## Solving Optimization Problems with Calculus: Expanding from Simple to Complex Examples

Optimization problems are a significant part of calculus, as they involve finding the maximum or minimum value of a function within given constraints. In this blog post, we’ll briefly explore how to solve a simple optimization problem using calculus and then discuss how the same methods can be applied to more complex problems with multiple variables. It will help to have this understanding as we convert a FanDuel lineup into an optimization problem to be solved with our code.

## The Basics of Solving an Optimization Problem

Consider a straightforward example: you have a limited amount of fencing material to create a rectangular enclosure for your garden. Your goal is to maximize the area of the enclosure while staying within the constraint of the available fencing material. Let’s say you have 100 meters of fencing available.

First, we need to set up the constraint equation. Since the perimeter of a rectangle is given by $P = 2l + 2w$ (where $l$ is the length and $w$ is the width), our constraint equation is $100 = 2l + 2w$. We can simplify this to $50 = l + w$ or $w = 50 - l$.

Next, we need to express the area we want to maximize in terms of a single variable. The area of a rectangle is given by $A = lw$. Using our constraint equation, we can rewrite this as $A = l(50 - l) = 50l - l^2$.

Now, we’ll use calculus to find the maximum area. We first find the derivative of the area function, $A'(l) = 50 - 2l$. To find the critical points, we set the derivative equal to zero and solve for $l$: $0 = 50 - 2l \Rightarrow l = 25$. Plugging this back into our constraint equation, we find that $w = 25$ as well. Thus, the maximum area occurs when the enclosure is a square with side lengths of 25 meters.

## Expanding to More Complex Problems

The method we used for solving the simple optimization problem can be applied to more complex problems involving multiple variables. For instance, imagine you need to optimize a function of nine variables instead of just two (like in a FanDuel Full Roster contest).

The process remains essentially the same:

1. Establish the constraint equation(s) involving the nine variables.
2. Express the function you want to maximize or minimize in terms of a single variable or a reduced set of variables using the constraint equation(s).
3. Use calculus techniques, such as partial derivatives, to find the critical points of the function.
4. Analyze the critical points to determine the optimal solution.

While the calculations become more complicated as the number of variables increases, the fundamental approach remains consistent. By understanding the basics of solving optimization problems in calculus, you can tackle more complex situations and make the most of your mathematical skills.

Fortunately, we will be able to use code for steps 2-4, but I think it’s helpful to understand what it will be doing behind the scenes. We also need to understand how to do step 1, and set up our equations for optimization.

## What’s Next?

In the next post, we will start talking about what the optimization equations will need to be for our optimizer. This will help us plan out our code before we start writing it. We will also touch on how we can adjust these equations based on specific DFS strategies we want to test.

If you want to play along and enter some FanDuel lineups of your own, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least $15 within 30 days of signing up, and youâll get a$15 bonus added to your account if you use that link.

## Solving Optimization Problems in Calculus: A Daily Fantasy Baseball Connection

Optimization problems are an essential part of calculus, as they involve finding the maximum or minimum value of a function within certain constraints. These problems often arise in real-world applications where resources are limited, and we need to make the best possible use of them. In this post, we’ll explore what an optimization problem is in calculus and discuss why we should care about them when making a daily fantasy baseball lineup on FanDuel.

## What is an Optimization Problem?

In a typical optimization problem, we are given two equations: one that represents the restriction or constraint and another that we aim to maximize or minimize.

For instance, imagine you have a limited amount of material to build a fence around a rectangular garden. In this case, the restriction equation represents the perimeter of the fence, while the equation to maximize or minimize represents the area of the garden. Solving an optimization problem involves finding the dimensions of the garden that maximize its area while staying within the constraint of the available fencing material.

If you want to read more about how to solve an optimization problem that you would come across in calculus, you can see an example worked out here.

## Why Does it Matter For DFS?

Now, let’s relate this concept to daily fantasy baseball on FanDuel. When creating a lineup, you are given a fixed budget to spend on players, which serves as the constraint. In FanDuel, it’s $35,000 that you have available for your entire lineup. Each player has an associated cost, or salary, and an expected number of fantasy points they will score. The goal is to maximize the total fantasy points of your lineup while staying within the budget constraint. There are a few additional constraints that FanDuel imposes on your lineup as well in a full roster contest. You need to make sure to have exactly one player in each position slot, with first baseman and catcher consolidated into one slot, and a utility player that can be anything besides a pitcher. You can also only have a maximum of 4 players from the same team. Clearly there are additional constraints in DFS beyond the constraints of a calculus problem which makes this more complex, but the strategy for solving this optimization problem is the same. First, we identify the restriction equation, which in this case is the budget constraint combined with the positional and team stacking requirements. Next, we formulate the equation representing the total fantasy points of the lineup, which we want to maximize. Finally, we use calculus techniques to determine the optimal lineup that maximizes fantasy points while adhering to the constraints. ## Calculus Can Be Used in the Real World This real-world application of optimization problems in calculus highlights my mission statement quite well: “These posts should inspire college algebra and calculus students to learn the basics taught in their required coursework, so that they can build on it with interesting, real-world applications like the ones discussed in these posts.” By connecting calculus concepts to practical scenarios such as daily fantasy baseball, I want to motivate you to master the fundamentals and encourage you to explore the myriad applications of calculus in the world around them. You just have to get a little creative and play around with the math from time to time. Understanding optimization problems in calculus opens up a world of opportunities for applying mathematical techniques to real-life situations. Whether it’s maximizing the area of a garden or assembling the perfect fantasy baseball lineup, the principles of optimization can help you make the most of limited resources and achieve the best possible results. ## What’s Next? In the next post, I’m going to get into how to solve optimization problems a bit more. I’ll show you the steps of a simple example, then we’ll start talking about how to set up a FanDuel lineup as an optimization problem. We’ll approach it more from the math setup perspective, as opposed to the general thought behind it, like in this post. If you want to play along and enter some FanDuel lineups of your own, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least$15 within 30 days of signing up, and youâll get a $15 bonus added to your account if you use that link. Some links in this article may be affiliate links or referral links, meaning I would get a small commission for your purchase at no additional cost to you. ## Effortless Python Setup for Beginners: Kickstart Your Daily Fantasy Baseball Optimizer Journey We have done our background research and figured out the basic strategies we’ll start with. Now it’s time to start building our optimizer and start winning some Daily Fantasy Baseball contests on FanDuel and DraftKings. If you’d like to follow along and apply what you read about, this post will help you get your computer set up to write and run the code we’ll get into as we build this optimizer. Don’t worry, all of the posts that follow will make sense and be helpful and interesting even if you choose not to code along with me. But I wanted to help get you set up so you can take this project further, or build your own optimizer with your favorite DFS strategies. ## 3 Simple Setup Options I’ve personally used the Python.org option for my projects, including this one. While it’s a great choice and the one I personally prefer, I believe Visual Studio Code and Replit might be easier for those with little coding experience. In this post, I’ll guide you through setting up Python with the packages we’ll need for our optimizer (PuLP and Beautiful Soup) using these three options. Choose the one that best suits your needs and comfort level. ### Python.org • Visit the official Python website at https://www.python.org/downloads/ and download the appropriate version for your operating system. • Install Python by following the on-screen instructions. • Open a terminal or command prompt and type “pip install pulp beautifulsoup4” to install PuLP and Beautiful Soup. • For a detailed, step-by-step guide, check out this helpful blog post: https://realpython.com/installing-python/ ### Visual Studio Code ### Replit • Go to the Replit website at https://replit.com/ and sign up for a free account. • Click “Create” and select “Python” to start a new Python project. • On the left sidebar, click “Packages” and search for “pulp” and “beautifulsoup4”. Click the “+” button next to each package to install them. • Your online coding environment is now ready for use. • For a more in-depth guide on getting started with Replit, refer to this blog post: https://www.freecodecamp.org/news/how-to-use-replit/ These three options offer different ways to set up Python with PuLP and Beautiful Soup. Take your pick, and you’ll be ready to build your daily fantasy baseball lineup optimizer with me! ## Whatâs Next? Now for the fun part – let’s get to building! This concludes the background research and general strategy portion of these posts. Next we’ll start talking about how to set up a daily fantasy sports lineup as a math problem that we can solve. And more importantly: solve optimally. If you want to play along and enter some FanDuel lineups of your own, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least$15 within 30 days of signing up, and youâll get a $15 bonus added to your account if you use that link. Some links in this article may be affiliate links or referral links, meaning I would get a small commission for your purchase at no additional cost to you. ## How Many Daily Fantasy Tournament Lineups Should I Enter? This is a great question to ask. And unfortunately, there isn’t one universally correct answer to this question. However, I think it would be a good idea to consider some reasons for entering a single lineup vs multiple. ## Reasons to Enter a Single Lineup We are trying to build an optimizer here, right? So, if that’s the goal, we are essentially trying to find the one perfect lineup in a given slate. We know there is such a thing. There’s always going to be a 9 player list that gets us more points than any other possible lineup from the players in that slate. If we know there is a perfect lineup, the point of an optimizer is to pick those 9 players. Of course, that’s easier said than done. Even the best optimizer will rarely craft the perfect lineup. But we can increase our odds of getting as close as possible with some predictive modeling. My point here, is that there is going to be one lineup that is as likely as possible to score a crazy number of points and win a tournament. If we know one lineup is mathematically most likely to win, why bother entering other, lesser lineups? That’s the logic behind entering a single lineup. Craft the perfect lineup, and ride with just that one. ## Reasons to Enter Multiple Lineups I’m sure by now you’re thinking it would be pretty freaking unlikely that even the most mathematically perfect lineup actually ends up scoring higher than all other possible lineups. And I think you’re right. We can put ourselves in the best position possible, but even the best optimizer, and best point projections aren’t going to predict the future perfectly. In these posts we will discuss ways we can get as close to all of that as possible. But by the end of it, I promise we won’t be nailing every projection and lineup perfectly. Fortunately, we don’t need to. We can still win often enough to be profitable anyway. But entering multiple lineups is a good way to spread out our bets to multiple players, and teams, and reduce our risk in a given slate. We will talk more about deciding when it would make the most sense to enter 1, 2, 3, or any other number of lineups into a slate from a mathematically optimal perspective later. We’ll design experiments to test the best approach. I think it’s a good thing to think about now though. At the end of the day, it’s up to your personal preference and what you find most fun. Winning is fun of course, but fun is the reason we play in the end. ## What’s Next? At this point, I have covered all of the background research and general strategy I wanted to cover. Now it’s time to start building a DFS optimizer. In the next post, I’ll talk about what software I’ll be using to write our code so you can follow along on your own. Ideally, you should take my lessons and experiments a step further and test out some of your own strategies. If you want to play along and enter some FanDuel lineups of your own, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least$15 within 30 days of signing up, and youâll get a $15 bonus added to your account if you use that link. Some links in this article may be affiliate links or referral links, meaning I would get a small commission for your purchase at no additional cost to you. ## Daily Fantasy Baseball Strategy: Stacking (Part 2) If you haven’t already done so, make sure you read the first part of this strategy breakdown here. In that post, I mentioned that there are 2 big reasons why stacking is a good idea when you’re making a DFS Tournament lineup for MLB. But I only talked about one of those reasons. So, let’s talk about the other big one. ## Correlation Between Teammates Just like before, I’m not going to show you the math behind this in this post. I just want to talk about the general thought and background behind it for now. If you want to read more about the math and numbers proving that teammates’ fantasy performances are correlated to each other, here and here are a couple good articles about it. If you think fundamentally about the way baseball works, we should expect correlation like this. ### Two players score from one event Letâs say you have Aaron Judge and Giancarlo Stanton batting 3rd and 4th respectively, for the Yankees. You put both of them in your lineup. In the 3rd inning, Aaron Judge hits a double, getting you some points. Then Giancarlo Stanton comes up and hits a 2-run homer. You would get the points for 1 run for Judge scoring, and the HR, 1 run, and 2 RBI for Stantonâs swing of the bat. As you could imagine, this effect is compounded even more if you have 3 or 4 players lined up from the same team. If they start stringing hits together, thatâs a lot of double counted points. ### Avoiding outs leads to more plate appearances Not only are there times when one event scores points for multiple players, but each time a player reaches base safely it creates opportunity. Typically, a full baseball game is 9 innings, with 3 outs per inning. So, if players on a team get out 27 times, none of them can score more fantasy points. Therefore, each time a player gets on base safely with a hit or a walk, that player scores fantasy points. Perhaps more importantly, he did it without using one of his team’s 27 outs. Each time a player does something that gets him fantasy points, it gives his teammates an extra opportunity to do the same. This creates a situation where players on the same team either give each other more chances to score and score more points together, or they take chances away from each other by not scoring. This creates correlations between teammates. In a Tournament contest, where a “boom or bust” lineup is the goal, you want correlation between the players in your lineup. Stacking is the best way to create that. ## What’s Next? In the next post we will start discussing when it would be a good idea to enter multiple lineups into contest, and when you should only enter one lineup. We will talk about some reasons for each so you can decide which approach you would like to take. If you want to play along and enter some FanDuel lineups of your own, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least$15 within 30 days of signing up, and you’ll get a $15 bonus added to your account if you use that link. Some links in this article may be affiliate links or referral links, meaning I would get a small commission for your purchase at no additional cost to you. ## Daily Fantasy Baseball Strategy: Stacking As I mentioned in the previous post, stacking is possibly the most common strategy used in MLB DFS Tournament contests. Perhaps a more accurate statement is that it is very common in winning Tournament lineups. If you want to win a large Tournament, your best bet is to employ this strategy. It works. At this point, you’re probably asking the first question most of us asked in our lives: why? Good question, let’s talk about it. There are several reasons why stacking can give you an advantage, but two main reasons carry more weight than the others. ## Take Advantage of Bad Pitching One thing stacking allows you to do is select multiple batters that are going to be facing off against a bad pitcher. Bad pitchers give up more hits and runs, which results in more fantasy points. It should be obvious why this is a good reason to consider stacking. But it goes even further than that. If you consider yourself a baseball fan and watch games often, think about what happens when a pitcher performs poorly. If a pitcher starts the game by giving up a lot of hits and runs in the first few innings, his pitch count gets too high early in the game. This usually leads to that team going to the bullpen to use relief pitchers a couple innings before they intended. On top of that, if they are already down by several runs, they probably won’t be using their best relievers. ## Why is this important? If you stacked 4 players in your lineup going against the starting pitcher that performed poorly, gave up a lot of runs, and got replaced early, your lineup is likely to see two main benefits. 1. The players in your lineup were likely a part of the fun against that starting pitcher. This means that they likely racked up a few hits, RBI, runs, or stolen bases just in their first 2 – 3 plate appearances. So, you already have a good chunk of fantasy points with a lot of game left to be played. 2. When a team is down by several runs early and has to replace their starter in the 3rd or 4th inning, they usually don’t put in their best bullpen pitchers. If this is the case, your players that you stacked go from seeing a bad starting pitcher to bad relieving pitchers. Bad relievers are typically even worse than bad starters. So, you get even more opportunity for high fantasy scores in the late innings. It really snowballs in your favor. ## What’s Next? In the next post, we’ll talk about the other big reason why stacking is a good strategy. Then we’ll touch on some of the other reasons as well. If you want to play along and enter some FanDuel lineups of your own, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least$15 within 30 days of signing up, and you’ll get a $15 bonus added to your account if you use that link. Some links in this article may be affiliate links or referral links, meaning I would get a small commission for your purchase at no additional cost to you. ## Common Daily Fantasy Baseball Strategy Now that we have discussed the basics about how FanDuel, DraftKings, and daily fantasy baseball works, we can start talking about the strategies we will want to use to build lineups. A quick Google search for “MLB DFS Strategy” yields tons of common strategies used by players across the inter-webs. These strategies can range from beginner to advanced. Let’s start with a general overview of some of the most common strategies in this article. I’ll come back and link to more detailed breakdowns as we deep dive into some of these in future posts. ## Stacking This is possibly the most common DSF strategy in baseball contests. Stacking just means that you select multiple players from the same team, usually 3 or 4. There are a few reasons why this strategy makes sense. I found many articles that prove these ideas mathematically. If you want to read more about that, you can check out some of them here and here. I’ll summarize the main takeaways, but since others have already done the math to prove it, I won’t bother with that here. I just want to talk about general strategy for now. • If you choose several players from the same team, it allows you to have several players going against a specific bad pitcher. Bad pitchers give up more fantasy points to batters, so we can capitalize on this more by picking 4 players against that bad pitcher instead of just 1. • There is a correlation between fantasy performances of players on the same team. Usually players on the same team will do better than average together or worse than average together. This goes back to the “boom or bust” strategy we talked about earlier. • Stacking allows you to choose multiple players in other advantageous positions. This can allow you to capitalize more on things like hitter’s parks, or good weather. ## Batting Order A good general rule of thumb: pick players closer to the top of the batting order. You can read more about the math behind this here, but the logic is simple. Players batting at the top of the order get more at bats. Extra at bats equals extra opportunities to score fantasy points, which may lead to actually scoring more fantasy points. ## Weather Most importantly, it’s probably a good idea to avoid players in games with a chance of rain. If you have a player in a game that gets postponed due to rain, that player gets 0 points. It’s nearly impossible to win a large tournament with any zeros in your lineup. On top of that, players playing in warm or hot games are more likely to score more points than players in cold games. The ball flies a little bit farther in higher temperatures, meaning home runs and extra base hits are going to be a little bit more likely. This translates to more runs scored in MLB games, and more fantasy points for players in that game. ## What’s Next? In the next several posts, we’ll start talking about these strategies in a bit more detail. More importantly, we’ll start talking about how we can set up experiments to test which variations of these strategies produce better results and win more DFS contests. If you want to play along and enter some FanDuel lineups of your own as we conduct this investigation, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least$15 within 30 days of signing up, and you’ll get a $15 bonus added to your account if you use that link. Some links in this article may be affiliate links or referral links, meaning I would get a small commission for your purchase at no additional cost to you. ## High Variance or Low Variance in Tournaments vs 50/50s We now know how to calculate variance of fantasy performances of a given player, but now youâre probably thinking: why is this important? You are asking the right questions. It is a good one. It all goes back to the differences between the payout structure and the number of lineups entered in the two types of contests. Payout structure differences have a more significant impact, so let us start with that. ## Impact of Payout Structure on Desired Variance #### Percentage of lineups entered that win • In a paid 50/50 contest, half of all entries win money giving an entry a 50% chance to win. • On the other hand, roughly 25% of all lineups entered in a Tournament end up winning. #### Payout received for winning • In a paid 50/50 contest, all winning entries win the same amount of money. Whether you are in 1st place or 50th place out of 100 entries, you receive the same payout. As a result, if you can consistently be slightly better than the median lineup, you would have a profitable strategy for 50/50 contests. • Tournament contests have a very top-heavy payout structure. As a result, you can still have a profitable strategy even if you win a lot less often than you would need to in a 50/50 contest. In fact, the lineup that ends in 1st place can receive 300-500 times their entry fee. This means that if you can manage to create a better lineup than everyone else in the contest, you may be able to enter 299 losing lineups and still break even. ## Key Takeaways The significance of these differences can be summarized quite simply. If you are entering Tournaments, you want players in your lineup with high variance in fantasy points scored per game. This would give you a higher chance of finishing in the top-heavy winning portion of entries. It will also make you more likely to finish at the bottom, but since you win$0.00 for finishing above 70% of lineups or for finishing in last place, that wonât make much difference.

However, if you want to enter 50/50 contests, you should select players with low variance that give you high chance of doing just a little bit better than half of the other entries.

In other words, if you want to enter Tournaments, the âboom or bustâ strategy is likely going to work better for you in the long run.  Keep in mind though that this approach requires a large sample size created by entering many Tournaments.  Even if we know we have a profitable system, since a 1st place finish may require hundreds of entries before it actually hits.  If this is the approach you want to take, you should choose an entry fee you can afford to pay 1000 times, not one that you can afford to pay once.

You would effectively be playing the lottery at that point.  That is not my goal with these posts.  Plan to achieve a large sample size when using math to create a profitable betting system. Again, nothing in these posts should be thought of as fanatical or gambling advise. However, if you want to implement any of the strategies discussed, it’s important to test their statistical significance.

If you want to play along and enter some FanDuel lineups of your own as we conduct this investigation, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least $15 within 30 days of signing up, and you’ll get a$15 bonus added to your account if you use that link.

## Lineup Strategy Differences in Tournaments vs 50/50s

As you might expect, the payout structure differences between Tournaments and 50/50 contests will impact our strategy. Number of lineups in the contest will likely impact our choices as well. However, the payout structure should be considered more significant. The players we choose to create a lineup will be different depending on what type of contest we are entering.

Both factors will impact our strategy for a similar reason. It all comes down to one main thing: variance.

## What is Variance?

If you have taken any statistics courses, you should be familiar with the concept of variance. If not, it can be thought of most simply, as how spread out a set of numbers are. A set of numbers that are generally close to each other will have a lower variance than a set of numbers that are more spread out. This is a bit of a vague oversimplification, but it should be enough to understand why it is important here.

The concept of variance materializes in fantasy points and sports in general as consistency. Consistent players would have a low variance in their fantasy production, and inconsistent players would have a high variance.

You need to be careful here though. Just because you have noticed a player getting 2 hits per game for the last week, or always coming through late in the game, does not mean he is consistent. We need to measure the variance of all his performances to get a ligament measure of how consistent he is.

## How to Measure Variance

First, you will need to find a list of fantasy points a player scored in games. This could be any sample of games you want to measure: last week, this season, career, etc. Once you have a list of fantasy points scored over the period you want to consider, you can simply use the variance formula.

Sample variance, often denoted as $S^2$, can be found by:

$$S^2 = \frac{\Sigma (x_i \ – \ \bar{x})^2}{n-1}$$

Where,
$S^2 =$ sample variance
$x_i =$ the value of one fantasy performance
$\bar{x} =$ the mean of fantasy points scored per game
$n =$ the number of game performances in sample

If this type of formula is intimidating to you, do not worry about calculating this with the formula. If you want to try calculating this for a specific player, it can be calculated easily using Microsoft Excel using the VAR.S function.

My main point here is that consistency of a fantasy player can be quantified. In the next post, we will discuss how we can use this measure to decide which players we want in a Tournament lineup vs a 50/50 lineup.

If you want to play along and enter some FanDuel lineups of your own as we conduct this investigation, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least $15 within 30 days of signing up, and you’ll get a$15 bonus added to your account if you use that link.

## DFS Contest Types: Tournaments vs 50/50s

Now that we have talked about the differences between FanDuel vs DraftKings scoring, we need to discuss the different type of contests. Tournaments and 50/50s are the two most common contest types if you want to enter a full roster MLB contest. FanDuel does also offer other contest types, like Head to Heads, Multipliers, and 3-100 Players, but those are less available and less popular than Tournaments and 50/50s. Plus, the payout structure for Head to Heads and Multipliers are very similar to 50/50s. As a result, I’m only going to go into detail on the main two contest types.

There are two main differences between these contest types we will discuss: the number of lineups in the contest, and the payout structure.

## Number of lineups in Tournaments vs 50/50s

Generally, Tournaments are going to contain a lot more lineup entries than a 50/50 contest. There are small tournaments with fewer than 20 lineups, but they are usually going to be much larger. There are typically going to be tournaments with several hundred or thousand entries for the main slate of games each day throughout the MLB season.

It does depend on what the cost to enter the tournament is with lower entry fee Tournaments usually allowing more lineups than those that cost more to play.

However, 50/50s are much smaller. 50/50 contest range anywhere from 10-100 total entries typically. You don’t really see any larger than 100, like you do with Tournaments. I will touch on how we might expect the different sizes of contests to impact our optimizer in the next post.

## Payout Structure in Tournaments vs 50/50s

50/50 contests have a simple payout structure in FanDuel. 50% of entries win, and 50% do not. The amount you win is 180% of whatever the entry fee is. So, if you enter a 50/50 contest with a $1 entry fee and finish in the top 50% of entries, you get back$1.80. In a 50/50 contest, FanDuel is paying out 90% of total entries paid, and keeping 10% for themselves.

The payout structure for a Tournament is a bit more complex. It’s more top heavy, so the winner gets a lot more than they paid to enter. And a lot more entries finish “out of the money” and receive nothing. The exact payout structure can vary depending on the entry fee and number of lineups allowed, but they all payout a larger amount of money to a smaller number of players than 50/50s. Here is an example of the payout structure for a FanDuel Tournament with a $2.22 entry fee in the 2022 MLB season. There was a total of 5,362 entries in this Tournament. In this case, there would have been$11,903.64 paid in entry fees by the players, and about 84.01% of that was paid out to winning lineups. The other 15.99% was kept by FanDuel. The top 25.18% of lineups entered in this contest won something.

## What’s Next?

In the next post we will start discussing how these differences will impact the strategy for entering different types of contests. We will need to keep this in mind as we set up the rules for our optimizer so it picks players that give us the best shot of winning in the specific contest we enter.

If you want to play along and enter some FanDuel lineups of your own as we conduct this investigation, you can use my FanDuel referral link here to get a deposit bonus. You should just need to deposit at least $15 within 30 days of signing up, and you’ll get a$15 bonus added to your account if you use that link.