My experience trying to get started in playing daily fantasy hockey during the 2017-2018 NHL season.

Following my experience playing daily fantasy basketball, I decided to see if I could compete in hockey. On the surface, the NHL seems very similar to the NBA. There are 82 games, the season lasts from Fall to Spring, and the arenas are often the same. With respect to daily fantasy, however, there are several key differences.

First, there are many more active players. In basketball, the vast majority of minutes go to no more than 10 players. In hockey, there are several lines of players, resulting in nearly 20 players getting significant minutes.

Second, not all players have the same scoring rubric: goalies and skaters are separate rubrics:

Goalies = 12 * Team Win + 8 * Shutout + 0.8 * Saves - 4 * Goals Against
Skaters = 12 * Goals + 8 * Assists + 1.6 Shots on Goal + 0.5 * Powerplay Goal Bonus + 2 * Shorthand Goal Bonus + 1.6 * Blocked Shots

Finally, the lineup composition differs. In hockey, each lineup needs the following positions:

1 Goalie
2 Centers
4 Wings
2 Defenders

With this information, I developed models for the goalies and skaters. Since this was my first time attempting to build a model for the NHL, my goal was to beat the predictions that Fanduel provides for free. To achieve this, here’s the process I went through:

Data

I kept the data pretty simple by limiting the number of features. I ended up using just the metrics mentioned in the scoring rubric along with the player’s team and the opposing team. For building my model, I used data from the beginning of the 2017-2018 regular season where every player had at least 15 games under their belt, had played in at least 3 games in the last 10 days, and had averaged at least 10 minutes of ice time. All of this performance and team data was pulled from hockeyreference. One last variable was the predicted fantasy points from Fanduel. To make a fair comparison between my model and Fanduel’s model, I withheld this variable from my comparison model. I did, however, add this variable back in to a second model to see its impact.

Features

For the performance variables, such as goals, assists, etc., I calculated the average during the past 5, 10, and 15 games. FOr categorical variables, such as team and opposing team, I converted those to dummy variables. Overall, the features were pretty straightforward for this first iteration of a model.

Model Selection

For skaters and goalies, I used the respective training dataset to choose and tune a model that predicted Fanduel points. I performed a grid search on the parameters for GBM and ridge regression models and selected the model with the lower MSE. For both models (one using Fanduel’s predictions and one not using it), the best performing goalie model was a ridge regression model, while the best performing skater model was a GBM.

Once I had my predictions, I had to choose which players to be in my lineup to maximize my fantasy points. Similar to my work with on the NBA lineups, I reduced the lineup selection to a mathematical problem and used a multiple integer linear programming optimizer to find the best lineup for each day.

To compare my two models and the Fanduel model, I first looked at the MSE amongst all eligible players that I had in my partial 2017-2018 regular season dataset:

Overall, the model’s didn’t differ much. Technically, the Fanduel model had the lowest MSE, but it’s difficult to tell if the difference is significant. To dig a bit deeper into this, I next looked at the MSE for players that got selected in the lineups:

Unfortunately, this data also produces strange results. It appears that my model and the Fanduel model are very close in MSE, but the model that incorporates all the variables of my comparison model plus the fanduel predictions is worse with a higher MSE. There is some selected bias with these MSE figures since the lineup compositions are influenced by the model’s preditions. Regardless, it’s interesting that the model with the most comprehensive features performs the worse.

Next, I looked at how well these models could produce high scoring lineups: | Model || Average Fanduel Points per Lineup | | My Model || 123 | | Fanduel Model || 113 | | My Model with Fanduel || 124 |

Finally, these results appear to make some sense. The worst performing model is the Fanduel model with the lowest average fanduel points. My models are slightly better, producing similar point totals that are higher than the Fanduel model.

It’s odd that MSE scores do not align with the best lineups. It is possible that this noise from a small sample, but it’s also possible that MSE is not a great indicator of lineup performance. As stated before, the lineup selection optimization is highly dependent on predictions, so it’s possible that another element of the predictions has a higher impact on the lineup performance. Without more data, it’s hard to tell if this phenomenon is common, but the lack of alignment does support my focus on testing as many models as possible.

Future convo

• Talk about data used
• Talk about features used
• Talk about models used
• Talk about model performance
• Talk about DFS lineup scores

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My results and expected long term success in playing daily fantasy during the 2017-2018 NBA Season

With another season of the NBA, I once again tried to compete in daily fantasy competitions using a statistical model. This year, I focused on refining my model and algorithms and on figuring out whether entering these contests is even remotely profitable.

Following the disappointing performance of my daily fantasy NBA model last year, I was determined to at least beat the predictions that Fanduel provides to everyone on their site. To achieve this, I made a few small improvements to my model and process:

1. First, I added additional features to my model. I added categorical variables representing the team the player is on and the team the player is facing.

2. I built and scored my model on a stricter subset of players. I limited the set to players who averaged at least 15 minutes per game and who have played at least 2 games in the past 10 days. This filtered out many players who had inconsistent playing time, who were unlikely to be placed in a lineup anyways.

3. I improved the lineup optimization algorithm by using a multiple integer linear programming (MILP) algorithm. Instead of relying on running numerous simulations to find the best lineup, the MILP algorithm can mathematically determine the optimal lineup. Not only did this result in higher scoring lineups, but the run times also decreased drastically.

With these improvements, I benchmarked my new model’s performance against my best model from last year and the predictions that Fanduel provides. First, I looked at the MSE of fantasy points predictions per player:

Compared to my older model and the Fanduel model, my new model has a substantially lower MSE. This is especially rewarding since I was previously unable to beat the MSE of the Fanduel model. Next, I looked at the average fantasy points per lineup for each model:

Similar to the MSE results above, my new model once again beat my older model and the Fanduel model. Looking at the this data day by day, my new model appears to consistently beat both models every day:

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During this NBA season, I also tried to get a better sense of what score is needed to win the competitions. For several days, I entered either the 50/50 or Double Up non-beginner competitions for typically $1 or $2. These two competition styles are very similar, where the top ~50% of entrants about double their money while everyone else loses. Throughout these days, I found that the average lowest winning score was 284, which is a touch above my model’s average. However, when looking at my model’s performance day over day, I found that my model would’ve placed in the top 50% 28/51 times for a win percentage of 55%.

If that 55% win percentage is indeed true over time, I’d expect to achieve a 10% return on money invested in these competitions:

E(Profit on a $x Double Up game) = P(Win) * x - P(Lose) * x
E(Profit on a $x Double Up game) = 0.55 * x - 0.45 * x
E(Profit on a $x Double Up game) = 0.1 * x

Based on this performance and expected return, I should try entering more live competitions next year using this model. The biggest limitation with this analysis is that I only have data on $1-$2 competitions. To make more serious money, I’d need to enter in more expensive competitions. The dilemma is that I don’t have data for these more expensive competitions. It’s very possible that the more expensive the competition, the more competitive it is. Next season, I’ll need to enter those more expensive competitions to get a better sense of the economics. **