How to Use Multiple Linear Regression to Predict WR Production

In my last article, I explained how Neural Networks were the future of predicting football. In this article, I would like to explain why that is not the case.  At least why that is not the case. YET. There are downsides to Neural Networks no matter how good they are at predictions.

  1. As I have said before, they are EXTREMELY complex. One formula could take upwards of three pages to write out and does not even make sense when written out.
  2. They take a TON of processing power. While making hundreds to thousands of models with hundreds to thousands of rows and using multiple explanatory variables (X’s) to predict a response variable (Y), it can stall your computer and take a lot of time and resources.
  3. After finishing the predictions, you can’t use the formula since it is immensely complicated. You can’t just show your friend and let them plug in their own numbers. They would need to be using the same statistical program as you and have a computer capable of applying the Neural Network.
  4. They just don’t make sense, at least for a while. Neural Networks are THE most complicated modeling method and will always be difficult to understand for anyone.

Multiple Linear Regression or Multiple Linear Models (MLMs) do not have these problems and in CERTAIN situations are better than Neural Networks. MLMs occur when you combine multiple Simple Linear Models to form one singular model (the MLM). Figure 1 illustrates this well. MLMs help us understand a single response while using as many predictors as we want/can.

Figure 1 came from a slideshow that does a pretty good job at explaining SLMs and MLMs in depth. I highly recommend looking into that presentation because MLMs are a big topic, and I cannot cover all of the details. Now, after all of that preface, let us talk about some football and why MLMs are great for fantasy football. I created an MLM for predicting Year Z Receiving Yards based off of Year Z-1 statistics. This provided adjusted R^2 values around .5 (using Neural Networks), which means my model was able to predict 50% of the variance in the data, I was not able to surpass this with Year Z-1 statistics alone.

I thought it would be fun to include the community more though and see what other people could do with my model. I created an MLM that included 5 Year Z-1 statistics and 1 Year Z statistic to predict Year Z Receiving Yards. This allows people to use their own projections for the Year Z statistic, and if that statistic is correct, they can obtain accurate predictions for Year Z.

Neural Network results:

Here we have the “almighty” Neural Network and its glory. This model took 30 minutes to fit, yes, 30 Minutes!!! Using every possible Year Z-1 statistic I could find the best it could come up with is around a .5 R^2. On top of that, we have no way of letting anyone else use or see the model.

Multiple Linear Regression:

Now instead of using an over-complicated Neural Network, let’s use an MLM. Using only 5 (critical) Year Z-1 statistics and a singular Year Z statistic, let us see if we can beat a Neural Network. Some key notes:

  1. The model uses Year Z Market Share of Targets. That means the graphs you will see are ASSUMING MS.Targets is CORRECT.
  2. Not All WRs are included – there are a ton of WRs to keep track of.
  3. You may notice ExpQBYards as a variable. THIS IS NOT YEAR Z QB YARDS. This is a number achieved by multiplying the Z-1 QB’s YPG by 16. I did this because it was a better predictor than simply having QB yards. This is because it helps project a pseudo-complete season.
  4. Lastly, when multiplying Year Z-1 MS.RecYards by ExpQBYards, make sure that MS.RecYards is a proportion and not a percent (%).

For this equation, you want to multiply the WR statistics by the coefficients of this formula.

This graph is how well the model predicts IF and ONLY IF MS.Targets is predicted accurately.

Here are my predictions for the 2018 season; ALL WRs ARE NOT INCLUDED. I used MS.Targets from 2017 so certain players that were injured may not appear. If you do not see a WR, but want to know his predicted statistics, try and use the equation yourself and see what you obtain.

Hopefully, this is cool, useful, and educational. I have a Bachelor of Science in Statistics from the University of Georgia, and I LOVE how I can apply what I have learned to football situations. I hope that you have learned something and feel free to follow me @DFF_Koala for tidbits to be the first to see more of my 2018 model predictions!


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Analytics Specialist for the Dynasty Football Factory with a B.S. in Statistics from the University of Georgia. You can find me on Twitter @DFF_Koala. #DFFArmy

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