The Current System

History

Back in 1996, the concept of Value Based Drafting (VBD) was born. The main principle of this system is that "the value of a player is determined not by the number of points he scores, but by how much he outscores his peers at his particular position." Based on analysis of player values using this system, the relative values of players across positions can be determined, and an optimal draft priority can be created which enables comparisons of RB#13 to WR#3 and TE#1. Problem solved. Use VBD, dominate your draft, have a nice day.

Note: If you are new to the VBD concept, please refer to the original VBD article for additional info.

The Current VBD Problem

Jump forward a decade to 2006. Today, more and more fantasy football leagues have transitioned away from drafts and now select players via auctions. During these past ten years, the VBD tool has been adjusted to calculate auction values for players. So, you might ask, what's the problem? The problem is that the VBD application doesn't calculate auction values correctly! Impossible? Well, let's review actual VBD data and see if the math adds up.

Proof of the Current VBD Problem

The current VBD application allows two teams with the same numbers of starters in each position scoring equal number of points, collectively, to cost very different total auction amounts. If player value is measured based on projections, and projections are used to calculate total points scored, this inequality means the current VBD calculation of auction value isn't correct, since Team A's starters scoring 400 points do not cost the same as Team B's starters scoring 400 points. Here are two specific examples, but it is easy to find other examples.

Example #1

In a typical scoring system, and regardless of baseline comparisons, Tomlinson scores 41 points more than Alexander (using 2005 projections). The auction cost difference between these two players per the VBD app is $6 (out of $2000 total auction dollars: $200 * 10 teams). Tomlinson's cost theoretically should equal Alexander's cost, plus the premium amount that 41 more points is worth.

We would therefore expect a 41 point premium above the baseline to be worth $6 elsewhere in the valuations. But when we look at another RB that is scoring 41 points more than the baseline (Julius Jones is that RB for the baseline I picked), the VBD auction value is $28. Even when we subtract the cost of the baseline back we would have to get anyway (Thomas Jones for $10), We're still at those 41 points costing $18!

These two examples cannot both be true. Looking at the fantasy points, we should pay the extra $6 for Tomlinson, bank his extra 41 points, and then take the baseline back (Thomas Jones for $10), resulting in a net savings to me of $12 (Julius Jones $28 - Thomas Jones $10 - $6 extra paid for Tomlinson).

Tomlinson (+132 points over baseline) + Thomas Jones (0 points over baseline) = +132 points over baseline (and we have $12 extra)

Alexander (+91 points over baseline) + Julius Jones (+41 points over baseline) = +132 points over baseline (but we don't have $12 extra)

In this one example, $12 is 6% of the total salary for players and is a very large error from an auction perspective.

Example #2

Let's look at this a different way to make sure we get inconsistent data from two different methods. If we see inconsistency from two independent methods, we can confirm a problem exists with the current model. Using the 2005 L1 VBD application with no changes, setting auction to "on", and generating the cheatsheet (12 teams, 2 RB starters), let's look at a sample of 5 RBs throughout the VBD range:

So Tomlinson is projected to score 25 more points than Alexander. That performance costs $7, or $0.28 per point. Alexander is projected to score 42 more points than Dillon. That performance costs $22, or $0.52 per point. Dillon is projected to score 23 more points than Westbrook. That performance costs $13, or $0.57 per point. Westbrook is projected to score 66 more points than Foster. That costs $21, or $0.32 per point.

As you can see, the per-point costs are inconsistent, ranging from $0.28 per point up to $0.57 per point, or more than double the lower per-point cost. This type of error naturally results in inconsistent auction costs. For a two RB pair with identical projected performances, there is an $8 difference in the auction costs.

Tomlinson + Foster = 440 points = $83
Dillon + Westbrook = 439 points = $75

On a per point basis, either Tomlinson is especially cheap or Alexander is especially expensive. This inconsistency should not exist if the auction calculations are working properly.

As can be seen from these two examples, the math doesn't add up. The VBD application is telling me to stop bidding on the most valuable player, to overbid on lesser players, and to spend more to build a team that gives less fantasy points than a cheaper option. There is no rational explanation for this inequality, other than an error exists in the calculation of auction values for the current VBD application. Before we fix this problem, and it can be fixed, let's first document what we want VBD to provide to us in an auction scenario.

The Auction Goal of VBD

The goal of VBD in an auction setting is to tell us the true theoretical auction values for players. These values are derived from actual projections for players, and are based on the specific scoring system in use, along with the roster requirements, number of teams, and total team salary cap. All potential upside for players is factored into the player projections. Teams with equal total points projected from starting players should theoretically cost similar amounts. Auction values should not be artificially adjusted to attempt to predict the behavior of other owners.

Using VBD to establish auction prices for players is a very different story than using VBD just to draft players. It's important to carefully differentiate between drafts and auctions. Calculating auction value is a much more quantitative exercise since it is necessary to be much more precise. In draft, the difference between #1 and #5 player is 4 draft spots, which is half of a regular draft round in a small 8 team league. In other words, this difference really won't be seen since you take the best on the board for your team and precisely how much better is less important. In auction, this early difference can be $30, or 15% of the total dollars available to a team. Since every team has the opportunity to bid on every player in an auction, every player has potential to be bought cheaply. Therefore, calculating an accurate theoretical auction price is essential to get the most for the money. This theoretical auction price tells an owner when a player has value based on actual projections in relation to others' projections. If a player is projected to be worth $30 and bidding stalls at $21, we know exactly how much value we're getting from owning that player.

The New Concept

Two Types of Players

First, let's make sure we're clear on the meaning of some terms we are going to be using. In the rest of this article, I have elected to call the top fantasy players who historically command most all of the auction dollars spent in our fantasy leagues (close to 85%), "premium players". The players we purchase with the remaining 15%, which can include many every-week starters, are termed "regular players". We will discuss this next, so it's important we are clear on the language that we are using.

Setting the Baselines

Every year, there are discussions about where to set the baseline that is used in the VBD calculations. Is it worst starter? Should we use last drafted? Is it something else?

If the goal is to determine accurate auction values, the answer is that we need to set TWO baselines within each position. It is obvious that we spend money differently for premium players vs. regular players. Our baselines must therefore account for these two different player populations. First, we must identify the premium players so we can calculate their auction value in relation to other premium players at different positions in standard VBD fashion. After that's done, we then do the same for our regular players. It is essential that the baselines be selected based on actual player scoring, and the actual break points between premium and regular players within positions.

For example, in an 8 team, start 1 QB league with a scoring system where there are 3 QBs scoring 50 points more than the rest of the QB pack, worst starter will incorrectly set a baseline of the 8th QB, and last drafted might set a baseline at the 13th QB (backups, etc). In actuality, nobody is paying a premium after QB #3. As fantasy owners, we know we either want to step up and spend to get one of these top QBs, or wait to get a regular QB cheaply while we spend our money somewhere else. So, our premium auction value must use a baseline of QB#4. Depending on the player spread, it's likely there is no reason to pay any extra for QBs as soon as they level off, which means the regular player baseline could be as shallow as QB#9. QB#10 and beyond are minimum bid players.

Allocating Auction Dollars

Once we have set the premium baseline for each position, we allocate ~85% of all auction dollars to the total points scored by those players (after subtracting the cost of minimum bids for all players). An owner can opt to allocate less than 85% on premium players to build a deeper team. This is a customizable option that each owner can set they way they want it. In setting this value, each owner is effectively deciding how much to rely on premium players. Once the premium baselines are set for each position, every point above the premium baseline has a specific dollar worth. Let's look at a specific example of how this is calculated in an 8 team league with a standard 1 QB, 2 RB, 3 WR, 1 TE, 1K, 1 DST roster, $200 auction per team, minimum $1 per player bid, with 120 total players auctioned:

• ($200 * 8 teams) - (120 players * $1 min bid) = $1480 total auction dollars available
• 85% * $1480 = $1258 for premium players
• 35 premium players identified using scoring drop-offs to set the premium player baselines
• Total points scored by these 35 players above premium baselines = 1301
• 1301 premium points / $1258 for premium players = $0.967 per premium point

If a player is projected to score 30 points above the premium baseline, his auction value is ($0.967 * $30 ) + $1. The extra $1 accounts for our removal of the minimum bid dollars in the initial calculation.

After all the premium players are accounted for, this leaves $222 for all the remaining regular players in the auction. The second baseline for regular players is applied, and the remaining players total points above the regular player baseline are calculated. In this example, these regular players score 1104 total points above the regular player baseline, which equates to $0.20 per point. All players below the regular player baseline are minimum bid players only.

Results

Using the 2005 data and this new system, here are the results of three randomly selected teams. As one can see from the data, these randomly selected three teams now cost the same amount and score the same amount. This is a significant improvement from the current system, and means our auction values are now working as intended.

• Team A
  Manning, 384 points, $80
  JuJones, 233, $24
  Dillon, 231, $22
  Marvin, 200, $53
  Burleson, 158, $13
  Moulds, 132, $2
  Vinatieri, 142, $3
  Pittsburgh, 190, $5
  $203 spent, 1670 total team points.
  
  
• Team B
  Collins, 304 points, $6
  Alexander, 273, $61
  JLewis, 216, $20
  ChadJo, 203, $57
  AndreJo, 180, $35
  MClayton, 154, $10
  Janikowski, 128, $1
  Baltimore, 214, $14
  $204 spent, 1670 total team points.
  
  
• Team C
  Favre, 287, $3
  Tomlinson, 298, $85
  Portis, 230, $22
  Harrison, 200, $53
  D. Bennett, 171, $26
  Bruce, 146, $6
  Wilkins, 125, $1
  Patriots, 200, $8
  $205 spent, 1659 total team points.

The fact we're that we're dead on for two typical teams, and within 10 points for a third team is very encouraging. All three of these example teams incorporate a mix of premium and regular players. With this new system, all of the large inconsistencies we observed in the current auction value calculations have been resolved.

Accomplishing the Two Line Fit

Since we are effectively using a two-line fit to calculate our theoretical auction values, there is an additional interim step required to ensure the intersection of these two lines is a smooth transition. The theoretical premium player baseline must be reviewed to ensure a smooth transition from premium to regular players. It is sometimes necessary to add one or two premium players to the regular player pool, or add one or two regular players to the premium player pool. The premium player baseline is established by the owner for each player position, however an adjustment of one to two players is sometimes necessary to prevent an artificial drop between two players due to mathematical artifact. This is the largest mathematical hurdle to automating this process, and is basically a smoothing of the transition from premium to regular players. Once the initial data are calculated using the owner input data, it only takes one iteration to smooth the two line fit into a model that doesn't artificially skew the results based on the intersection of the two projection lines.

Applying the New Concept

The changes to VBD to apply this new concept are as follows

1. Based on the actual scoring data generated from initial calculations using the league specific information, the owner sets the theoretical premium player baselines for each position, and the regular player baselines for each position. (Note that less precise default selections would be included in the standard VBD application to help those who aren't able to do this on their own.)
2. Owner has option to use default 85% of auction dollars for premium players, or change to higher or lower number (e.g., higher amount would result in more dependence on premium players).
3. Spreadsheet then uses the owner baseline inputs to calculate initial auction values, and then mathematically smoothes the two-line intersection to provide the final auction values.

Summary and Conclusions

The current VBD application allows two teams with the same numbers of starters in each position scoring equal number of points, collectively, to cost very different total auction amounts. There is no rational explanation for this inequality, other than an error exists in the calculation of auction values for the current VBD application. This error has been proved to exist via two separate methods.

The goal of VBD in an auction setting is to tell us the true theoretical auction values for players. Teams with equal total points projected from starting players should theoretically cost similar amounts. The proposed system accomplishes this goal.

In closing, I have created a spreadsheet that uses the scoring projections from the current VBD application and then implements the proposed system. This spreadsheet is available by request (email me at inca911@hotmail.com) or by clicking on the link below.