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Hey everybody, just working on the ladder calculations for this season. So if they seem off right now they probably are.
Trying to improve from last time we did the ladder and the calculation will consider scores for determining rank.
Cheers!
Marc |
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You're the best Zabuddy!
And don't let anyone tell you any different (no matter all overwhelming evidence to the contrary)
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The Elo rating system is a method for calculating the relative skill levels of teams or players in competitor-versus-competitor games such as chess. It is named after its creator Arpad Elo, a Hungarian-born American physics professor.
The Elo system was originally invented as an improved chess rating system.
The difference in the ratings between two teams/players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%.
A player's Elo rating is represented by a number which increases or decreases based upon the outcome of games between rated players. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. In a series of games between a high-rated player and a low-rated player, the high-rated player is expected to score more wins. If the high-rated player wins, then only a few rating points will be taken from the low-rated player. However, if the lower rated player scores an upset win, many rating points will be transferred. The lower rated player will also gain a few points from the higher rated player in the event of a draw. This means that this rating system is self-correcting. A player whose rating is too low should, in the long run, do better than the rating system predicts, and thus gain rating points until the rating reflects their true playing strength.
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This is all well and good, but is the end result in a 16 league team going to be the same as 2-3 yrs ago when we ended up playing the same 4 teams throughout the season because the point movement wasn't large enough. And yes I get we didn't use the ELO system then (or I don't believe we did), but is the actual result going to be different?
Can anyone run a test based on last years results to see?
As for a comment Bryan brought up (brother's stick together), this really should have been addressed in August. It is pretty close to 50/50 chance we were going to run into this situation, so not something that should really have shocked us (ie. 13 teams).
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| Just a thought, what if you gave the teams that signed up for rec an initial elo of 1300, and the comps 1500? |
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Alright, standings should be updated now. I won't go into too much depth unless there is interest, so here are a couple of things:
* Teams are grouped into 3 tiers, top (1500), middle (1480), and lower (1460).
* Points awarded/subtracted are based on the current rank of both teams, and how they scored against each other. So teams ranked the same would be expected to tie. If there is a win/loss then points assigned are based on the expected score and actual score.
Expected score is a percentage based on the rank of each team. Es = R1/(R1+R2).
Also interesting to note that if a strong team and weak team play against each other and the weaker team loses but does well enough the stronger team may lose points even if they win their game.
Cheers!
Marc |
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| Scowgie wrote: | Alright, standings should be updated now. I won't go into too much depth unless there is interest, so here are a couple of things:
* Teams are grouped into 3 tiers, top (1500), middle (1480), and lower (1460).
* Points awarded/subtracted are based on the current rank of both teams, and how they scored against each other. So teams ranked the same would be expected to tie. If there is a win/loss then points assigned are based on the expected score and actual score.
Expected score is a percentage based on the rank of each team. Es = R1/(R1+R2).
Also interesting to note that if a strong team and weak team play against each other and the weaker team loses but does well enough the stronger team may lose points even if they win their game.
Cheers!
Marc |
Thanks for the work on this Marc.
Do we know if we're ignoring the first week of games for the ladder (and for tiering)?
Our team (Fast Count) is a comp team, and we beat another comp team by 14 in our first and only game, but we've landed in the lower tier.
Seeing as the schedule's already been made up for this week, we'll probably just move forward as is, but I obviously have to be advocating for my crew.
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I would have thought the easiest thing would just have been to rank teams based on standing last year, adding the new teams at the bottom in their respective divisions, and run the 6-4-6 from there.
Now that we have a first week played, it could easily just be Turf/Awesomest/Fast Count/Hammer in the 4 slot, and then all other teams fall where is obvious.
I do agree that Jamie's team should have a higher ranking than Hammer based on the win, and likely all Comp (and likewise all Rec) should just have started with the same points if you weren't going to sort from the get go. |
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I was wondering about Fast Count when looking at last week's scores.
In any case it looks like initial rank for Fast Count has already been updated, so hopefully the ladder will sort itself out as the games go on. |
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Is there anyway to increase the amount of variance in points for winning and losing? I think this was the problem last time we had the ladder attempt. Just didn't move teams enough.
I see there were a few "blow outs" last week, and the most points lost were 6 (my team included). I would think that since we are starting with close to 1500, 6 is really not going to cause much change.
Mark can you explain how that limit is set, or if it not set and that was just purely coincidental that a bunch of teams had that.
Thanks |
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The limit is set based on the K-factor and ranks of teams. Since most teams which played against each other had identical ranking then their changes would seem similar.
In any case, I will try and explain how the new ranks are calculated, hopefully it will help.
The formula we use for determining the rank for Team 1(a) is as follows:
R'a = Ra + K(Sa - Ea)
R'a = New Rank
Ra = Rank of Team 1
K = K-factor constant. We are using 32.
Sa = Actual score of Team 1 (a)
Ea = Expected score of Team 1 (a)
It is the K factor which specifies the maximum amount of points that you can win/lose based on the perfect scenario. Anything in between is a percentage of 32.
So to illustrate, here is an example were a team would get the maximum points. Team A is expected to lose by a shutout but actually wins by a shutout. ie, Sa = 1.0 & Ea = 0.0. In this case, Team 1 would get 32 points and Team B would lose 32 points. But of course this would probably never happen.
So getting down to business, here is a real life example using your last game versus Fast Count.
We determine Ea using the following formula:
Ea = 1 / (1 + 10^((Rb-Ra)/400))
Team A = Drop (Rank: 1480, Scored 13 out of 40 points)
Team B = FC (Rank: 1480, Scored 27 out of 40 points)
40 points = 13 + 27 (scores of both teams added together).
Calculating expected scores for both teams gives us:
Ea = 0.5
Eb = 0.5
This makes sense because both teams have the same rank and are expected to tie (ie 50% of the total scored points for each team).
Calculating actual score for both:
Sa = 13/40 = 0.325
Sb = 27/40 = 0.675
Then finally calculating rank as follows:
R'a = 1480 + 32(0.325 - 0.5) = 1474 (-6 change)
R'b = 1480 + 32(0.675 - 0.5) = 1586 (+6 change)
If the score was 40 to 1. Then the rankings would change by +/- 15 with a K-factor of 32.
I do know that a K-factor of 16 is used for stronger players (ie Masters), while 32 is the norm for most. I think for our purposes it is easier just to use 32 for everybody. We could potentially increase the K to say 64, but I would hesitate for now.
We have already adjusted the formula this year to include the score in determining rank. If we adjust too many things at once, it will be tougher to determine what really works well for us.
Anyway, hope this clears things up a little bit for everybody.
Cheers!
Marc |
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| Marc, that sounds good to me. Thanks for answering Mike's question. |
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Great explanation Marc. Thanks.
But it does seem to highlight the problem I raised. If I recall a few years ago when we experimented with the ladder it was a straight win/loss system. For some reason I recall it at 6pts win. What I remember was the separation wins and losses created wasn't significant enough to result in any real movement in the ladder and as a result we ended up playing the same teams throughout the entire season.
How would this ladder address that issue? (and yes I know we are currently not suggesting the use of the ladder...but just raising the issue for future) |
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I know when I played in TUC with a ladder, they created the schedule for the next 3 weeks, and you wouldn't necessarily always play the team directly above or below you.
Some weeks one team could end up paired against a team 4-5 spots above/below them, but usually not more than that.
I think if you do it this way, the ladder is still there for guidance, but you can set the actual matchups each week to attain a variety of opponents.
With that said, you still want to be able to see movement in the ladder. If you placed the strongest team at the bottom of the ladder, they should be able to climb to the top eventually.
And yeah, thanks for that explanation Marc! |
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| Mike, I know you are a numbers guy so if you have a suggestion as to a formula you think would work better let us know. There were some teams that moved 9 points this weekend so it does allow teams to move more than 6 points. After this next week I will be moving to the round robin schedule but in case we ever go strictly by a ladder it would be nice to know the best formula. |
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Marc,
Can you update this now that I see there has been a change in the tracking. Did you just zero everyone so we were all ranked the same again? I ask because I would have thought us losing to a much higher ranked team by 3 points would actually have been a positive for us, but instead we lost 1. Or is this just going to be a method of tracking within each round robin cycle?
Thanks |
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The rank seeding for this week just needed to be copied from last week in order for it to calculate properly.
Usually they are copied over prior to the Sunday games.
So check out the standings now. The +/- results have changed since the initial seeds have been updated appropriately.
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Are we doing the "brackets + round robin" model, or the elo ladder?
Just looking at the standings right now, Bonk (who have played all of their games against very competitive teams) are 0-4. We, Fast Count, are 3-1, and that includes a 3-point win over Bonk this past weekend. Despite that, Bonk is still 9 ELO points ahead of us. Obviously that has to do with starting scores and difficulty of competition, but it just....seems off.
I am not so concerned with the actual standings, but it does seem like a slow process to move up the rankings. (There was only one game this week that saw a +/- swing of more than 3 points). |
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The only time you are going to see any substantial movement is when there is a larger than expected point spread while giving up the least amount of points.
If you wanted to move 13 points to take Bonk's position in one game. You could have done so if the final results were something like 14-2.
But since Bonk had scored 16 points, you would have had run up the score 110 to reach the 13 rank increase.
So the more points the other team scores, the less movement you can expect to make.
On the format front, I'm not sure what the plan is. |
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Maybe it's not the game-to-game movement so much as the initial point spread (which was 20 points I believe?). That's a lot to overcome when you're looking at movements of 1 or 2 points per game.
The gap between 4th and 5th is huge, which probably shouldn't look like that when there is a team in the top 4 who has lost their first 4 games. You also have telefrancais, who seem to have played great and deserve to be in first - but we're 4 weeks into the season and they are now basically impossible to catch for anyone who didn't start in the top tier.
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| I agree it needs tweaking. Not sure of the solution though. For this year we will likely look at records for the standings as opposed to the ELO rankings. The format is round robin with a 6-4-6 grouping. |
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| I think part of the problem is the Expected score. If I understand the formula, based on the current rank of the top team and bottom team, they are expected to tie. So if the bottom team beats Telefrancais by 1, they both end up with 0 points. That is very very wrong. |
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| Bottom team is never going to beat top team. moot point. |
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| Attachment: |  |
Just to clarify, this is what Sigs looks like when he's thinking..
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