What’s a beatpath graph?
A beatpath graph is basically the picture of an entire sports season. It shows every game in a season, with certain redundant data and ambiguities removed. It’s the clearest possible picture of the dynamics of the season and who is better than who, as judged by wins and losses. Every win and loss is accounted for.
What’s a beatpath?
If team A has beaten team B, and team B has beaten team C, then team A has a beatpath to team C, even if they haven’t played each other.
If a team A has a beatpath to another team B, then the odds are that A is better than B. But, a beatpath can only exist if all beatloops have been removed first.
What’s a beatloop?
This beatpath logic is commonly used to determine who’s better than who when teams don’t have a lot of common opponents. The problems start happening when beatpaths get contradicted. What happens if A beat B, who beat C, who beat A?
This is called a beatloop. A beatloop means that within that loop, we don’t really have enough information to determine who’s better than whom.
How are beatloops resolved?
A simpler question to ask is what happens if two teams split a two-game season series? In the absence of other information, what’s easiest to say is that it’s unclear which team is better.
The beatpaths system attempts to work out a league’s pecking order based only off of wins, losses, and who beat who. The best way to get a general sense of this is to rely on the obvious data, and punt on the ambiguous data. The easiest way to deal with a beatloop is to simply remove the beatloop matches. When we are attempting to judge the overall hierarchy of an entire league by paying attention to every game played in the league, removing beatloops simply serves to remove ambiguity. What’s left over is the clear data of who is better than who, according to every team’s wins and losses.
What about really long beatloops?
Beatloops are removed in order, from smallest to largest. Why do we do this? Here is a simple example. In the 2005 NFL season, Miami beat Denver. Denver beat New England. New England beat Miami. This was a beatloop, so all three victories (and losses) were removed from each team’s record. The beatloop existed because while there was clear evidence that New England was better than Miami, Miami had also managed to beat a team that had beaten New England. In the absence of any other information, it was impossible to determine who was better than who.
But let’s say hypothetically that later in the season, Miami beat New England to split the series. That would have made it ambiguous as to which of those two teams was directly better than the other. That would have changed things. While there was still evidence that Miami was better than New England (since they had managed to beat a team who had beaten New England), there was no longer any clear evidence that New England was better than Miami. So logically, in the absence of other information, there would then be clear evidence that Miami really was better than Denver, and that Denver really was better than New England. While Miami wouldn’t have a direct beatpath to New England (because of the season split), they’d have an indirect beatpath to New England, through Denver.
For this reason, two-team beatloops (splits) should be resolved before we search for any remaining three-team beatloops. (All beatloops of equal size are removed all at once.) This same logic can be abstracted to beatloops of any size. Since small beatloops are removed first, longer beatloops end up being quite rare due to most of them being first busted apart by smaller beatloops. The 2005 NFL season had a few five-team beatloops very early in the season. Midway through the 2005 college football season, the longest beatloops were of eight teams.
How are power rankings determined?
Once all beatloops are removed, we end up with a graph of how all the teams relate, from top to bottom. From there it is relatively easy to see how power rankings shake out. There are some teams that have no beatlosses. If a team has no beatlosses, it means that no other team has a beatpath to it. All the teams with no beatlosses could arguably be ranked #1.
From that point, it’s a matter of applying a tiebreaker. Once the tiebreaker is applied, the team is removed from the graph. The other teams with no beatlosses will be considered for the #2 slot. And, if the #1 team had a beatpath to another team that suffered no other beatlosses, that team will also be considered for the #2 slot. The tiebreaker is reapplied, and the process repeats.
How do you choose a tiebreaker?
This is the emphasis of most of the current research. We are finding that the most accurate tiebreaker so far is one that judges the strength of a team’s beatwins – meaning, the teams it has a beatpath to that it has directly beaten. A team’s strength is determined by its placement in the graph.
What other stats are figured in to the system?
None of them! The overall assumption of the system is that teams will continue to perform about as well as they have in the past, all things considered. Other variables will eventually cancel out in the mix of an exhaustive season. The system does not pay attention to matchups, statistics, injuries, or home field advantage. Due to this, the system will undoubtedly be less accurate than other more exhaustive systems. However, the beatpaths system has one major advantage – the graph gives you a way to get one all-encompassing look at how all the teams are relating to all the others, in an entirely objective fashion. It’s a great way to make sure your expectations aren’t out of whack. In the 2005 NFL season, there have been a few pretender teams. San Diego pretended to be good, and many power rankings systems had them in the top five all season long – the beatpaths system tended to keep them near the middle of the rankings. In contrast, Minnesota pretended to be bad – their win over the Giants gave them a major boost in the beatpaths rankings, even while most other systems kept them very low in the rankings until much later in the season.
The beatpaths system is objective, based entirely off of wins, losses and who beat who. It can occasionally pick up on emerging team momentum that other systems might not. It can also react to imbalances in strength or weakness of schedule. Referring to the beatpaths system to supplement other judgments based off of statistics, home field advantage, injuries, and matchups can help you come to more informed opinions of how a game might turn out.
Who are you?
I’m Curt http://okessay.org Siffert and I’ve always got my hands in a few projects. I have a music website over at curtsiffert.com, and you can also follow me on twitter at #://twitter.com/CurtSiffert.
impressive theory you’ve worked out.
and the obvious follow up question: have you tested it with any sports handicapping?
i’m an nfl guy and i obsess over team stats and other data before i place any wager.
so i was drawn to your theory. conduct any trials?
Mike in California