People in DS City love sports. Statistics. And betting. While all stats are readily available, the question still remains how to compose your fantasy teams so that your chances of winning are maximized.
The simplest sports bet is on the DS favorite passtime, Wobbleknock. Each team has four members, but the goalie in Fantasy Wobbleknock is always given. That leaves just three players that we can choose. There are 18 players in total, 6 for each position.
One can only purchase one ticket in Fantasy Wobbleknock. On this ticket, we get to select two teams, i.e., two times three players that form two teams. If one or both of those two teams scores at least as many fantasy points than anyone else's bets, the ticket wins the jackpot. If multiple tickets win, the jackpot is split equally among all winning teams.
The same player may appear in both teams. The only constraint is that the total salary paid to all members on a team cannot exceed $100. The stats table above gives, for every player, the mean fantasy points score as well as the standard deviation for a normal distribution around that mean.
The simple task for you is to form two teams from the players above so that the chances are maximized that at least one of the two teams gets the high score.
What is your bet? Have fun posting your solution! We will post ours in a couple of days.
Note that the two teams constitute a portfolio. However, unlike traditional finance portfolios, it does not matter how badly the second highest scoring team does. As long as one team hits the jackpot score, you win.
We also have one more statistic for you: The jackpot score is typically 10% above the score that the deterministically best team would actually achieve. Meaning, the score to beat is 1.1 times the value of the Knapsack solution that was constructed for the mean expected values of each player, but evaluated for the actual points that the players then actually scored.
There are two ways we can go about this problem. The first is to maximize the maximum score of the two teams we are selecting. If we go for this option, we would select
- Team 1: Sturla, Sebastian, Martin
- Team 2: Lou, Elvira, Quentin
The expected maximum score for these two teams is 90.13.
However, as we have historical data on how well the winning ticket does when compared to the deterministically best team, we can maximize our odds of winning directly. We need to determine the deterministic solution first:
- Deterministic Team: Julia, Eric, Quentin.
This team gets a score of 86 on average. However, how it fares from week to week fluctuates, of course. And with that fluctuation, the score we must beat fluctuates also. To maximize the odds that one of our teams beats the deterministic team by at least 10%, InsideOpt Seeker selects:
- Team 1: Ingrid, Elvira, Hanna
- Team 2: Sturla, Sebastian, Martin
On average, these teams both lose against the deterministic team. However, together they give us a win rate of about 31.2%. Therefore, we can expect to win the jackpot about 17 times per year.