Many countries have laws restricting gambling. These laws generally make exceptions for games where the player's skill either partially or mostly determines the winner. Poker, for example, has been the subject of much debate about how much skill is involved. Several researchers have attacked the problem to try to provide an answer for the judges, attorneys, and politicians that are involved in the legal aspect of gambling. One method was developed by Marcel Dreef, Peter Borm, and Ben van der Genugten. They are part of the economics department at Tilberg University in The Netherlands. We will examine their method and try to apply it to fantasy football. First, we will define the concepts and terms used, and then look at the equation suggested by Dreef, Borm, and van der Genugten. Finally, we will see what this says about league rules.

Skill is a measure of the outcome that is determined by a player's ability, experience, and aptitude. Luck is the part of the outcome determined by things outside of the player's control. We will express the total result in terms of what percent is due to skill and what percent is due to luck. For example, if a result is 30% skill, then it is 70% luck. Luck can be split into two different types. The first type is luck due to events controlled by other people. This generally has to do with the other owners in the league. For example, even if you are skillful enough to know who the highest scoring running back in the league is going to be, you still might not be able to get him if he is drafted before your first pick. The second type is luck due to random events. Examples of this are injuries and suspensions that prevent a player from performing.

Result or outcome in fantasy football could be either winning percentage or winning the championship. We will look at both to see if there is a difference. An advanced player is someone who has a combination of ability, experience, knowledge of the game, and natural aptitude. A novice is someone who knows the rules of the game, but lacks the other qualities of an advanced player. For example, the new player who picks a kicker in the sixth round and doesn't stock up on running backs early in the draft would be a good example of a novice player. An all-knowing player knows exactly how many fantasy points every player will score in every game before the season starts. This type of player does not exist in reality, but is used to remove the element of random luck from the game.

The method developed by Dreef, Borm, and van der Genugten says that the results of a game are due to a combination of a learning effect and a random effect. The learning effect has to do with the parts of a game that the player can control. It is an attempt to gauge how much a player’s ability may be improved by experience or study. In this method, the learning effect is the difference in outcome between an advanced player and a novice player. The random effect has to do with the chance elements in a game. For example, the offensive linemen of the Jacksonville Jaguars suffered more injuries than normal last year. This brought down the production of their skill players. Since this could not have been known before the season started, it is part of the random effect. In the method we are using, the random effect is the difference in outcome between an all-knowing player and an advanced player. This is because luck does not affect how often the all-knowing player is successful since they already know the outcome of all the events that are random for other players. Thus, the difference between an all-knowing player and an advanced player gives us a measure of how often random events dictate the outcome of a game.

The level of skill in a game is what percent of the total outcome is determined by the player. Therefore, skill is the ratio of the learning effect to the learning effect plus the random effect. The equation for skill is:

Substituting for the learning effect and random effect, we get:

We can simplify the denominator by cancelling out the two “Advanced Player Result” terms:

For our purposes, we are going to focus on leagues with twelve teams. We will make an upper end, lower end, and average estimate for each of the three player types. This will give us a range of values for the amount of skill involved. Let's start by considering winning percentage. We are trying to estimate the winning percentage of each player type over a large number of seasons, so the number of games in a particular season is not important.

Every week there seems to be a player that comes out of nowhere and has a huge game. Call it the Mark Campbell effect. If you don't believe how often this happens, take a look at any of Mike MacGregor's “FF in the Groin” articles from 2004 and 2005. Combine this with perfect knowledge during the draft, and the all-knowing player should win 95% of their games. For high and low estimates, we will use 100% and 90%.

We will assume that there are eight typical players, two advanced players, and two novices in a typical league. If the average players win half their games, then the combined win percentage for the advanced and novice players must be 100%. Furthermore, let’s estimate that an advanced player will win ten out of fourteen games. This would give a 71% win rate. From this, we could assume 75% for the high end, 70% as a typical value, and 65% at the low end for an advanced player. This gives corresponding values of 25%, 30%, and 35% for the novice player, respectively.

To double-check our assumptions for an advanced player, we will look at the results from one of the three leagues I regularly play in. Every owner in this league has at least five years of experience. It is quite competitive and there are no easy wins against “dead” teams late in the year. I added up the wins and losses for the thirteen owners (one owner quit and was replaced) over the last three years. Then I found each owner's winning percentage. Here are the top five:

There is a relatively large drop from third place to fourth, so we will call the top three players advanced. They have a combined win percentage of 68%. This is close to our assumed middle value of 70%, so we have some confidence that our assumption for an advanced player is good. Unfortunately, there are no players that would be classified as novice in the league, so we don't have an easy check for those numbers.

Using the equation for skill shown above, let's take a look at the results so far:

• High End: Skill = (75 – 25) / (90 – 25) = 0.77 (80% skill)
  
• Middle Value: Skill = (70 – 30) / (95 – 30) = 0.62 (60% skill)
  
• Low End: Skill = (65 – 35) / (100 – 35) = 0.46 (50% skill)
  
  

Now let's re-run these numbers using winning the championship game as our measure of success and see if the results are similar or different. The all-knowing player now has to field a team that is just good enough to make the playoffs and then win two or three games in a row, depending on how long the league's playoffs are. Using the same logic as before, it seems to be an easy task to obtain players through the draft or waiver wire that will have great games in the last three weeks and good enough games during the regular season to make the playoffs. We will use a high and middle estimate of 100% success and a low estimate of 95%.

We will make the same assumptions as before regarding the number of advanced, typical, and novice players. Furthermore, we will assume the typical player will win one title every twelve years. For the advanced player, we will assume a title every six, eight, and ten seasons for the high, middle, and low end estimates. The corresponding results for a novice player are no titles, one every 24 seasons, and one every 15 seasons. These estimates give the following skill levels:

• High End: Skill = (16.67 – 0) / (95 – 0) = 0.18 (20% skill)
  
• Middle Value: Skill = (12.5 – 4.167) / (100 – 4.167) = 0.09 (10% skill)
  
• Low End: Skill = (10 – 6.67) / (100 – 6.67) = 0.04 (0% skill)
  

We have found that success over the long term (several seasons) is mostly skill, but success over the short term (winning a title) is mostly luck. If we want to reward the most skillful owners, then how should we set up our fantasy league? First, the regular season should be as long as possible. In a twelve team league, this probably means a fourteen week regular season with the top four teams making the playoffs. Even though winning the title is still mostly luck, at least we can be reasonably certain that one of the top teams will win it. If we allow six teams into the playoffs, then the chance of a mediocre team winning the title is much higher. If there are payouts, then consider increasing the prizes for the team with the best regular season record, most points scored during the season, and making the playoffs and reducing the money for playoff wins.

If you didn't win last year's championship, now you can confidently tell the winner that it was just dumb luck when he starts bragging at this year's draft. If you won last year's title, go ahead and rub it in their faces until the other owners threaten to drum you out of the league. If any of them say it was luck, point out all the skill you showed while kicking their sorry butts en route to the playoffs.