet_Result
Bet Against Favourite	241	1259
Bet Favourite	39	-62

Win/Loss by Confidence Level (Click to expand)

Check if there’s a bias in win/loss by confidence level. This same info is shown in graphical form below.

BetDiffNom	Number_of_Bets	Total_Bet_Result
0.05	46	1099
0.06	63	-1216
0.07	45	694
0.08	36	618
0.09	34	-115
0.10	24	-1022
0.11	14	24
0.12	11	1071
0.13	2	-200
0.14	3	-300
0.17	2	544

Lets take a look at a few of those biggest disagreements (model vs market):

GameID	HomeTeam	AwayTeam	HomePred	AwayPred	HomeOdds	AwayOdds	BetTeam	BetDiff
2021020270	Arizona Coyotes	Detroit Red Wings	0.5874	0.4126	0.4137	0.6263	Arizona Coyotes	0.1738
2021021287	Dallas Stars	Arizona Coyotes	0.6314	0.3686	0.8413	0.1987	Arizona Coyotes	0.1700
2021020667	Detroit Red Wings	Buffalo Sabres	0.4971	0.5029	0.6801	0.3599	Buffalo Sabres	0.1430
2021020999	San Jose Sharks	Arizona Coyotes	0.5272	0.4728	0.7095	0.3305	Arizona Coyotes	0.1423
2021020814	Arizona Coyotes	Los Angeles Kings	0.4427	0.5573	0.3060	0.7340	Arizona Coyotes	0.1367
2021021230	Arizona Coyotes	Chicago Blackhawks	0.5280	0.4720	0.3956	0.6444	Arizona Coyotes	0.1324
2021020137	Philadelphia Flyers	Arizona Coyotes	0.5631	0.4369	0.7302	0.3098	Arizona Coyotes	0.1271
2021020908	St. Louis Blues	Ottawa Senators	0.6219	0.3781	0.7858	0.2542	Ottawa Senators	0.1239
2021020607	Arizona Coyotes	Chicago Blackhawks	0.5374	0.4626	0.4137	0.6263	Arizona Coyotes	0.1237
2021020844	Arizona Coyotes	Winnipeg Jets	0.4578	0.5422	0.3350	0.7050	Arizona Coyotes	0.1227

Plots

Plot a few things!

Plot of bet results as the season progress (Click to expand)

Total season bet results:

Bet Results by Team (Click to expand)

Bet Results by Team. The total bet results by team are listed above as well.

Win/Loss by Confidence Level (Click to expand)

Check if there’s a bias in win/loss by confidence level. This same info is shown in tabular form above.

Last Seasons Bet results

Click to Expand

Using the model outputs from last year, run through the same code, we get the following results:

## Log Loss: 0.65173

## Accuracy: 62.96%

## AUC: 0.6627

HomeBets	484.00
AwayBets	424.00
HomeBetResults	-233.00
AwayBetResults	1340.00
HomeUnits	-0.48
AwayUnits	3.16
TotalBets	669.00
TotalResults	1107.00
TotalUnits	1.22

Total season bet results:

Totals/xG Model

Model performance

This doesn’t mean as much because we’re looking for totals, but here’s the model performance for win/loss. Naturally, a xG model would be expected to have reasonable W/L performance as a byproduct of being good at predicting goal performance.

## Log Loss: 0.66601

## Accuracy: 58.46%

## AUC: 0.6457

In addition, the model performance for total xG vs. G (this is the important part):

## Test R2: 0.0121

## Test RMSE: 2.35

We trained the model using RMSE as the optimized metric.

Bet Results

Setting up bet results of over/under bets placed with a difference in 0.5 xG:

OverBets	44.00
UnderBets	82.00
OverBetResults	88.00
UnderBetResults	198.00
OverUnits	2.00
UnderUnits	2.41
TotalBets	126.00
TotalResults	286.00
TotalUnits	2.27

Optimization

This feels like it could be improved - very good performance to betting overs, but poor performance with unders. The betdiff of 0.5 xG was just a random number.

We’ll tune the over/under cutoffs by using the training data (2017-2018 to 2020-2021), and then use that to determine what we would have expected to get from 2021-2022

Click to view code!

optresults<-expand.grid(
  "over"=c(0.5, 0.6, 0.7, 0.8, 0.9, 1),
  "under"=c(0.1, 0.2, 0.3, 0.4, 0.5)
  )
optresults$TotalResults<-NA_real_
optresults$TotalUnits<-NA_real_
optresults$NumBets<-NA_integer_
optresults$Units_2122<-NA_real_
optresults$Results_2122<-NA_real_
optresults$NumBets_2122<-NA_real_

for(i in 1:nrow(optresults)){
  b<-HockeyModel:::compare_market_line_xg(predictions_xg$train, overbetdiff = optresults[i,]$over, underbetdiff = optresults[i,]$under, juice = juice)
  optresults[i,]$TotalResults<-b$TotalResults
  optresults[i,]$TotalUnits<-round(b$TotalUnits, 2)
  optresults[i,]$NumBets<-b$TotalBets
  b<-HockeyModel:::compare_market_line_xg(predictions_xg$test, overbetdiff=optresults[i,]$over, underbetdiff = optresults[i,]$under, juice=juice)
  optresults[i,]$Results_2122<-b$TotalResults
  optresults[i,]$Units_2122<-round(b$TotalUnits,2)
  optresults[i,]$NumBets_2122<-b$TotalBets
}

Our best results come from betting overs if we differ by 0.8 and betting unders by differing by 0.3, In doing so, we got final results of $8502 (or 14.97 units on 568 bets). Remember that this was a 4 season performance (a total of 4877 games) so these values are picked to ‘on average’ produce those results across a long period of time.

Using those parameters, we get a result of $-2175, or -9.62 units for the 2021-2022 season.

The top 20 mixes of over/under bet (sorted on Total profit on 2017-2021) are shown below, as are the results of those parameters applied to the 2021-2022 season.

over	under	TotalResults	TotalUnits	NumBets	Units_2122	Results_2122	NumBets_2122
0.8	0.3	8502	14.97	568	-9.62	-2175	226
0.6	0.3	8298	10.73	773	-6.84	-1676	245
0.9	0.3	7933	14.91	532	-9.62	-2175	226
0.7	0.3	7792	12.35	631	-8.39	-1964	234
0.8	0.1	7639	6.14	1245	-11.07	-4241	383
0.5	0.3	7474	7.36	1015	-7.73	-2087	270
0.6	0.1	7435	5.13	1450	-9.31	-3742	402
1.0	0.3	7184	13.90	517	-9.62	-2175	226
0.9	0.1	7070	5.85	1209	-11.07	-4241	383
0.7	0.1	6929	5.30	1308	-10.31	-4030	391
0.5	0.1	6611	3.91	1692	-9.73	-4153	427
0.8	0.2	6326	7.37	858	-12.29	-3700	301
1.0	0.1	6321	5.29	1194	-11.07	-4241	383
0.6	0.2	6122	5.76	1063	-10.00	-3201	320
0.9	0.2	5757	7.00	822	-12.29	-3700	301
0.7	0.2	5616	6.10	921	-11.29	-3489	309
0.5	0.2	5298	4.06	1305	-10.47	-3612	345
1.0	0.2	5008	6.21	807	-12.29	-3700	301
0.8	0.4	4597	13.17	349	-2.81	-424	151
0.6	0.4	4393	7.93	554	0.44	75	170

All that’s left is to decide how many bets/season you’re looking for, and optimize for that with total performance taken into consideration.

We’ll look at over/under of 0.8/0.3 xG to direct our bets from now on.

OverBets	8.00
UnderBets	226.00
OverBetResults	211.00
UnderBetResults	-2175.00
OverUnits	26.38
UnderUnits	-9.62
TotalBets	234.00
TotalResults	-1964.00
TotalUnits	-8.39

Determining the Market xG

There are multiple methods of determining the market’s xG value. This is a possible opportunity to enhance the model performance - if you can get an edge on the market here, it can make or break a model’s performance.

The market data provided contains a determined market xG using the one listed above. An alternative method could be considered using Poisson fitting. Testing the market with this to see if they’re different.

OverBets	37.00
UnderBets	111.00
OverBetResults	601.00
UnderBetResults	609.00
OverUnits	16.24
UnderUnits	5.49
TotalBets	148.00
TotalResults	1210.00
TotalUnits	8.18

Digging into the differences a bit further, we’ll plot the correlation between the supplied market xG and the poisson determined xG:

## Warning: Removed 94 rows containing missing values (geom_point).

## Warning: Removed 94 rows containing non-finite values (stat_bin).

We can dig further into each method of determination by plotting the histogram of each xG implied method:

## Warning: Removed 94 rows containing non-finite values (stat_bin).

Lets look at the difference between our suspected xG and see what we have as a cause for it. Remember from above that most differences are <0.5 xG value.

## Warning: Removed 94 rows containing missing values (geom_point).

Lets look at the highest diff values to see if a tabular form helps us understand.

GameID	Totals	OverOdds	UnderOdds	ImpliedxG	ImpliedxGPoisson	ImpliedDiff
2021020883	6.0	-135	-118	6.432090	5.552015	0.8800752
2021020504	6.0	-125	-133	6.293083	5.413719	0.8793640
2021020726	6.5	-138	-110	6.971515	6.184691	0.7868235
2021020934	5.5	-139	-110	5.984436	5.209304	0.7751323
2021020649	6.0	-133	-105	6.405244	5.828398	0.5768452
2021020511	6.5	-125	-111	6.793083	6.239732	0.5533509
2021020626	6.0	-118	-118	6.188190	5.652752	0.5354379
2021021023	6.0	-118	-118	6.188190	5.652752	0.5354379
2021020998	6.0	-139	102	6.484436	5.952844	0.5315921
2021020767	6.0	-118	-115	6.188190	5.711087	0.4771035

It looks like a pretty large juice on these - that might explain the discrepancy. It also looks like these all happened in the last half of the most recent season, despite us comparing 9 season’s worth of games.

Now that we know there’s a correlation, but meaningful difference between xG methods, let’s optimize the xGPoisson betting cutoffs. This has the same format as above, so…

Click to expand!

Our best results come from betting overs if we differ by 0.8 and betting unders by differing by 0.3, In doing so, we got final results of $8003 (or 13.82 units on 579 bets).

Using those parameters, we get a result of $1210, or 8.18 units for the 2021-2022 season.