What Is BeatPower?

Here’s an easier explanation of BeatPower, which is how we go from the Beatpath graph to the Power Rankings.

Take a look at the results for after Week 9 of the 2005 NFL Season:


And the beatloops that were taken out of the graph:

  • NO=>CAR=>GB=>NO
  • NE=>PIT=>SD=>NE
  • SD=>NYG=>DEN=>SD

Read on for how we determine BeatPower using both sets of information.

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To explain BeatPower, we’ll use Denver as an example.

Denver has beatpaths to 27 of the 31 other NFL teams. That’s clearly pretty dominant at this point of the season.

However, Denver has lost a couple of times this season – to Miami, and to the Giants. Now, Denver is good enough that they’ve managed to create beatloops to those two teams, which is why the Giants and the Dolphins don’t have beatpaths to Denver.

Here are Denver’s beatloops: MIA=>DEN=>KC=>NYG and SD=>NYG=>DEN=>SD

To determine a team’s BeatPower, you want their beatwins to count for them, and their beatlosses to count against them. You could just subtract the beatlosses (In DEN’s case: 0) from the beatwins. The problem with that is that it ignores beatloops. If you ignore beatloops, Denver would be ranked ahead of Indianapolis, which isn’t right.

If a team is very bad, beating a team will most likely create a beatloop before it creates a beatwin, and that’s because just about every other team already has a beatpath to that team. So for a bad team, creating a beatloop is a good thing, and evidence that they’re trying to improve.

The reverse is true for good teams. Losing will probably create a beatloop – not as bad as a loss, but evidence that their beatpath heap is starting to rot.

So a team with more beatloops should be pulled towards the middle of the rankings.

There’s an easy way to figure this. In instances where someone suffers a lot of wins, losses, and ties, the winning percentage doesn’t tell the whole story (at least, not when the total number of wins, losses, and ties varies from team to team). You have to figure in all three stats together.

So BeatPower is the number of winning relationships, minus the number of losing relationships, divided by the number of total relationships (beatloops).

Denver is in beatloops with five teams (including itself). So its BeatPower formula is (27-0)/32. Normally a possible BeatPower rating is between +1 and -1, but I normalize it to a scale of between 0 and 100 (add 1, and divide by 2). This results in a rating of 92.2 .

I am strongly considering a subtle variant of this method, which makes more sense to explain. Of Denver’s four other beatloops teams (not including itself), it has managed to develop alternate beatpath routes to three of them: SD, MIA, and KC. The only one that it still has an ambiguous relationship with is NYG – when it had a chance to make it unambiguous by beating them. So in this variant, the only beatloop team that would count against Denver would be the NYG. That would make Denver’s BeatPower (27-0)/28, or a normalized rating of 98.2 .

After Week 9, Denver is currently ranked #2. If I used the variant, Denver would be ranked #3, because Carolina has managed to develop alternate beatpath routes to every team that they beatloop with. Carolina ties Indianpolis with a normalized rating of 100.0, and is ranked second due to the tiebreaker of relying on the previous week’s power ranking.

BeatPower will continue to have its own column in the power rankings, so you can see how it’s calculated. You’ll be able to see the formula in this format: (beatwins/total – beatlosses/total), where total is the sum of beatwins, beatlosses, and beatloop teams.

19 Responses to What Is BeatPower?

  1. Pat says:

    I’m still not sure about the way the algorithm deals with shared loops (the infamous NO/TB/DET/MIN example). I think the main reason the filtered version cleans most of it up is because the NFL has the possibility of splits.

    I’m really curious to see what happens with the other conferences in college football if you try this (although I might do them as well).

    It just disturbs me that a team can win, and win, and win, and since they can’t invalidate a 3-team loop without a 2-team loop, those 3-team loops just keep adding up, and lowering the rating.

    I guess the main problem I have is that a beatloop normally consists of a win and a loss for a team, so it makes sense to lower a team’s rating the more of those they have. But it seems very strange to be able to lower a team’s ranking as they add more and more and more wins.

  2. ThunderThumbs says:

    I had a long reply about that here. Week 9 is significantly cleaned up with the altered algorithm, and we haven’t yet had any splits this year. It’s all because of alternate beatpath routes.

    At that point, my defense becomes that the situation you’re thinking of would almost never happen. Which, I admit, doesn’t sound like the best defense. But if it happened, it would mean that there really wasn’t enough data to determine if any of those teams were better than the others, because there would be no other mitigating beatpaths.

    If you can think of a way to help me conceptually justify what exactly we’d be counting if we accounted for shared beatloops, then that would help. So it would be something other than an adjustment.

  3. ThunderThumbs says:

    By the way, and just to keep driving a point home – it isn’t that they would keep winning and winning and winning, and that their rating would keep going lower. This would only be true if the team were in the top half of the standings.

    If the team were in the bottom half, and kept winning and winning and winning (adding more teams to the shared beatloop), they’d keep going up in the rankings. Neither would go past the middle.

    And if a A lost to another team (B) that was so bad that it lost to all the other teams A beat, it means that there’s definitely a big red flag about A – there’s more ambiguity about the team’s ranking, which means it should sink. The plus side of that, though, is that there’s more room for the team to rise (dramatically) if it resolves that ambiguity, or manages to find alternate beatpaths to the other teams (which you’d expect a good team to be able to do).

    And I suspect that will even be true in college football. I don’t think we’ll end up with a lot of unseparated sections of the graph – we’ll probably just have longer beatpath segments, less crossover arrows, and longer beatloops. It’ll be interesting to see what actually happens.

  4. david says:

    Saw you on King Kaufman’s article…. interesting graphic and rankings!

    A question though…. Looking at the Carolina Panthers… you account for all of our Ws and Ls except for the win at DET on 16 Oct.

    9/11 New Orleans L 20 – 23 (Loop BUF=>MIA=>NO=>BUF)
    9/18 New England W 27 – 17 (shown as a line)
    9/25 @ Miami L 24 – 27 (Loop MIN=>NO=>CAR=>MIN)
    10/3 Green Bay W 32 – 29 (Loop NO=>CAR=>GB=>NO)
    10/9 @ Arizona W 24 – 20 (Shown as a line)
    10/16 @ Detroit W 21 – 20 (??????????)
    10/30 Minnesota W 38 – 13 (Loop MIN=>NO=>CAR=>MIN)
    11/6 @ Tampa Bay W 34 – 14 (Loop MIA=>CAR=>TB=>MIA)

    Am I missing something?

    Thanks…. interesting stuff!

  5. ThunderThumbs says:

    That’s just because Carolina already has a beatpath to Detroit, so I kept the redundant arrow from showing up on the graph. The system still knows it is there, though.

  6. david says:

    How is it redundant? There’s not even an indirect relationship on the graph that I can see…. what am I missing?

  7. ThunderThumbs says:

    I describe it in more detail here, where I talk about the “long swoopy arrow”. πŸ™‚ As for this graph, follow Carolina through Atlanta through San Francisco to Detroit. I don’t make a distinction between direct and indirect relationships, I just see it as an extra arrow when the team already has a route to the team in question.

  8. david says:

    Thanks! I couldn’t find my way CAR > NE > ATL > PHI > SF > TB > MIN > DET…. that’s a long beatpath for a direct win. Great stuff!

  9. Amateur says:

    I have a question. A while back this paper was brought to my attention (via SportsFilter):

    A network-based ranking system for American college football

    I am not an expert, but is this not closely related to what you are calling BeatPower?

  10. ThunderThumbs says:

    Yeah, I hadn’t heard of that paper before yesterday. It’s pretty funny. Bummer that his work was funded by a grant from the national science foundation!

    It’s different in ways. He rewards each win in a beatpath by a different weight. The weight goes down if the team is really far away in the beatpath. As for “how much” it goes down each time, that’s the focus of most of the paper – there are all kinds of possible values to choose, and different values lead to different rankings. I guess that’s the part I don’t like (and don’t fully understand). I’m trying as hard as I can to structure my algorithm so it either makes no subjective choices, or “punts” where a subjective choice may be necessary (like canceling out beatloops, allowing other dynamics in the graph to make the decision for me).

    So the similarities are more about the fact that he’s also using directed graphs. But he doesn’t resolve beatloops the same way (if at all), and there isn’t anything analogous to BeatPower as far as I can tell. His directed graphs for each week are probably very different than mine.

    His method seems further along, because it seems like it might solve something that has been bugging me – the fact that some long beatpaths are easily broken apart and others are stable (due to alternate routes), but in my opinion his approach is also less fun and harder to explain. Overall I think it’s pretty funny, I just put this together one week when I was sick and didn’t know there had been all this research done into stuff like this (as is in his references). The method I stumbled into seems surprisingly solid when you consider all the research I didn’t know about. Heh.

  11. sam Fuentes says:

    forget everything. throw names into a hat & good luck. that seems like it will solve all the problems. but on second thought, they’ll probably argue about that!

  12. Pat says:

    By the way, just to point out:

    At that point, my defense becomes that the situation you’re thinking of would almost never happen.

    Actually, it almost did, last year. If you switch Miami and New England’s split (so put Miami’s win first, and their loss second), before the second win, you would’ve had

    digraph G{

    which is a pretty impressive loop! So when New England beats Miami the second time, all of those beatloops would explode, and New England’s ranking would rocket upwards (as it should’ve been positive already).

    That being said, I think the filtering mechanism you have would’ve cleaned this up as well. The rating still goes up considerably (as it should) but probably nowhere near as dramatically.

    For some weird reason it took me a while to figure out what you were actually filtering, but then I read your description in here again and it makes sense. The “NYG is the only team to which their relationship is ambiguous” makes perfect sense.

  13. ThunderThumbs says:

    Yeah, you know, I think this discussion has moved me on which variant to use. I think I’m going to switch to using the one that filters the beatloop teams. It just seems to make more sense, and in a way seems less subjective. I decided against it mostly because it didn’t seem right that CAR leapfrogged DEN, but then again, I’m a Denver fan, so I might have been a bit guilty there. πŸ™‚ The variant will lead to some more dramatic and interesting movements in the top and bottom ten, but nothing out of control… and that might honestly make it more fun.

  14. Pat says:

    Hey, nothing to worry about with DEN going overtop of CAR. Different conferences, so they only way they could meet is in the Super Bowl, and then they’d have a chance to prove themselves anyway. πŸ™‚

  15. Pat says:

    er, DEN overtop of CAR.

  16. ThunderThumbs says:

    WOW, Pat. πŸ™‚

  17. Pat says:

    er, CAR over DEN. Dangit!

    Incidentally, if you check Bleed Blue ‘n White, I added the Pac-10 as well, just for fun.

    The interesting thing here is that you can see what college football is going to start looking like when I try to merge the two together. There are so few connecting points, that the conferences basically just get shoved against each other. Their relative positioning is basically determined entirely by Arizona State beating Northwestern.

    I might add a third conference, just for sheer insanity. Hence the reason why I just started doing them conference-by-conference – there are so few “mega-huge-loops” that conference by conference is easier. πŸ™‚

  18. Amateur says:

    in my opinion his approach is also less fun and harder to explain


  19. Paul says:

    I read that pdf with the alternative method. The biggest differences between your method and theirs is that you cancel beatloops and every indirect win counts once and equally. Their methods does not cancel beatloops (as far as I could tell) and the first indirect win counts alpha, the second alpha squared…and so on. The choice of alpha has a limiting point, obviously less than 1, but typically can be no higher than 0.2 to 0.3. The choice of alpha is best chosen in the range of 0.7 to 0.85 of the theoretical limit due to beatloops.

    The assumption is that once the equations are applied a higher ranked team should beat a lower ranked team. Every beatloop involves at least one case of a lower ranked team beating a higher ranked team. With ranks A>B>C, this typically involves A beats B beats C who beats A, but it could also be C beats B beats A who beats C–2 ‘upsets’ compared to 1. Part of choosing the best value of alpha (the only parameter involved) was examining the number of ‘upsets’. The choice of 80% of the limit, which depended on the number of games played by each team, gave them their best results–fewer ‘upsets’.
    For NFL, your system may work as well or better than theirs as beatloops are very common, particularly with how the schedules are developed. For college, I would tend to believe their method would be better. It would definitely be interesting to compare the two in both college and NFL.

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