Monday, August 24, 2009

Current Fantasy Models vs. Revenue Model

In the previous post, I briefly explained the problem with long-term keeper fantasy leagues. There was one aspect of the league structure that I left out: the tournament model. A tournament model is often used in sports like Golf and Tennis in order to incent only those players who guage their probability of winning the tournament to participate as reasonable, or about as high as everyone else in the tournament. The tournament finds a balance where the payout is large enough that people with a 'relatively' smaller chance still do participate (Tiger Woods vs. Rich Beem). Among the obvious reasons of 'they won't let me because I just plain stink', the PGA understands that golfers like me would not bother entering in the US Open because there is literally a zero probability of me winning. Mulitplying that probability by the payouts, and I still have a $0 return on participating. I therefore have no incentive to put forth extra effort. So who participates? Only those golfers that feel they have a legitimate shot at winning. The 120th ranked golfer still plays in the US Open because of the large payout, since their probability of winning is MUCH higher than mine, and the payouts are large enough. This incents 'effort' as well, which is exactly what the PGA wants. The best players playing at their highest level. In order for everyone to put forth this effort, the tournament also must bring together the players with the closest skill set, and closest (relative) probabilities of winning. If players mostly see their chances of winning as being equal (more or less), they will all make sure to try as hard as they can. If one golfer feels he has no chance, he won't try. If one golfer thinks he has a 100% chance of winning, he also won't try. The trying and high absolute quality are what creates revenue for the PGA.

The interesting place that we seem to see the 'low effort' hypothesis take place is actually in the PGA, when Tiger Woods plays in a tournament. According to one study, by Jennifer Brown at Berkeley, players average 1 stroke worse over the course of the tournament when Tiger plays than when he doesn't. He likely affects their evaluation of the probability that they win the tournament, and they--apparently--put forth less effort (though it could be nerves, or just random chance still, but it seems significant and has some application here). For more information and a manuscript of this study, go here:

Because of the time and money that one needs to put into practice, equipment, etc. in order to compete at that level, I watch from my couch. There is a cost to participation, whether it be time or money. Because my probability of winning/advancing multiplied by the payouts does not surpass the cost to my obtaining that higher probability of winning/advancing (or at least does not surpass it by a significant enough amount), I do not participate, or bother to try (extreme example). However, this is assuming an efficiently structured tournament. If one makes the payout TOO big (winner gets a trillions zillion dollars), everyone with a .0000000000000000001% chance will participate, desipte low odds of winning. Perhaps that's good for some things, but I'm not sure it would be ideal for the PGA.

In the Fantasy World, the entire league participates to some effect. So where does the 'not participate' decision come in? Well, it comes in at the trade deadline. Staying competitive can be viewed as the participation, while dumping would be viewed as non-participation. Unfortunately, the 'non-participation' here actually involves participating in the competition and having unintended effects on the balance of the league. These undesirable effects are our externalities, as explained in the previous post. And because there is also NEXT season, the payouts become skewed. If you increase your chance for next season, you have expected value for THIS season AND next season coming into the beginning of each year (and the next, and the next, etc.). So our payouts may become too large, or not distributed correctly (a marginal increase in performance this year for Rebuilding Team creates $0, where a large increase for next year creates $50 and costs the team $0 this year if the entry fee for this year is thought of as a sunk cost).

The league payouts are often similar to a tournament model (No payout for the bottom teams, small payouts for the better teams, huge payout for the winner). So at the deadline, with payouts of $10 for advancing to the playoffs, $20 for winning the first round, $50 for winning the next round, and $500 for winning the final round, owners make an educated guess at their probability of winning (it is now educated given the length of season passed), and decide to continue competing, or play for next year. Why? Because if they can increase the probability of winning NEXT year's tournament by enough, they would make enough money to cover not only next year's entry fee, but possibly even this year's thanks to the large payouts. By treating this year's fee as a cost to be allowed to play next season, they can reevaluate their expected payout. They could even simply see this year's fee as a sunk cost (and with a low enough probability of winning this year, should be thinking of it in that way), in which case it becomes even easier for them to begin dumping players and trying to marginally increase their expected value for the following season alone. This creates a situation where probabilities of winning the Championship can vary too widely, and create incentive problems for owners (just like the sure winner or loser in the golf tournament). In the end, it's not so much to the rebuilder's disadvantage, but the integrity and fun of the league is at stake.

Let's look at a simple extreme example:

Right before the trade deadline, Team X has decided it has a 1% chance of winning the championship in a league that gives all the money to the winning owner. In a 20 team league, at $50 per team, that's $1000. What is the 'expected value' of the season for Team X? It's simply $1000*.01=$10. It just wouldn't be profitable for the owner of Team X to continue to compete this year (though without a keeper league, competing would be better than punting the season). However, WE are talking about next year as well.

Let's say Team X's owner decides that if he trades Albert Pujols, Manny Ramirez and CC Sabathia (contracts expiring) for Evan Longoria, Tim Lincecum and Andre Ethier who have very cheap contracts for the following season, he could increase his chances of winning NEXT year by 200%. By doing this he also decreases his chances of winning this year to 0%. Then, when deciding to dump, he will also take next season's expected value into account (we'll assume a 0% inflation rate). Assuming all teams have a 1 in 20 chance beginning the first, non-keeper depleted season, that's a 5% chance of winning when the league starts. Team X feels his chances are now 15% thanks to his blockbuster trade. Given this evaluation, his expected value for next season is $150! Not only does that cover his entry fee next season ($50), but it also covers his investment for this season ($50) plus a profit (another $50).

So the problem is the ROI this season for continuing to compete and the easily evaluated likelihood of seeing a payout. How can this be resolved? We could increase the return for continuing to compete despite a low probability of winning the championship and/or decrease the ability to guage whether or not an owner can win the league. In most leagues, there is no return on investment for hanging on to Albert Pujols through the end of the year only to release him back into the player pool unless he will help win the ultimate Championship prize. So how do we create this?

There are multiple ways to improve the return for doing so, as discussed earlier, but there is one I am quite partial to and recently developed myself (others may have had this idea, but I have yet to see it anywhere and I honestly created this at my computer based on the problems we've had in our keeper league with the help of our current league rules designed by my friend--and Law Student--Jesse). It's a fantasy league based on a revenue model. In this model, ROI is based on the marginal production of a team's players. In other words, a slight advantage does not result in enormous payouts. In a 2-team league ($500 entry fee), if one team has a 900% chance of winning, while the other has a 10% chance, the end results is not a difference of $1000. That is where the tournament model incents undesirable behavior (though my previous examples showed when a team decides dumping is better by using a more extreme case). In a revenue/marginal production model, the 10% team would produce $100 of league output, while the 90% team produces $900. These teams would be paid accordingly.

Heres' the key: Using a payout structure that gives owners ROI continuously through the season would incent them to continue to participate, rather than focus on the end result. We can design this to create the same expected payouts as the tournament model (and true payouts, if the tournament were repeated), but in a way that allows for the league to operate correctly. In addition, we can include a tournament at the end, as to not lose the gambling/excitement aspect of the league...and allow for all the trash talking to continue. So how do we do this? Check out the next post.

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