Cogito Ergo Decathlon

DPI History 

The Decathlon and both Pentathlons were originally determined by adding up each player's participation, besting, honor, skunk and bonus points. Whoever earned the most points in the games that comprised the athlon was its winner. During Decathlon VI, Rob noticed that shorter games earned points faster than longer games, so he played 31 Foosball matches and accumulated so many points in that single game that points in the other games were irrelevant. This clever strategy rightfully earned him the Decathlon title, but if imitated, it threatened to turn the Decathlon into a Foosball tournament. 

Hence, the Decathlon Performance Index (DPI, otherwise known as the Rob rule) was created, thereby neutralizing Rob's strategy. Instead of determining the athlon ranking by a sum of points, where one game played excessively could skew the results, DPI made games equal to each other by awarding points for ranking within each of the games. A 1st place in Foosball became equal to a 1st place in Blokus; a 2nd in Scrabble became equal to a 2nd in Disc Golf; etc. Applied to Decathlon VI, Rob, once he had established an unassailable lead in Foosball, would have had no incentive to continue playing Foosball with anybody. Instead, he would have had incentive to play the least popular game, because that game offered the easiest opportunity to move up its respective rankings and accumulate more DPI.

This scoring system, without further modification, would have continued to favor choosing Foosball over Blokus when a player's ranking was the same in each. Worse, it would have instituted a scoring system that in effect penalized players for playing their favorite games and perhaps rewarded anti-social strategies - not the spirit of the Decathlon. Therefore, the DPI includes a second weighting system that weights points earned in games according to the average time it takes to play each kind of game. For example, three matches of Foosball takes about the same time it takes to play one match of Blokus. Therefore, the DPI awards three times as many points to Blokus as it does to Foosball. Now, it is still advantageous to play the least popular game, but less so, because there is always reward for playing any game.

Astute readers may object that it is still possible for Rob to stockpile points in Foosball long after he has established himself as front runner. This is true. If this is his favorite game or a newcomer wants to challenge him, he will be rewarded for continuing to play Foosball, but now he will have more incentive to play a different game. More importantly to the overall Decathlon scoring system, Joyce can stockpile them in Blokus, Sara in Scrabble, Teresa in Horseshoes, etc. - all at the same rate. No longer is playing Foosball (or whatever short game) the most efficient way to accumulate points.

The Laurelstein ethos values winning and clever strategy, as well as hard work and endurance. The DPI is designed to cultivate these values by combining these two weighting systems. Additionally, it rewards contributions to the Decathlon event not captured by the two weighting systems through bonuses, such as doping, cleanup, Steiners, etc. Fortunately all this complexity distills into a simple strategy: help out, play quickly, play different people and win. If you’re not helping or playing, you’re losing.

Automated Recommendations

Because the scoring system is complicated, the software calculates recommendations about which games you should play next in order to best advance in the rankings. If you have participated in the Decathlon before, the recommendations factor in your past performance in a specific game. When you are inside the top 10, the points start to really add up and the all-knowing Carnac will point you in that direction.  If you have not yet played a match of a particular game, no recommendation will be given.

Consider the following: Shawna is in 2nd place in Scrabble with a total of 7 points. Anders is in 1st with 8 points. If Shawna played Scrabble and lost completely, earning 0 besting points, she would still earn 1 participation point and would move up in rank for a tie with Anders in 1st. The DPI spread between 1st and 2nd is 500 (2000-1500). Scrabble is estimated to take 60 minutes to play, so in this example, Shawna will earn 8.3 (500/60) DPI points per minute. This value is calculated for all the other games. The game that offers you the highest possible DPI points per minute is recommended.

Sometimes scoring only the guaranteed participation point won't change your rank, but will change the rank of others. This can occur when a tie is broken. Actually, three things can happen when a tie is broken:

  • You can advance to a tie at the next highest rank.
  • You can remain at the same rank and those who were previously tied will lose rank (called a "bump").
  • You can advance in rank and others can lose rank (when scoring more than the single guaranteed point for participation).

The recommendation considers all these scenarios - not just the positive potential impacts of your spreads to your DPI score, but also the negative possible impacts of bumps to opponents' DPI scores.

Consider the following tie scenario: Shawna and Anders are tied for 1st in Hearts. If Shawna played Hearts again, neither her rank nor her DPI points would change, because she's already in 1st place. However, Anders is poised to make the same move. If either of them played another Hearts game, he or she will hold 1st place outright and the other will be demoted to 2nd place. Their recommendations take this into account in the same way as described above - by establishing the spread (or bump) and dividing by the estimated time it will take to attain it. In this case, the bump is negative 500 DPI points in 50 minutes, or -10 DPI points per minute. So the recommendation for either Shawna or Anders would be Hearts, because -10 DPI per minute in Hearts would have a greater impact per minute to their Decathlon standings than will 8.3 DPI points per minute in Scrabble. In other words, even though the DPI point spread of 500 would be the same for both Hearts and Scrabble, Hearts is recommended because it takes less time to play.

The algorithm does not recommend:

  • which opponents to play
  • games you must play to qualify for an athlon
  • games you haven't played yet
  • games based on Decathlon rankings; only game rankings are analyzed
  • a short game when the gaming window is about to close

Strategy

In conclusion, much thought and effort have gone into the scoring systems to ensure fairness, encourage socializing and reward effort as much as performance. While the system may not be simple to understand, it's been designed to be simple to use. Just play a lot of games, play a lot of people and follow the automated recommendations.