Predicting Fantasy Football Success with Multiple Linear Regression

What is Multiple Linear Regression (MLR)?

Multiple Linear Regression (MLR) is a method used to predict an outcome like how many fantasy points a player will score based on several factors or stats. In Fantasy Football, these factors might include rushing yards, receiving yards, touchdowns, or the number of targets a player gets.

Think of MLR as a way to combine all these important stats into a formula that helps you make a good prediction about how well a player will perform. It’s like using data and numbers to make smarter Fantasy Football decisions.

Key Stats to Use in Fantasy Football

To predict how many fantasy points a player will score using MLR, you need to choose the stats or independent variables that matter most in your fantasy league. Some common ones are:

• Receptions: How many catches a player makes
• Receiving Yards: How many yards a player gains from those catches
• Rushing Yards: How many yards a running back gains from running the ball
• Passing Yards: How many yards a quarterback throws
• Touchdowns: How many touchdowns a player scores
• Targets: How many times a receiver is thrown the ball
• Interceptions: How many times a quarterback throws the ball to the opposing team

The total fantasy points a player earns is what we are trying to predict. This is called the dependent variable.

How Does MLR Work in Fantasy Football?

Let’s say you want to predict how many fantasy points a wide receiver will score in a game. Using MLR, we can combine different stats like catches, yards, and touchdowns into a single formula. This formula gives us a good guess about how many points that player will earn in a game.

Example Formula for Fantasy Points

Here’s a simple formula that could be used to predict a wide receiver’s fantasy points:

Fantasy Points = -5 + (1.5 * Receptions) + (0.1 * Receiving Yards) + (6 * Touchdowns)

In this formula:

• Receptions: Each catch is worth 1.5 points
• Receiving Yards: Each yard is worth 0.1 points
• Touchdowns: Each touchdown is worth 6 points
• -5: This is the starting point (called the intercept) which adjusts for the average score

Predicting Fantasy Points for a Wide Receiver

Let’s predict how many fantasy points a wide receiver will score if they:

• Catch 5 passes (Receptions = 5)
• Gain 80 receiving yards (Receiving Yards = 80)
• Score 1 touchdown (Touchdowns = 1)

We plug these numbers into the formula:

Fantasy Points = -5 + (1.5 * 5) + (0.1 * 80) + (6 * 1)

Breaking it down:

• Receptions: 1.5 * 5 = 7.5 points for catches
• Receiving Yards: 0.1 * 80 = 8 points for receiving yards
• Touchdowns: 6 * 1 = 6 points for the touchdown
• Intercept: The formula starts with -5

Now, adding it all up:

Fantasy Points = -5 + 7.5 + 8 + 6 = 16.5

So, the wide receiver is expected to score 16.5 fantasy points in the game.

Understanding the Formula

• Coefficients like 1.5 for receptions, 0.1 for yards, and 6 for touchdowns tell you how important each stat is. For example, touchdowns are worth a lot more points than each yard gained.
• The intercept -5 is like a starting point that adjusts the score to fit the average player's performance.

Each stat is multiplied by its coefficient, and then everything is added up to get the final predicted fantasy points.

Why Use MLR in Fantasy Football?

MLR helps you make data-driven decisions. Instead of relying on guesswork to figure out how well a player will perform, you can use past stats to build a formula that predicts how many points a player will score. This gives you an edge in:

• Setting lineups: Predict which players are likely to score the most points
• Making trades: Decide which players are most valuable based on predicted performance
• Waiver wire pickups: Choose players who are expected to perform well in the future

Steps to Apply MLR to Fantasy Football

1. Choose the Stats: Pick the stats that matter most in your league. These could be rushing yards, receptions, touchdowns, etc.
2. Collect Data: Gather data from previous games to see how many fantasy points players scored and what their stats were for those games.
3. Build the Formula: Use MLR to create a formula that predicts fantasy points based on the stats. You can do this in Excel or with an online tool.
4. Make Predictions: Once the formula is ready, plug in a player's stats from recent games to predict how many fantasy points they’ll score in the upcoming game.

Example: Predicting Fantasy Points for a Running Back

Let’s predict how many fantasy points a running back will score. We’ll use the following formula:

Fantasy Points = -3 + (0.1 * Rushing Yards) + (6 * Touchdowns)

If the running back:

• Rushes for 120 yards (Rushing Yards = 120)
• Scores 2 touchdowns (Touchdowns = 2)

We plug the numbers into the formula:

Fantasy Points = -3 + (0.1 * 120) + (6 * 2)

Breaking it down:

• Rushing Yards: 0.1 * 120 = 12 points
• Touchdowns: 6 * 2 = 12 points
• Intercept: The formula starts with -3

Adding it all up:

Fantasy Points = -3 + 12 + 12 = 21

So, the running back is expected to score 21 fantasy points.

Conclusion

Using Multiple Linear Regression in Fantasy Football allows you to predict how many fantasy points a player will score by looking at key stats like rushing yards, receptions, and touchdowns. By building a formula based on these stats, you can make smarter decisions for your fantasy team. Whether it’s setting your lineup, making trades, or picking up free agents, MLR gives you a mathematical edge to help you win your league!

Binomial Distributions Made Easy: A Practical Guide for Everyday Understanding

What Is a Binomial Distribution?

A binomial distribution is used when something can only have two possible outcomes for each attempt, like success or failure.

For example:

• Success: You catch a football pass.
• Failure: You drop the football.

The binomial distribution helps you figure out how likely it is to get a certain number of successes when you repeat the same task several times.

---

When Should You Use a Binomial Distribution?

You use a binomial distribution when:

1. You have a fixed number of tries (called trials). For example, you throw a football 10 times.
2. Each trial has only two outcomes: success (catch the ball) or failure (drop the ball).
3. The chance of success is the same every time. For example, you have a 70% chance of catching the football each time.
4. Each trial is independent, meaning the result of one try doesn’t affect the next.

---

Example 1: Fantasy Football Wide Receiver

Let’s say your Fantasy Football wide receiver is targeted 10 times in a game, and he catches the ball 70% of the time. You want to know the chances that he will catch exactly 7 passes out of 10 targets.

Problem:

How likely is it that your wide receiver catches exactly 7 passes out of 10 targets?

Solution:

To find this, you can use Excel’s BINOM.DIST function.

In Excel, use the formula:

=BINOM.DIST(7, 10, 0.7, FALSE)

• 7 is the number of catches (successes) you’re interested in.
• 10 is the number of passes (trials).
• 0.7 is the chance of success (70%).
• FALSE gives you the probability for exactly 7 catches (not cumulative).

The result will show that the probability is 27%. So, there’s about a 27% chance that your wide receiver will catch exactly 7 passes.

---

Breaking It Down:

• Number of Attempts (Trials): In this example, it’s 10 football targets.
• Success or Failure: Each trial has two outcomes: either catch the ball (success) or drop the ball (failure).
• Chance of Success: Here, the receiver has a 70% chance of catching the ball.
• Number of Successes: You want to know the probability of exactly 7 catches.

---

Example 2: Coin Flips

Now imagine you flip a coin 5 times, and you want to know how likely it is to get exactly 3 heads.

Problem:

What are the chances of getting exactly 3 heads in 5 flips of a fair coin?

Solution:

You can use Excel’s BINOM.DIST function again.

In Excel, use the formula:

=BINOM.DIST(3, 5, 0.5, FALSE)

• 3 is the number of heads you’re interested in.
• 5 is the number of flips (trials).
• 0.5 is the chance of success (50% for heads).
• FALSE gives you the probability for exactly 3 heads.

The result will show the probability is 31%. So, there’s about a 31% chance of getting exactly 3 heads in 5 flips.

---

What Does a Binomial Distribution Tell You?

A binomial distribution helps you answer two key questions:

• What’s the most likely outcome? It shows what will happen most often. For example, if your wide receiver catches 70% of his passes, 7 catches out of 10 is the most likely outcome.
• What are the unlikely results? It shows how rare or unlikely certain results are. For example, it’s unlikely he’ll catch all 10 passes or drop every single one.

---

Example 3: Fantasy Football Quarterback

Let’s say your Fantasy Football quarterback completes 65% of his passes. In a game, he throws 20 passes, and you want to know how likely it is that he’ll complete exactly 13 passes.

Problem:

What are the chances of completing exactly 13 passes out of 20 attempts?

Solution:

Use Excel’s BINOM.DIST function.

In Excel, use the formula:

=BINOM.DIST(13, 20, 0.65, FALSE)

• 13 is the number of completions you’re interested in.
• 20 is the number of passes (trials).
• 0.65 is the chance of success (65% completion rate).
• FALSE gives you the probability for exactly 13 completions.

The result shows that the probability is 18%. So, there’s an 18% chance your quarterback will complete exactly 13 passes.

---

What Is a Random Variable?

A random variable is a way of representing the possible outcomes of an event in numbers. Random variables can be:

• Discrete: These have a countable number of outcomes. For example:
  • The number of catches in football.
  • The number of heads in a coin flip.
• Continuous: These can take any value in a range. For example:
  • The time it takes to complete a race.

---

Types of Discrete Random Variables:

1. Number of Catches in Football: You can count how many passes your wide receiver catches.
2. Number of Heads in a Coin Flip: You can count how many times a coin lands on heads after several flips.

---

Probability Distribution Function (PDF):

A PDF shows the probability of each possible outcome. For example:

• If you flip a coin, the chance of getting heads is 50%.
• If you roll a die, the chance of rolling any specific number (1 through 6) is 1/6.

---

Conclusion:

By thinking of events as either successes or failures, binomial distributions provide a simple and practical way to predict outcomes. Whether you’re calculating how many passes your quarterback will complete or how many heads you’ll get when flipping a coin, binomial distributions allow you to make informed predictions with ease.

You can use Excel formulas like BINOM.DIST to quickly find the probability of specific outcomes. Now, even without any complex math, you have a simple tool to make better predictions in real life!