The Power Ranking Dilemma

# The Power Ranking Dilemma

## Why power rankings are not as easy to produce as people may believe.

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In any competitive activity, power rankings are an all too familiar face to any watcher interested in the likelihood of their favorite team performing well. Usually, power rankings are issued at regular intervals based on results of the team since the last power ranking. They are determined by two factors: the previous ranking of each team and the team's wins and losses accrued in the ranking season. The previous ranking serves as a starting point for each ranked team while the wins and losses dictate how much the team has risen or fallen since the last ranking. However, just how much should each individual win and loss matter? This is something has been debated by many statisticians and ranking experts, with conducive arguments for all sorts of answers.

Consider a simple 4 team league, teams A, B, C, D. Team A has so far beaten B, C, D for a 3-0 record. Team B has beaten C, D and lost to A for a 2-1 record. Team C has beaten D, lost to A, B at 1-2, while team D has no wins, 0-3. Imagine Team A now plays Team D, and Team D wins. This would traditionally be considered an upset, as the #1 has lost to the last ranked team. Before this game, the power rankings are crystal clear (Teams A, B, C, D in that order). However, where would the teams rank after the game? Team A has to fall at least 1 rank, and Team D has to gain at least 1 rank, right? It is actually not so simple. Let us look at the records after the game. Team A is now 3-1, Team B is 2-1, Team C is 1-2, Team D is 1-3. If we look purely at statistical win percentages, the rankings should not change. Team A has a 75% win rate, Team B 67%, Team C 33%, Team D 25%. However, if we look at wins, it is arguable Team D has one of the strongest "resumes" of wins now. A win over the top seed is definitely more valuable than Team C's lone win over the bottom seed, and likely more valuable than Team B's 2 wins over the bottom 2. But on the flip side, Team A might have one of the worst loss "resumes" now, with a loss over the worst team compared to Team B's loss over the best team and Team C's loss over the top 2. We can see that in no way has D surpassed A, since they are still tied 1-1 but A has a much stronger resume, but where would they fall compared to B and C? Based on the "resume" algorithm, the correct ranking would be B, A, D, C. However, is B really so far away from C now? They really only share one difference (B beat C in their only meeting), while everything else is the same. Say the game was extremely close (final score 100-99), if C had theoretically won they would have jumped from last to first? Now we are beginning to see the flaws of these algorithms.

Looking at this very simple toy situation, one can already begin to visualize the complexities of these rankings. Imagine a league of 30+ teams and trying to compile the data and generate an unbiased power ranking every week. Computers can assist with the computational side, but there will always be some sort of bias with every ranking. In the end, we have to understand that there is no subjective nor objectively correct ranking for any situation, and that there is a lot of wiggle room to discuss potentially different permutations of teams. The most ideal methods usually are not sensitive enough to allow one win/loss to fluctuate the current standings too much, but also consider the amount of games played and the relative strengths of all the teams both a priori and a posteriori.

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