<<< Previous Problem #2: The values given to the different rounds in a pool do not reflect their relative importance.  There are two popular ways to value the different rounds of a tournament office pool.  One way, probably the most widespread, is to increase the rounds in value geometrically, so that games in the first round are worth one point and picking the national champion is worth 32 points.  In this method each round receives the same value.  Another way is to let the winner of each game receive one point, which makes the first round thirty-two times as valuable as the final round.  Other methods, like increasing the rounds arithmetically (1-6) are used as well.  At AUBNMBTP, we reject outright the idea that games in every round should be scored equally.  Correctly picking the national champion is much more valuable than picking even the most remarkable upset in the first round.  But should it be worth 32 times more? The �geometric� method (1-2-4-8-16-32) has two main tenets, one good and one bad.  The good one is that since our tournament participants are diminishing at a constant rate, the scoring should increase at a constant rate.  The bad idea, which derives from the good, is that the points per game should increase at the same rate that the teams decrease.  Using the geometric method, if the Kentucky Wildcats are my national champions, then their win in the first Monday in April will be worth more than their five other wins combined.  We don't believe that anybody prefers this type of back loading of a tournament pool; we think people accept it as the best way to have the games� values increase at a steady rate.  We would like to introduce those people to Leonardo Fibonacci.  Fibonacci was a 12th century mathematician who, when given a problem dealing with population growth, discovered a series of numbers in which each number is the sum of the previous two.  The remarkable thing about these numbers was that they increased at a nearly constant rate, a rate that, as the numbers grew, more closely approximated the irrational number we know as phi.  Phi is approximately 1.618, and it is called the golden number because it has an amazing number of applications in art, music, architecture, botany, anatomy, and geometry.  We are only concerned with its applications in the very limited field of office pool design.  An office pool that uses Fibonacci numbers will have the following characteristics: The final game will be worth a little more than ten times as much as a first round game, or about one-third as much as the entire first round. The regional final round will remain about as valuable as it had been under geometric scoring.  The earlier rounds become more valuable, and the later rounds will lose value.  The final game will be worth about 10% of the entire pool. Each game in the first round will represent less than 1% of the entire pool, which is still more than double the value of the geometric method.  For simplicity sake, we have decided to assign to the pool an early portion of the Fibonacci series (the entire series is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, �).  So the first round will be worth 2 points per game, the second round 3, the third round 5, the fourth round 8, the fifth round 13, and the final round 21.  Higher numbers will be slightly more accurate, but these numbers will work just fine.  At Americans United for a Better NCAA Men's Basketball Tournament Pool, we have experimented with thousands upon thousands of scoring systems to assign to the different rounds, and the Fibonacci system is the only one that properly rewards what should be rewarded among office pool competitors. Combining the Fibonacci round scoring with the individual game results we discussed earlier gives us the following result:     1 2 3 4 5 6 1 0.00 0.39 1.45 4.53 10.09 17.96 2 0.11 1.07 2.70 6.32 11.63 20.17 3 0.34 1.62 3.88 6.95 11.97 20.45 4 0.42 1.66 4.28 7.26 12.66 20.72 5 0.63 1.97 4.74 7.68 12.66 21.00 6 0.63 1.97 4.74 7.68 12.66 21.00 7 0.82 2.53 4.74 8.00 13.00 21.00 8 1.00 2.68 4.74 8.00 13.00 21.00 9 1.00 2.92 4.93 8.00 13.00 21.00 10 1.18 2.53 4.93 8.00 13.00 21.00 11 1.37 2.61 4.93 8.00 13.00 21.00 12 1.37 2.49 4.93 8.00 13.00 21.00 13 1.58 2.88 5.00 8.00 13.00 21.00 14 1.66 2.92 5.00 8.00 13.00 21.00 15 1.89 3.00 5.00 8.00 13.00 21.00 16 2.00 3.00 5.00 8.00 13.00 21.00 This, given what's currently available to the designers and administrators of tournament office pools, is the best that we can do.  It will do a much, much better job of determining which participant knows the most college basketball, but perhaps its best feature is that it will keep out the artificial participant.  An alarming trend in March Madness pools is that some have found ways to cheat the system, to use computers that can maximize points based on the scoring system that is being used.  This system, with its normalizing of historical tournament performances and its numerous possible scores, all but eliminates the advantage of the computer-generated bracket.  At AUBNMPT, we pride ourselves on being on the cutting edge of office pool issues.  We feel that when our scoring system is adopted, all of the complaining, the cheating, and the uninspired brackets that plague the current office pool environment will be brought to an end.  In fact, our only real fear is that we've made ourselves obsolete.