TDC ELO Ranking System

[Karvon]

With the recent release of updates, Slitherene has added an ELO ranking system. It is a more generic than what we use for TDC. 1) It is separate for the two games. 2) It does not distinguish the level of victory. 3) It doesn't factor draws.

Our own ELO is tracked by period, game and combined ranking. We also have several seasons of accumulated data at this point. Thus, we will continue to use our own ELO for TDC and our ranking purposes.

Regards,

Karvon

[Indibil]

Hi, can you explain how the ELO rating is calculated?
Thanks

[Triarii]

Hi, can you explain how the ELO rating is calculated?
Thanks

Any ELO rating is based on the system developed by Professor Arpad Elo (hence the name) the next two posts will try to explain first the system used in TDC and second give an example.

[Triarii]

Hi, can you explain how the ELO rating is calculated?
Thanks

1/2

The TDC rankings (ELO system)

Anyone who participated in TDC1 to TDC4 has an overall score for their TDC ranking.
Before TDC1/TDC2 scores were set for most players with a Slitherine Tournament, or a DLC record in FoG, at that time (Eric Doman completed this mammoth task). Since TDC1 all games in TDC1, TDC 2, TDC 3 and TDC 4 have been used to alter the involved player’s TDC ranking.

The overall TDC score gives a current TDC rank. However, since TDC 2 we have maintained separate but contributory, scores for the periods and platforms that a player participated in. Therefore, it is possible one player will have any or all of these scores:

• 1. FoGII Ancient Score (aggregate of i, ii, iii, & iv)
  i. Bronze and Iron Age score *Only since TDC4
  ii. Classical Score
  iii. Imperial Score
  iv. Dark Ages Score

• 2. FoG Medieval Score (aggregate of v & vi)
  v. Early Medieval Score
  vi. Late Medieval Score

• 3. TDC Overall ranking (aggregate of 1 & 2).

Please remember that there is a structural mathematical relationship between overall score and your period scores and the Medieval and FoGII Ancient scores, but this is not an averaging nor is it easy to see by inspection. The relationship is set out in an example of TDC ranking calculations explained in the next post.

The principle of TDC ranking scoring is an ELO* zero-sum formula# with three factorial modifiers so

• 1) in any one game the total ranking points of both do not change.
  2) in any one game the ranking points are redistributed between the two players dependent upon three modifying factors
  • a) The result for each player victory, defeat, or draw.
    b) The difference between the players current TDC scores
    c) The margin of victory, defeat or draw for each player.

This gives a TDC change for both players where one player will receive a positive TDC score change and the opponent an equal and opposite negative TDC score change. The only time there would be no TDC ranking change is in the unlikely event of an equal % damage score draw between two players of equal TDC ranking.

So, a higher ranked player beating a lower ranked player will always receive a positive score based on:

• (a) their standard victory factor but with
  (b) a negative factor for their higher ranking and
  (c) a positive factor moderated by how big their victory was.

The defeated lower ranked player has an equal and opposite negative score.

While the lower ranked player receives

• (a) their standard victory factor but with
  (b) a positive factor for their lower TDC ranking and
  (c) a positive factor moderated by how big their victory was.

The defeated higher ranked player has an equal and opposite negative score.

If they players draw the same principles apply but with no win adjustment (a).

In short beating a higher ranked player well will give a very big positive change, beating a lower ranked player will give a lower positive unless the margin of victory was very big while defeat to a higher ranked player will be less damaging unless it was an absolute thrashing.
A draw with a lower ranked player means a loss unless there was a big damage difference in your favour e.g. draw timed out at turn 24 at 56-32 for instance. The reverse is true for the lower ranked player.

* Named for Hungarian -American Professor Arpad Elo who developed the formula for this ranking system.
# Zero-sum formula means for two participants the gain for one is equal and opposite to the loss for the other – a net zero effect.

[Triarii]

Hi, can you explain how the ELO rating is calculated?
Thanks

2/2

The TDC Rankings and how changes to scores work

Whenever individuals have played in TDC they will have a change to their TDC score for each game they have played.
The net change to player’s scores is tracked in each period division.
At tournament end each player’s net change for each period is taken, added to their relevant period score(s), and then aggregated for the platform and then for the overall score.

So; changes in Bronze & Iron Age (B&IA), Classical (CLA), Imperial (IMP) and Dark Ages (DA) results are applied and then aggregated for FoGII Ancient platform (ANC Aggregate).
Changes for Early Medieval (EM) and Late Medieval (LM) are aggregated for FoG Medieval Platform (MED Aggregate)
All the changes that player has had, in all periods participated in, are aggregated for their overall score.
What causes confusion is an apparent lack of relationship between aggregate platform and overall scores and the period scores. However, there is a clear mathematical relationship that comes out of the aggregation and allows the different period rankings that we use to set up divisions as intended.
To show an individual working from the two previous TDC tournaments.

In TDC2 player A played in no Medieval Divisions and played in all 3 Ancient Eras. For TDC 2 player A started (as did everyone else) with a single TDC score (courtesy of Eric’s work). For Player A the starting score for TDC2 was 1319 and was altered as below at the end of TDC2

• • +0 with no Medieval participation so MED remained 1319.
  • • +100 for DA 1319 became 1418.
      +72 for IMP 1319 became 1391.
      +66 for CLA 1319 became 1385.
  • +238 on ANC so ANC 1319 become 1557.
  
  Overall change was +238 moving the overall TDC score to 1557.

In TDC3 Player A took part in Early Medieval (starting 1319), DA (starting 1418) and IMP (starting 1391). At the end of TDC 3 Player A’s results meant these changes

• • • +31 for EM so 1319 became 1350.
    Med is +31 so 1319 to 1350
    • +90 for DA so 1418 became 1509.
      -21 for IMP so 1391 became 1369* (*rounding diff)
    ANC sis +69 so 1557 becomes 1626.
  Overall, that was +100 so Overall Ranking score of 1557 moves to 1657.

For the start of TDC4 this was the data for Player A.

To rank players in Divisions the period scores are used, not the Overall score. So, in TDC 4 Player A would be placed higher in DA (score 1509) than in IMP (score 1369) because he has won against the opposition, he has had, more consistently in DA.

Remember that in each period the movement is a relative one as is the movement in Medieval Aggregate and FoGII aggregate and teh movement overall. The net effect on the total ranking points in the whole population is always zero. Because the MED, ANC and Overall Rankings are aggregates they are more likely to see greater change but there is a mathematical relationship and one which preserves the differential performance in periods.

It is the case that someone who enters more periods might move their overall rating up more than someone who enters fewer periods. However, they could, equally probably, come crashing down or not move significantly. Reward and risk are both potentially greater the more games a player has but actual movement will be decided by the proportion of victories to defeats and importantly against whom, with their relative position, those results occur.

[Indibil]

Many thanks for your explanation, but theses scores +100 -21 or whatever after every battle, how is calculated?

[Triarii]

Many thanks for your explanation, but theses scores +100 -21 or whatever after every battle, how is calculated?

Here you go - I have transferred the formulae to this graphic. The type of result is guided by Slitherine's rules but for a draw we default the player with least % loss to player 1.


Here are two worked examples. Bear in mind this is individual games and there is now a record for all TDC games from TDC1 to TDC4 where most common division size has been 10. That means 45 games per division and 3 to 4 divisions per period with 5 periods in TDC 1 to 3 and 6 in TDC 4.

TDC RANKING ELO FORMULA.png (39.01 KiB) Viewed 3888 times

Here is a win loss

TDC RANK CALC Example 1.png (31.01 KiB) Viewed 3888 times

Here is a draw

TDC RANK CALC Example 2.png (34.22 KiB) Viewed 3888 times

[Karvon]

I'd like to take this opportunity to thank Mike(Triarii} for all of his hard work in helping us develop and maintain the spreadsheets and working with us implement our ideas for ELO in TDC. He is our resident expert on the technical side of all this, and I appreciate him stepping up to provide this background info on how our version of ELO works.

I'd like to thank kronenblatt, who helped immensely in creating the ELO spreadsheets I use in my own tournaments which served as the initial template for TDC season 1.

I also like to thank carpenkm who took up the challenge in season 1 to adapt and expand my crude intial template from a simple 2 sheet tool to a more useful and more automated multipage tool which served as the basis for what we use today.

Finally, I'd like to thank Eric for all the hours he's put in collecting and collating data from the various tournaments which has been used to help set initial ELO ratings. He's also continued to be a source a useful suggestions and creative input both for our ELO ranking system and the development and promotion of TDC in general.

Regards,

Karvon

[principesromanes]

ELO seeding question based on this quote from the post about sign ups.

We will use your ELO rating for the period you played in, or the overall rating if no period rating, to place you in a division with similarly rated players.

My overall ELO currently is 1626, with Biblical ELO 1214, Classical ELO 1535, No Imperial or DA ELO, 1010 EM ELO and no LM ELO.

If I were to enter the Imperial division (where I've never played), it seems strange that I would be seeded notably higher than I would be if I entered the Classical division (where I've admittedly done rather well the past two seasons). It also strikes me that if I entered Late Middle Ages I'd be seeded a full 600 points higher than if I played Early Middle Ages. And this last one is probably just a me situation, but it strikes me that 1626 ELO is potentially A division, if not high B division. It strikes me as strange that it's easier for me to get into A division by playing in a division I have never played in than it is to get there in the Division I've had my best results in (i.e. Classical).

Is that working as designed? Is perhaps the average of existing ELOs a better marker for joining a new division for the first time than the cumulative ELO?

[Karvon]

ELO seeding is done in the following order: 1) Period, 2) Game, 3) Overall.

Thus, if you join a period for the first time, your game (ancient/medieval) will be used to place you.

I can't speak to the math, Mike and Keith were the one's who sorted through ELO formulas and adjusted them to our needs. If you want further details, I'd suggest opening discussion in the ELO forum.

Regards,

Karvon

[tyronec]

The period ELO values are going to be more representative for players as they play in more seasons.

The overall season ELO however is not really an ELO. It is calculated using the base value modified by the sum of the +ve or _ve scores for each period the player played in that season. So if a player has a good season across several periods it can dramatically increase and if they have a poor season it can dramatically decrease. So maybe it should be called something like 'Performance in their last season'.