Optimal 2022 Fantasy Auction Strategy

Click here for a link to our GitHub containing code to find your own optimal fantasy auction strategy!

Coming up with your fantasy auction strategy going into the draft is perhaps the most fun part of the season. There are countless different approaches in auction drafts when compared to snake drafts. However, the mathematics of coming up with the best fantasy auction strategy are much simpler than coming up with the best snake draft strategy.

In this article, we’re going to pump the numbers through our model to see what is the best theoretically possible fantasy auction strategy. At the end – after we include all of our data and analysis – we’ll go back and describe the mathematics underlying the analysis. Our methodology is based on solving a binary integer programming problem to find the best team.

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How to Make Your Own Optimal Strategy

Because our code is available freely (with a creative commons license) on GitHub, you can run your own version of the optimization problem with your own projections, preferences, and predictions! The requirements are only that you have R installed on your computer and know how to hit “run”. I recommend the RStudio IDE.

If you download R using the indicated link and install the required packages listed at the top of the scripts, you can run the code. To install, for example, the ompr package, you use the command install.packages(“ompr”).

Finally, when you pull the github repository, you will also get data in a ./data subdirectory which contains the relevant projections. These files are .csv files which are easy to edit so that you can adjust certain players’ projections up or down as you see fit. In this way, you can use the code we’ve provided to compute your own optimal auction draft strategy.

Quick Methodology Notes

We’ll skip the heavy math up here. Two assumptions underlie all our analysis:

1. The team that scores the most points has the best chance of winning the championship. Thus, maximizing the points scored by your team leads to the optimal draft strategy.
2. Projections aggregated from multiple expert projections will be more accurate than nearly any individual person’s projections.

We designed our algorithm to maximize the projected points of your starting lineup while holding back a percentage of your budget for bench slots. We ran a few different scenarios to help you determine your own optimal auction draft strategy. These scenarios differ by league settings and how much of your total budget you want to spend on starts. Stir all these together in a pot, and your optimal fantasy auction strategy comes out at the end.

After we compute the ‘optimal’ fantasy auction strategy in the next section, we’ll look into how these projections change due to the natural variance of auction draft values.

Our analysis assumes 12 team leagues. If you want to adjust the average auction costs for smaller league settings, you can copy-paste the data from Fantasy Pros to do so. Also note that in superflex, the costs of quarterbacks changes dramatically. If you want to run this data to compute the optimal fantasy auction strategy for superflex leagues, we recommend changing the projected cost of the quarterbacks by hand.

2022 Optimal Fantasy Auction Strategy

We’ll go through each of the different scoring formats (Standard, Half PPR, and PPR) to determine the best strategies. In each of these settings, we’ll compute the optimal draft strategy with a total auction budget of $200. We’ll run the numbers holding back 7.5%, 15% and 25% of your total budget for your bench.

One last point. None of this analysis is based on us being “high on” or “low on” a player. It is simply maximizing the value of your team with a given budget. If, for example, you don’t like Antonio Gibson this year, then you can find a similar player at a similar cost and the same position (like AJ Dillon or Miles Sanders!) and substitute them in for Antonio Gibson. The point is to help you figure out how much to spend on each roster slot, not necessarily to recommend specific guys.

However, if players show up consistently, then this data is valuable. A player showing up consistently means that his auction value is much lower than it should be for his projected points total. This might be something to take into account when constructing your auction draft strategy.

2022 Auction Half-PPR Strategy

• No matter what, our methodology loves taking the #1 quarterback. I’ve argued at length that the fantasy community undervalues quarterbacks. Because of this, it is the best value to get the best quarterback because the price will always be lower than it should be. This is why the optimal fantasy auction strategy in standard leagues always starts with Josh Allen at the top.
• In half-PPR, our model also likes to take a stud tight end. This agrees with prior analysis which suggests that the value of elite tight ends is underestimated. Interestingly, it doesn’t like Kelce’s value, but it does like Andrews’.
• With the exception of taking Deebo as your WR1 in the aggressive column above, our model likes taking running backs and receivers in the #20-#30 overall range to fill out your starting roster.
• Because of how inexpensive kickers and D/ST are, our model always suggests paying a dollar or two to snag the best at those positions.

2022 Auction Standard Single QB Strategy

• Just like above, our model recommends paying top dollar to secure the best quarterback. Again, this is because the market for quarterbacks undervalues them so even shelling out for the best is a steal.
• Interestingly, the model no longer likes spending to secure an elite tight end. I suppose that the argument comes down to the decreased value of tight ends in standard leagues when compared to half or full PPR. Still, this surprises me.
• The dollars that are saved by not securing an elite tight end are actually best spent on the receiver position. To me, this is surprising. This means that – even though receivers have decreased production in standard leagues – the auction cost has overcompensated for this fact. As a result, elite receivers like Kupp and Adams are now very good values.
• Elite running backs still appear to be overpriced with our model preferring to take backs in to #20-#30 range.
• Elite defenses and kickers are still the way to go because of their minimal required investment.

2022 Auction Full-PPR Single QB Strategy

• Finally, now, we come to optimal team constructions that don’t start with Josh Allen. Burrow and Brady are now the recommendations. A lot of the reason for this is that because other positions now score points comparable to what quarterbacks score the position becomes less valuable.
• As catches get more valuable, so too do tight ends. In standard we got a non-elite TE, in half-PPR we got the #2 TE, and in every scenario of full-PPR we got the #1 TE. This means that everyone forgot to adjust the values of the elite tight ends so their resultant production/$ is very good.
• Especially in our aggressive spending column, wide receivers are king. We spent 51.5% of our budget on wide receivers in our starting lineup. Again, all this says to me is that though everyone agrees that receivers are more valuable in full PPR, the community doesn’t know how to adjust their auction value. A good fantasy auction strategy in PPR starts by securing elite receivers and tight ends and figuring out how to make the rest work.
• The running backs here are the usual suspects: Elijah Mitchell and Miles Sanders. Good value for their cost but leaving money to spend on the players that matter more.
• Again, we got the best kicker and best defense.

Next, we’re going to vary the analysis we provided above to give you a sense of how the optimal teams change when the natural variance of pricing comes into play come draft day.

Variance of Optimal Auction Draft Strategy

Things never go according to plan in your auction draft. Some players end up going for either a lot more or a lot less than their average auction value. So, we wanted to see how much the optimal strategy changed when the natural variance came into play.

We simulated 300 drafts where each players’ value was adjusted randomly either up or down by 20%. Then, to replicate how overspending on some players forces underspending on others, we made sure that the amount spent on starters remained the same across experiments. We have two takeaways, bulleted below.

• Certain players were taken much more often than others because their values remained good even with the cost variance. The numbers in parentheses show often the player was drafted in our 300 simulations.
  • Quarterbacks: Josh Allen (35%), Mahomes (26%), Kyler Murray (14%)
  • Wide Receivers: Ja’Marr Chase (19%), Mike Evans (18%), Cooper Kupp (16%), Diggs (16%), Deebo (16%), Davante Adams (16%), Jefferson (15%), AJ Brown (15%)
  • Running Backs: Akers (14%), Dobbins (13%), Miles Sanders (12%), Elijah Mitchell (12%), Najee (11.5%), Chubb (10%)
  • Tight Ends: Kelce (26%), Mark Andrews (19%), Schultz (11%)
• Our algorithm only drafted the elite running backs if their value fell far below their average auction value (AAV). That is, our algorithm thinks that running backs are way overpriced in auction leagues and rarely takes them as a result. The numbers below show the max amount our algorithm spent on any individual elite running back compared to their AAV.
  • Jonathan Taylor: Max spent $59 relative to AAV $68
  • Christian McCaffrey: Max spent $52 relative to AAV $60
  • Ekeler: Max spent $52 relative to AAV $59
  • A similar trend continues for nearly every running back in the RB1-RB20 range

The Mathematics of Our Method

We used binary integer programming to compute the optimal fantasy auction strategy. Binary integer programming is related to linear programming with the added constraint that each of the variables need to be binary (0 or 1).

In our case, each player available to be auctioned off in the fantasy auction draft is assigned a variable x_i that can either be x_i=0 or x_i=1. If the output of our model says x_i=1, then player i is on the optimal team, if x_i=0 then player i is not on the optimal team. Binary integer programming requires the definition of an objective function and constraints which are linear in each of the variables.

The specific setup of our problem is:

• Each player i is assigned a variable x_i which can either be 0 or 1
• Maximize the projections of our starting lineup.
  • The objective function is the sum of the products of the variables x_i with coefficients given by their projections. Because only those players on the team get x_i=1, the objective function value is the projected points of our starting lineup.
• Subject to
  • The cost of our starting lineup is less than the allotted budget. This constraint is linear because it is the sum of the products of each player’s variable x_i and their cost.
  • The number of receivers, running backs, quarterbacks, tight ends, kickers, and defenses on the roster is correct. This is harder to see as a linear constraint. We get one equation each for each position. We sum up the variables x_i for each player at the position and ensure that this sum is large enough to fill the required roster slots.
  • We have a similar linear constraint to make sure the flex and superflex slots are filled and the starting roster has the right number of players.

Because each of these constraints and the objective function is linear in the variables we wish to optimize, we can use binary integer programming methods to find the solution.

I would love to be able to talk about the theory of linear programs and integer programs (of which, binary integer programs are a special case) at length here. However, the theory surrounding each of these methods could easily fill a semester long course and are not important to understanding the methodology of optimizing your fantasy auction strategy.