BeatGraphs

The Rules

Now that we know how to create a set of BeatWins without BeatLoops using all three methods, we need to have a consistent set of rules with which to make the graphs. While destroying BeatLoops gets rid of much of the ambiguity, it doesn’t eliminate it all. These rules help establish some conventions to keep graphs consistent from week to week. Take for example a graph with these two BeatPaths:

A→B→C→E
A→D→E

From this we know D is both better than E but worse than A. However we are unable to determine from this if D should be graphed on B’s level or on C’s level. Or take this case:

A→B→C
A→D

Here we know D is worse than A, but now it could be equal to B, equal to C, or potentially worse than both. This brings us to the first set of rules with regards to the graph.

• • All arrows must point down, and therefore...
• • A team must be graphed at least 1 level higher than its highest surviving direct BeatWin.
• • A team must be graphed at least 1 level below its lowest surviving direct BeatLoss.
• • Placement for teams with space between lowest loss and highest win will be determined by GraphScore.
• • All redundant arrows must be removed.

The final rule cleans up the graph to make it easier to read, but in doing so removes some information from the graph. Take the following example:

A→B→C
A→C

Instead of graphing the extra arrow from A to C, it is removed as the relationship is implied through B. While this link is removed from the graph, it is not removed for the purpose of calculating a team’s rating, as every distinct path is important.

Informative Arrows

Beyond the rules that are mentioned above, each method has a special quirk when it comes to drawing their arrows to help display the relative strengths of the BeatPaths. Since the Standard Method doesn’t really use weightings, the setup is easy.

• Standard Method Only
• • If a team has 2 or more net wins against another, the arrow is drawn bold.
• • All other arrows are drawn solid.

This takes into account the possibility of season sweeps for division rivals, or playoff rematches. With the Iterative Method you start with the same principle, but as the strength of a BeatWin lessens, the arrow changes form.

• Iterative Method Only
• • If a BeatWin has strength of 1.5 or greater, the arrow is drawn bold.
• • If a BeatWin has strength greater than or equal to 1 but less than 1.5 it is drawn with a solid arrow.
• • If a BeatWin has strength greater than or equal to 0.5 but less than 1 it is drawn with a dashed arrow.
• • If a BeatWin has strength less than 0.5 it is drawn with a dotted arrow.

Using this set of rules makes it easy to spot the weakest links in the graph. Similarly, the Weighted Method uses a set of rules to show relative weights of the BeatWins, but uses color to differentiate it from the Iterative Method and its scale.

• Weighted Method Only
• • If a BeatWin has strength equal to a blowout win, it will be drawn in blue.
• • If a BeatWin has strength equal to a standard win, it will be drawn in black.
• • If a BeatWin has strength equal to a narrow win, it will be drawn in red.

The threshold for what constitutes a blowout or a narrow victory varies by sport. Additionally, teams in the same division have the same background color, and teams in the same conference have the same border color. As mentioned above, any team whose placement is still ambiguous will have its placement determined by their GraphScore. Continue to the next page to see how these are calculated.