Math is Easy: Lessons from the WFTDA Ranking Structure

The WFTDA rankings measure are not a precise ranking of relative strength. Instead, it tracks teams with a record of winning or narrowly losing against very the best of the WFTDA.

The WFTDA has just released their all-important tournament rankings. As you are well aware, the WFTDA has implemented a new method to rank its leagues. Most of us are familiar—in passing—with the bullet points of the technique. As you are likely aware:

  • Wins matter, but so do points.
  • When you play a more difficult team, you may reap bigger rewards.

You’ve already seen the numbers and the rankings that will take us into the tournament season. If so, you are almost certainly comparing them to DNN, Flat Track Stats, Derbytron, or some other favorite metric.

You might be wondering what the leagues that voted this system in may have been thinking. The top 60 are a jumble of up-and-comers, established teams, and teams that look like they’re simply in the wrong order.

Before the numbers were released, the RDIT staff were very curious about how the new rankings will affect this year’s tournaments—and what effect the equation that the WFTDA uses will have upon booking, scheduling, and play. Let’s take a look at the formula, then glean some lessons about how the system might work out in real life.

WFTDA points 101

We’ll be referring to the results of the WFTDA formula as ‘WFTDA points‘—as opposed to the actual points a team scored in the course of a game. We’ll use an example to walk through a bout.

Here’s our example: on May 11th 2013, Texas defeated Rocky Mountain, 281 to 130.

How many WFTDA points did Texas get for this bout? How about Rocky Mountain?

The answer is A * B * C * D.

A: 300 points. At its base, every game is worth three hundred points. Each team starts with that number points…and then the formula starts modifying that number. We know that the formula posted on the WFTDA board represents this as two constants—3 and 100—but 3 * 100 always comes out to 300.

At this point in the equation, both Texas and Rocky have 300 points.

B: The number of points you scored as a fraction of all points scored. The percentage of points in the game scored by a team OVERALL in the game. Rule 2.2.2 says the winner is the team with the most points. In WFTDA-sanctioned games, that’s still true…but the more points that you score (and the less you allow your opponents), the better you do.

B is a number from 0.0 to 1.0. In a near-tie, both teams receive slightly more or less than .5. As a team piles on points, the winning team’s B starts moving toward 1.0. Since this is multiplied into the equation (and higher numbers are good), you want your team to get the biggest fraction of points—not the highest score—possible. In other words, blowouts are really, really good for your WFTDA points.

Example—Texas scored 68% of the points. Rocky Mountain gets 32%. Now—let’s multiply. A * B means Texas has scored 204 (.68 * 300) for the bout. Rocky has gotten 96 (.32 * 300) points. Fairly simple. Each team gets a proportional cut of the pie.

C: The power of the opposing team. If you’re playing a powerful team, you get a bigger ‘multiplier’ (we’ll refer to it as Power). This is another equation: # of teams in WFTDA – rank of opposing team * 2, divided by the # of teams in WFTDA = Power.

The max for Power is just under 2—the minimum is .5 (although the equation could take a team’s Power down to zero, there’s a ‘floor’ of .5). There’s no such thing as a worthless power in derby. The bigger the team you play, the more WFTDA points you have a shot at. However…remember that a big team is liable to smoosh a much less-experienced team. Getting that Power multiplier doesn’t mean much if you only score 20% of the game’s points.

Example – In April, Texas was 5th, so Texas’ Power was 1.94. Rocky Mountain’s was 1.89. So…Texas got .68 * 300 * 1.89, or 386 points. Rocky took .32 * 300 * 1.94, or 186 points. Each team gets a large bonus for playing such a difficult team.

D: The tournament bonus. Every team in a WFTDA year-end tournament gets a multiplier. The further you go, the higher the multiplier. If you’re playing a plain, sanctioned bout, you multiply by 1 (in other words, you get the same score you would’ve gotten otherwise.) Any other tournament bout gets a multiplier between 1.15 and 1.5 (the bonus for playing at the Championships).

In our example, Texas v Rocky is a standard WFTDA game. No tournament multiplier!

Final WFTDA points score
Texas (281): 386 points
Rocky (130): 186 points

FINALLY: follow that formula with every game you play over a 12-month period, then average them. That’s the number that WFTDA uses to create their rankings ladder.

Here’s the biggest lesson you need to take away: rankings are not about overall strength of a team. If you are looking for an accurate representation of who can beat another team at a given time…look elsewhere (I happen to be fond of the FTS method algorithm at present).

The WFTDA rankings measure how well a team has played other teams over the past year. At the June ranking, it’s not a precise ranking of relative strength. Instead, it appears to bunch together teams at the top that have a track record of winning or narrowly losing against very the best of the WFTDA.

Solving math problems at the chalkboard

So what lessons fall out from the analysis of the ranking system?

  1. Whup mid-ranked teams; go to the tournament. I think we’re going to get comments on this one.The easiest path to the tournament for a talented league is to start playing teams that are established mid-rank, Division Two leagues. Because the WFTDA is so large (155 leagues and counting…) the difference in Power is pretty small as you walk through the rankings. The Power multiplier, for example, between the 55th and 75th ranked team is 1.29 vs .96. That’s not a major difference. The number of teams with a Power of ranking of 1.0 or better will continue to grow as the WFTDA takes more leagues.A cynical (but mathematically sound) method to guarantee entrance into a tournament would be to book bouts against leagues that you know you can win with a high Power level. If your league’s travel team has the capacity to win against mid-ranked leagues, your path will be pretty clear. Beating the big leagues isn’t needed. You just have to do better than the ones behind you…but don’t take on the killers like Gotham, Denver, or Windy; that’ll screw your average.
  2. Big leagues in Spring = big risk in tournaments. Let’s consider Minnesota’s recent trip out west to Colorado for a moment where the MNRG battled Denver and Rocky. Many teams go on these weekend runs, playing several teams to get in games against non-local opponents. Oftentimes, these runs are against teams that are slightly better than them so that they can learn in a game environment.In previous years (under the voted-upon rankings system), the results would be a marker of where a league stood in their region. In 2013, a trip like Minnesota’s generated two scores (about 230 WFTDA points for Denver; about 220 points for Rocky) under their February average of 314 WFTDA points. Those results knocked them down the rankings ladder to 310 in April; the Gotham bout (where they scored 137 WFTDA points) at the Brewhaha will do even more damage to that score, despite similar scores against the Bronx Buzzsaw by other high-ranked teams.Does that mean Minnesota is necessarily a weaker team? No, it simply means that Minnesota at this point is playing above their weight, just like many teams in the upper tier. The result of a dipping average score is that Minnesota will be placed lower on the ladder with more challenging teams to bypass in September.And that’s potentially trouble. A great tournament league like Rose, London, or Minnesota doesn’t want a low seed. They want an easy opponent in the quarters so that their path to the semis (where Championship berths beckon) is nearly assured. A learning trip is great…but only if they can flip that knowledge into the tournament. By taking the chance to learn against some of the best teams in the nation, the formula may hinder a league’s tournament dreams.
  3. Hedging next year. Despite the tournament ‘bonus modifier’, a league in the lower echelons of tournament ranking (29–40, 53–60) risks big by entering a tournament. Why? Because teams in the 7–10 seeds can get beaten pretty badly. Two or three defeats creates several low-scoring games on your record that will send your league’s average score crashing down come the next year and will stay until the following tournament. A team in that position would do well to schedule (if possible) a few games with amenable lower-ranked leagues to balance out those losses.
  4. Run up the score. If there’s a single part of the equation that your league can affect, it’s the overall point percentage. Depending on your league’s bookers, you may not have much choice in who you play…but the tactics that you play with are going to be everything if you want to reach the top division under the present system.Your starting number in the equation is 300 * point percentage. Every extra point you score means a higher percentage of that initial 300. Every minute you keep the opponent’s jammer off the track nets you a higher percentage.If you want a clear understanding of why the jammer penalty/power jam/passive offense combo so permeates the sport at present, this is it. Pressing for jammer penalties and scoring easy laps will give you huge gains with this formula.
    It’s not just running up your score, though…the difference between a 150–to–50 win and a 300–200 win is significant. You start out the equation with 225 (75% of 300) instead of 180 (60% of 300), so blowouts are a path to the higher seeds.
  5. None of this matters much if you’re new. The strong exception to everything that’s been written up to this point is the new league. Unless you’re a team like Victorian or Sac City, you need to have a lot of patience.The bottom quarter of teams play with a Power multiplier of .5. Let’s say that you are one of those new leagues that has an outstanding year against the other small leagues in your area. You had five interleague, WFTDA-sanctioned bouts with your nearby bottom-quarter leagues and each of them you won, 150–100. You played one game with your sponsor league (#30 WFTDA) and lost, 300 to 75. Seriously, you had a great year.If each of those opposing teams were in the bottom quarter, you scored an average of 91 WFTDA points. That puts you just over the bottom quarter of teams in April rankings. That’s not a lot of headway, and you’re unlikely to continue to progress much up the ladder as a travel team—even with a capacity to take out the other teams in your region of the ladder. Breaking your way through 95 or more leagues (and more every year) into the tournaments are going to be difficult with a structure built around victory over teams in the top half of the ladder. It’s a particular challenge because the top 60 teams will have an opportunity to snag an even larger share of points at tournaments.

This is the current state of the tournament season. The present method of ranking is certainly imperfect; as I’ve mentioned, there are many ways to game the system. Some behaviors that build strong teams (such as tours) can be penalized.

That said, these are the rules of ranking. Teams that have won significantly during the year will be rewarded with tournament berths…but as always, a trip to a tournament is no guarantee of wins.

If you find this information concerning, certainly feel free to discuss in the comments…but then do something productive; talk with your WFTDA rep about it.

Good luck to all of the teams out there heading to the Big Seven.

Bonus section:

To get your mind around the way that the WFTDA is scoring the year for each league, we have three teams that may be indicative of teams across the ladder. (Obviously, this article was written before the rankings were released, so we could be wrong!) We encourage you to show your work.

  1. London had an incredible run through the PNW in June. They played against the very best in the West. How did that help Europe’s finest team?
  2. We’ll return to Minnesota for a moment. Their win/loss ratio is lower than most, but—as of April—they were #10. How did playing three other top ten teams (Gotham, Denver, and Rocky) affect them?
  3. Carolina. One of the giants of early roller derby, they had a very tough two months. Where does six losses put them?
  4. Finally, Texas. Almost as unbeatable as Gotham, though they did lose to them by nearly a 5:1 margin in June. How much higher would Texas have been if they hadn’t played The Great Beast?

Many thanks to Flat Track Stats and the WFTDA for all of the scoring and ranking data from previous months mentioned here.

Images courtesy of Jules Doyle and Public Domain

About Garrison Killer

Garrison Killer writes about roller derby. He's the league reporter for Saint Paul's Minnesota RollerGirls, has written about the North Central tournaments for the WFTDA and Blood and Thunder Magazine, and is a founding contributor to Queen of the Rink. You can egg him on Twitter @garrisonkiller.