Predicted Payoffs
Let's say that you wanted to invest in the stock market. You go to a broker and he tells you that he has two stocks that he would recommend for you. One costs $100 a share and is about a 50/50 shot to make you $20 per share this year. The other stock costs $10 a share and is also a 50/50 chance to make you $20 per share this year. Which stock would you choose? Obviously you would choose the second stock since it has a much greater payoff relative to your initial investment.

So what about if I offered to sell you two different stocks- one was another $100 dollar stock, this one with a %10 percent chance of gaining a $50 dollar profit. The other stock also costs $100, and has a 90% of gaining $40 dollars. Which stock would you choose. Again, the answer is obviously the second option.

While these two examples are pretty extreme, I used them to introduce the concept of what I will call the "Predicted Payoff" of a draft pick. This is basically a technique borrowed from the investing world. It is used for comparing the cost of an investment to its predicted payoff and the probability that the payoff will actually happen. In fantasy football, this can be used to help determine which picks are worth a higher investment and which picks should be gambled on at a lower cost later in the draft.

What I did for research was to break up all positions into tiers, depending on their position and where they were drafted. Quarterbacks were broken up into groups of six, as were kickers, tight ends, and defenses. Running backs and receivers were broken up into groups of twelve since twice as many are usually played and drafted. For each position I did three groups. Because quarterbacks are usually drafted a little deeper than other positions with one starter, I added an additional group to equal four total groups. I also added an extra group of defensive teams and a half group of wide receivers so that they would fit in with my baseline (You will see why later).

What I did was divide the total amount that the players in each group scored, by the amount they were projected to score. This ratio is what I would call the predicted payoff, or the percent of their expected output that the players actually reached. Back to our stock market example, this could be considered the likelihood at certain dollar amounts, that a stock would payoff. Like in the stock market example you want the stock that has the highest product between the probability of reaching the payoff and the amount of the payoff.

The equation used to figure the predicted payoff is a pretty simple one: the amount of the payoff multiplied by the probability that it will happen. So Stock A with a 50% chance of $70 dollar pay off is equal to Stock B with a 25% possibility of a $140 dollar pay off which is equal to Stock C with a 100% predicted payoff of $ 35 dollars. Or in football terms, quarterback #1 might have a 65% chance of him "predicted payoff" (which is however many points you projected for the season), while running back #15 might have a %75 chance of reaching his projected numbers.

Once you have all of your projections you should modify each player relative to his position and draft order. To modify the numbers simply multiply the payoff (their projected points) by the percent likelihood that those points will be reached. The modifiers are listed below in percentages. Again, the data for defenses is only for one year, so it will be slightly less accurate.

P E R C E N T A G E  M O D I F I E R S QB 1-6: 63.3% QB 7-12: 69.7% QB 13-18: 66.9% QB 19-24: 72.1% RB 1-12: 73.8% RB 13-24: 76.4% RB 25-36: 77% WR 1-12: 76.7% WR 13-24: 88.6% WR 25-36: 73.7% WR 37-42: 72.5% TE 1-6: 84.9% TE 7-12: 91% TE 13-18: 76% PK 1-6: 74.1% PK 7-12: 79% PK 13-18: 82.4% DT 1-6: 65.3% DT 7-12: 76.4% DT 13-18: 79.9% DT 19-24: 78.9%

After examining the numbers I think we can make a couple of assumptions about fantasy football performance. First off you will notice that not a single group actually achieves or outperforms their expectations. This is a testament to how volatile positions are, because the number amount left over is produced by guys who didn't even start off ranked. Every year a fair number of surprise players will account for a lot of production.

Also, those positions less dependent on other positions, at least for producing numbers, are less likely to reach your desired payoff. For example, a quarterback's production seems to be more dependent on other positions (like a decent offensive line, solid running game, etc . . .) than a tight ends is. A running back seems to be more dependent on his offensive line than a receiver is on his quarterback. I think this might be relevant when looking at how free agent or injury changes will affect the production of a particular player.

You can modify your projections either before or after you do the baseline (see below), but you must make sure that, if you do the modification first, your baseline player's numbers (again, see below) are also modified. Or you can just modify the difference between your projections and the baseline afterwards, whichever is easier. The rest of the article is written as if you were modifying the projections before you take your baseline.

The Baseline
Once you have generated your modified projections, you need to decide what your baseline will be. A baseline is a number to which you compare all other players from a position. For example, a common baseline is the worst ranked starter from each position. So in a twelve team league you would use the 12th ranked quarterback, the 24th ranked running back and receiver, and the 12th ranked tight end, kicker, and defense. Another approach is to use the "last player drafted" baseline, which usually is about twice as deep as the "starter" baseline.

What you do with the baseline is subtract the modified projected totals for the baseline player from all player's modified projections. This is essentially measuring how important it is for a particular position to get a top player. If, for example, one position varies a lot from 1-12, but another only a small amount, it places a greater importance on getting the player who the alternative will produce much fewer points. Another way of saying this is that the baseline is the yardstick for a player's comparative advantage.

Which baseline you choose can significantly change your results: For example, the smaller your baseline, the higher you will end up rating the top tight end, kicker or defense, and the less emphasis on the running back position. This is because every position has a sharp decline among its top few players before realizing a steady descent. A position that descends very slowly is less valuable the farther you get from the initial drop, where as a position like running back descent quickly all the way through. Below are some common methods for picking a baseline.

W O R S T  S T A R T E R » This approach assumes that since every team will have a starter at a particular position, that alternative that you should compare other players to is the worst of all of the starters. While it is true that all positions have starters, it doesn't account for how deep a position may go. For example, you might elect not to pursue a top 12 tight end- than your tight end will be off the charts or in negative territory. However, it is still a very solid method.

A V E R A G E  S T A R T E R » This approach seems to have make sense, and you can do it either by averaging the production for all starters or by picking the "average" starter, meaning the starter ranked halfway down your rankings. However it will have you picking a kicker in the third round if you don't pay close attention. The average starter technique inflates the value of normally insignificant positions, but is a good approach to build a team with a good breadth of scoring positions.

L A S T  P L A Y E R  D R A F T E D » This is an approach that works better if you emphasize quality throughout your roster before getting all of your starting positions filled. With this baseline, you might end up picking several backups before filling in your starting positions. When I used this method my first three picks were invariably all running backs. While that isn't necessarily a bad thing, sometimes getting your top kicker is more important than your third quarterback or fifth running back, simply because the player you select instead of your kicker might never play while your kicker might play 16 weeks.

S T A R T E R  A N D  A  B A C K U P » I really like this approach because it involves more common sense - you will probably play your top backup at a position so you treat them like a starter, but after that you don't put a higher emphasis on getting your starting spots filled.

L A S T  P L A Y E R  Y O U  W I L L  U S E » This is another personal favorite that is basically like the last one, but a little more flexible. I decide how many players I am going to use at a particular position for a team, and I use the last possibility as my baseline. Usually that means I consider two quarterbacks, four running backs, four receivers, one tight end, one kicker, and two defenses. However, it can change from league to league, and is really just a specific subset of the "Starter and a Backup" approach.

L A S T  P L A Y E R  Y O U  W O U L D  S T A R T » This approach is a little different than all the others, but is probably the most accurate. What you do for this is draw your baseline from the last player you feel comfortable starting. However, if you just did that, the numbers who actually increase if there were lots of players you wanted to start and decrease if you were only comfortable with a few. You want the opposite affect, so in this case you would divide the first number by the number of players that are start-able. So if you were comfortable starting 9 tight ends, you would use the ninth tight end as a baseline and then divide each of the values by 9. It seems weird but if you spend some time thinking about it- it really works. If this method makes sense to you I definitely think it is the best. However it is also much more time consuming.

Above I listed the average "Last Player You Would Use" baseline average over three years, keeping the cutoff the same for each year- 24 quarterbacks, 36 running backs, 42 wide receivers, 18 tight ends, 18 kickers, and 24 defenses. I mentioned earlier that this baseline favors quarterbacks, defenses and a little bit for wide receivers. This is an example of how you can most effectively utilize baselines- by tailoring them to your draft strategy. The above example is how many players I will draft to fill my "semi-active" roster spots. By semi-active I mean that I will rotate more players than my starters on a regular basis. So I plan my roster to have a semi active roster of 2 Qb's, 3 Rb's, 3.5 WR's, 1.5 Te's, 1.5 K's, and two D's. The halves mean I might draft a player if their skill is right, not that between two halves there will definitely be a player. The rest of the roster spots I reserve for guys that I think might breakout but haven't yet. You may decide to try a different combination of players, and all you need to do is simply adjust your baseline to put a heavier emphasis on those players you want more of.

Conclusion
The number you have now, is the player's "Modified Value." And is essentially what, given your own projections, that player is worth. Hopefully now you can use the modifiers listed above and come up with your own value rankings. However, that isn't to say that I am done.

A couple of paragraphs ago I listed my own roster specifications that I use for a baseline. I pointed out that I use this to have a large "semi-active" roster, meaning a number of players that I will rotate at a given position. The purpose of this, however, isn't to draft players higher- it is to draft them lower. But that doesn't make sense since I gave all of those positions higher ratings, didn't I? Yes, and the reason that it doesn't make sense is because if you want to utilize a combination of players at a particle position, there is more to come. Specifically, in the next article I will show you how to adjust values for a decision to rotate players at a particular position.

Anyway, thanks for reading, I know draft time is getting close so I will try to have the next section out in just a few days. Good luck.

» Value Based Drafting: Part 3