Additional Resolution Rules

Obviously, bigger and more complex loops than the simple A>B>C>A example described above, will occur as the season progresses. One of GridMap's fundamental principles is to minimize the number of upsets required to resolve all these loops. To do this, GridMap has developed a set of logical rules, still based solely on games won or lost, for resolving all loops. I won’'t go into all the rules here, but will give an example of a slightly more complicated extension of the A>B>C>A example above, by including team D. In the simple example above, A, B, and C all have records of 1-1. If team D beats all the others, or loses to all the others, there is no complication. So suppose D beats 1 of the teams, team A, but loses to the other two, team B and team C. Now D is 1-2, A is 2-1, B is 2-1, and C is 1-2. (Though there are two other possible combinations of results with team D and A, B, and C, but they all result in two teams with 2-1 records, and two with 1-2 records, which create the same resolution as described below.) GridMap resolves this loop by placing team A, the 2-1 team that defeated the other 2-1 team, at the top of the thread. Team B, the only other 2-1 team, is placed on the tier just below team A. Team C, the 1-2 team that defeated the other 1-2 team, but lost to teams A and B, is positioned on the tier just below team B. Finally, the 1-2 team D, that lost to 1-2 team C, is placed on the tier just below team C. The only game result with a lower position team defeating a higher position team (an upset or Ranking Violation) is team D, on the bottom tier, who defeated team A, on the top tier. Any other ordering of these teams will result in MORE THAN ONE RV. Try it! Though the objective of this loop resolution was to minimize upsets, note that this ordering is also the way most leagues actually break their ties! So GridMap’s minimization of loops is consistent, at least for this elementary loop, with generally accepted practices of breaking ties. An unexpected, but validating, outcome. Application of this minimization objective can be demonstrated in a more complex loop system. Suppose A>B>C>D>E>A, creating one loop, and F>G>C>D>E>H>I>F creates another, seemingly independent, but intertwined loop (or “tangle” as GridMap calls it). Now using non-objective criteria, pollsters might “"know”" that A is a much better team than E, andconsider E's win over A as an upset. Similarly, they may "know" that F is a much better team than I, even though I beat F. They would then rank the teams with A>B>C>D>E and F>G>C>D>E>H>I. Even a quantitative system like Sagarin may do the same. But these rankings include 2 “ranking violations” or “upsets”. GridMap’s minimization principle REQUIRES untangling this loop by cutting it in the common element, C>D>E. The loop could still be resolved in either of two locations, between C and D, or between D and E. GridMap would use another of its logical rules to determine which. Assuming it was between D and E, the POSITIONING (not ranking) of these teams now becomes D>E>A>B>C, and D>E>H>I>F>G>C. This results in A being positioned on a lower tier than E, and F positioned lower I, contrary to the pollsters ranking of those teams. However, GridMap's positioning of the teams this way results in just one upset, or ranking violation, versus the 2 RV's in the other systems, and is one of the reasons GridMap is one of the most accurate systems. As additional game results are included each week, loops often become larger and more tangled. As a result, the location of the cut that resolves any particular loop may change from week to week. But GridMap tracks each loop throughout the season, and shows the teams involved, and any changes that occur. You can find the entire list of loops, and the teams involved in each, on the sheet titled “upsets”.