Part 1: The Mathematics of Point Differential and Risk

It is a common practice for fantasy football players to make projections. Maybe you're one of these ambitious individuals who spends countless hours predicting next season's statistics just to get an edge on your competition. You name a player and you have projected his stats. LaDainian Tomlinson? Sure. Randy Moss? Absolutely. Cortez Hankton? Of course.

In the junior high school of fantasy football, the projection wizards are like the big bullies who walk around punching kids in the stomach so that they can get their next bottle of YooHoo with someone else's lunch money. The difference is that the advantage these people have comes from knowledge and not brute strength. Nevertheless, they won't hesitate to use this advantage to get their way.

It's OK if you're one of these big bullies. This article will still help you. It's also OK if you're one of those kids who's always losing his lunch money. Your luck's about to change. Be warned though, what follows is not for the faint of heart. This article gets into some fairly complicated concepts and you will probably need your thinking cap to follow along. Now without further ado, on with the show.

It's been said that if ain't broke, don't fix it. The trouble is that most systems are broken, or at least flawed. There are few things in the world that need no improvement. Laetitia Casta and "The Godfather" come to mind. Other than that, just about everything could use some tweaking here and there. Certainly most of the projection techniques used by serious football fans could be improved.

While many individuals make projections, they probably don't realize how those projections should be used. Most people simply project a player's point total and then give that player a positional rank and perhaps an overall rank. While this is a worthwhile practice, it is one that can be improved dramatically.

Fantasy football games are won when your team outscores the other team. It's not about how many points your team scores. It's about how many points your team scores relative to the other teams in the league. The difference between the amount of points your team scores and the amount your opponent scores is your team's point differential. It's an important thing to keep in mind.

If winning games is about point differential then isn't that what your projections should focus on? Of course it is. Let me show you how point differential can be used in your projections. Let's say that you are trying to decide on a quarterback for your fantasy team. You are interested in Jake Delhomme and have projected him to score 340 points in your league's scoring system. If your league has a 17 week schedule then you can expect Delhomme to average 20 points for every week that he plays (340 points divided by 16 games). On its own this data is not very useful. It has no context. It's up to you to give it one.

The best way to put Jake Delhomme's projected production into perspective is by comparing it to a standard. The easiest way to create that standard is by looking at last year's QB production. If you are in a 12 team league then you should be concerned with what you can expect an average starting QB in your league to score in any given week. The smart thing to do would be to find the average points per game of the top 15 QBs from last year. I picked the number 15 because it is slightly above 12, the number of teams in your league. You want the number to be slightly above the number of teams in your league because some teams will inevitably have to start a less than ideal option.

Anyway, let's say that based on last year's data you can expect the average starting QB in your league to score 18 points/week. You now have a context in which to place your projections for Delhomme. You can conclude that if your projections are accurate then Delhomme will provide you with a +2 point advantage over the average starting QB you will face. I call this number the projected point differential. While the value is arbitrary in this particular case, the method that I used to reach it is fairly sound. You can use this same method for every position from RB to PK, although you will have to double, triple, or quadruple the number of players used to obtain the standard value at positions where you start multiple players (this example assumes that you only start 1 QB). Nevertheless, the basic idea is the same for all of the positions.

One thing that I need to mention is that you can change your statistical standard as you see fit. I suggested making the standard the average per week production of the typical starting QB you will face. The problem is that this standard does not account for the increased quality of opponents that you will face if you make it to the playoffs. Because you're probably only interested in winning championships, it might be wise to create a more strict standard such as the per week production of the top 50% of starting QBs in your league. This will give you a better idea of a player's value relative to the top dogs in your league.

While doing projections with the point differential system that I've outlined is a major improvement over standard methods, it's still highly flawed. The major problem is that it assumes that the projections are 100% accurate. It doesn't account for the risks associated with a given player. This deficiency can be accounted for using some basic probability concepts.

Let's say that you have Peyton Manning projected to produce a +5 point differential. You are extremely confident that he will reach this level because he is a proven talent with a long history of production. So you set his odds of achieving the forecasted point differential at 95%. The 5% deduction represents his odds of getting injured or benched. (.95) x (+5) = (+4.75). This new number, which I call the expected point differential, is a better value for Manning than +5 because it accounts for risk.

While you are very confident in Manning, you are not very confident in Aaron Brooks. You have him projected to produce a +3.5 point differential, but you feel that there is significant risk of him being benched. You think that the combined percentage chance of him being benched or getting injured is 25%. That leaves him with a 75% chance of producing the statistics you project him to produce if he stays healthy and plays all 16 games. (.75) x (+3.5) = (+2.625). Again, you now have a number that takes into account not only the expected production, but also the perceived risk of the player in question.

While this is fairly useful, you might be wondering what to do for player's who you've projected to have a negative point differential. You'll need to alter the formula slightly. Instead of using (Projected Point Differential) x (Projected Odds of Reaching Production) = (Expected Point Differential) you will want to use (Projected Point Differential) x (1 + Projected Odds of Not Reaching Production) = (Expected Point Differential). The second part of the equation must be altered to take into account the presence of the negative number in the first part.

One final thing that I'd like to point out is that this system has one glaring weakness. It values longshots too highly. Let's say that you have Jon Kitna projected to produce a +1.5 point differential if he somehow manages to start all 16 games for Cincinnati. Even if you place his odds of starting all 16 games at 5%, using the equation above would yield a positive expected point differential. This means that this system would rate Kitna higher than a probable starter like Kyle Boller (who would almost certainly have a negative expected point differential). For this reason I would generally recommend focusing on probable starters when you use this projection method. The numbers it will give for longshots can be misleading. If a player's chances of starting all 16 games are under a certain number, perhaps 70%, then you probably shouldn't draft that player until the final few rounds regardless of what his expected point differential is. The reason for this is that you usually won't have a big enough roster to constantly be gambling on long shots, even if it might appear to be the mathematically correct thing to do.

Creating rankings using this method would be far more time consuming than simply projecting total points. Nevertheless, the system that I've outlined in this article offers the potential for highly accurate rankings and projections. If you are willing to take the time to learn and implement this system then it can provide you with the edge that you need to become the class of your league(s). But the discussion is not over yet. There are still concepts that need to be discussed. The most important of these concepts is opportunity cost.

Part 2: The Importance of Opportunity Cost

If you were to use the method that I outlined in Part 1 of this article then your overall player rankings might look very strange. You might find that Mike Vanderjagt has a higher expected point differential than someone like Kevin Jones. Don't take this to mean that you should draft Vanderjagt over Jones. That would be an extremely foolish thing to do.
It is important to rank players within their position based on the expected point differential that you have calculated for them, but you need to remember the idea of opportunity cost when you construct your overall rankings. This idea is probably fairly intuitive to those who have been participating in this hobby for a long time, but it is still extremely important and worthy of discussion.

What is opportunity cost? As I understand it, opportunity cost is an economic principle that essentially places a value on an action by comparing the benefits of taking that action with the cost of whatever action is not taken as a result of taking the chosen action. I know it sounds complicated, but it's simple. I'll put it into fantasy football terms. The opportunity cost of drafting Deuce McAllister in round one of your fantasy draft is the highest player on your board who you proceed to miss out on before your second round pick comes up. To give you a better idea of how this principal might affect your draft, I'll give a more thorough example using the terms from the first portion of this article.

Let's say that you're on the clock at pick 9.04 in a 12 team league. Kevin Jones has tumbled in the draft for no apparent reason. For the sake of argument let's say that you've narrowed your choices down to Jones and Mike Vanderjagt. You only need one more RB and one more PK before your roster is set. You have Mike Vanderjagt as a +1.1 expected point differential while you have Kevin Jones as a +0.89 expected point differential. If all you did was look at the values then Vanderjagt would seem like the right pick. After all, you think that he's going to give you a bigger advantage over the teams you will face than Jones will. But that's where opportunity cost comes into play.

Perhaps Vanderjagt is going to give you a bigger edge over your opponents than Jones will, but at what cost? If you draft Vanderjagt over Jones then you won't be able to address your RB situation until the next pick. There are sixteen picks until your next pick. For the sake of argument let's say that you go ahead and draft Vanderjagt. To your horror, all sixteen of the picks before your next one are used on RBs The top option left at the position is Chris Perry, who you have down as a -3.1 expected point differential. All you need now is a RB, so you draft Perry. Adding up the value of the two picks is simple. +1.1 for Vanderjagt and -3.1 for Perry adds up to a net total of -2.0.

Now let's try it the other way. It's the same exact situation. You're on the clock at pick 9.04 in a twelve team league. It's down to Kevin Jones (+0.89) and Mike Vanderjagt (+1.1). You decide to gamble and take Jones despite having his expected point differential a little bit lower than Vanderjagt's. There are sixteen picks until your next pick. To your horror, all sixteen of those picks are used on PKs The top option left at the position is Billy Cundiff, who you have rated as a -1.09 expected point differential. All you need now is a PK, so you take Cundiff. Once again, adding up the value of the two picks is simple: +0.89 for Jones and -1.09 for Cundiff adds up to a net total of -0.20. As you can see, this second course of action appears to be the best option. The overall expected point differential is higher for the second scenario than it is for the first.

Why does it work this way? It comes down to opportunity cost. Although Vanderjagt technically has more value than Jones, the opportunity cost of selecting him over Jones is far greater than the opportunity cost of drafting Jones over him. What does this mean in plain English? It means you can't afford to pass up Jones in this situation because the drop-off at RB is far steeper than the drop-off at PK. You lose some value in the short term, but you more than make it up with your next pick.

This example is obviously a bit ridiculous and extreme, but it serves its purposes of showing that you shouldn't always draft the player with the highest expected point differential. You need to consider how much value is left at all of the given positions and how long you think that value is going to be there.

As you might see, there is a great deal of potential in the point differential system. It can be implemented in trades, drafts, and waiver pick ups to provide your team with a mathematical edge over your competition (assuming you and your opponents have equal projection abilities). While this article really only scratches the surface of what expected point differential can do, I hope that I've opened your eyes to its powerful potential. As I said early in the first portion of this article, there are very few systems in life that could not stand to be improved. I feel very strongly that the point differential method is ultimately going to be a major improvement over old projection methods for those individuals who come to understand and take advantage of its raw capabilities.