King maker

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Background

This topic arised after an analysis on the APS rating system, and a lengthy discussion. Also, the article on Wikipedia helped a lot.

What is it?

King-maker scenarios are situations when weaker competitors have the power to influence the position of stronger competitors. The first place (king) is made by someone else.

Examples

For example, if the rumble was reduced to only 3 competitors, A with strength 4, B with strength 3, and C with strength 2. Competitor A and B have a match and the score is 57% for A and 43% for B. Then they both have matches against C and the scores are 67% for A, 33% for C, and 60% for B, 40% for C.

  • APS for A would be (57%+67%)/2 = 62%
  • APS for B would be (43%+60%)/2 = 51,5%
  • APS for C would be (33%+40%)/2 = 36,5%

Good! The APS ratings have the same order as the strengths, showing the system is accurate. But what would happen if competitor C performs worse against B on purpose, or because of some bug only B is exploiting? Then the score for B would be 100% and C would be 0%:

  • APS for A would be (57%+67%)/2 = 62%
  • APS for B would be (43%+100%)/2 = 71,5%
  • APS for C would be (33%+0%)/2 = 16,5%

Competitor C crappy performance overweights the "final match" between competitors A and B, and decides who is the king.

A more bizarre scenario can emerge if competitor C leaves the rumble:

  • APS for A would be 57% = 57%
  • APS for B would be 43% = 43%

The positions are swapped back, without any of the 2 competitors involved doing anything.

What would happen if only wins/draws/losses are taken in account?

  • Winning rate for A would be 2/0/0 = 100%
  • Winning rate for B would be 1/0/1 = 50%
  • Winning rate for C would be 0/0/2 = 0%

If competitor C performs even worse against B, it would still be 0% for C and 50% for B:

  • Winning rate for A would be 2/0/0 = 100%
  • Winning rate for B would be 1/0/1 = 50%
  • Winning rate for C would be 0/0/2 = 0%

If competitor C leaves the rumble:

  • Winning rate for A would be 1/0/0 = 100%
  • Winning rate for B would be 0/0/1 = 0%

The only way for B to take the throne from A is defeating it. And the only way for C to put B in the throne is also defeating A. In a king-maker resistant system, you need to be the king to make another king.

Winning rate is by no means the only way to fight king-maker scenarios, but it is a simple and popular one. Premier League system also fights king-maker scenarios in an effective way.

Why should I bother?

King-maker scenarios usually disrupts the competitive mood in games as the outcomes are not dictated by a competitor's own performance, but by other competitor's performances. But it is good in games where diplomacy should be a factor. In the example above, B and C joining forces against A is a kind of diplomacy. If diplomacy is desirable in the rumble is another matter entirely.

In RoboRumble, after competitor C screws up the ranking in the example above, the consequences would be:

  • Either competitor A becoming pissed off and leaving the rumble
  • Or competitor A joining the king-maker fest starting to overvalue matches against C, and undervaluing an otherwise decisive and elaborate match between A and B.

In another scenario where a king-maker scenario wasn't happening, competitor B would be having a hard time figuring out how to defeat competitor A. After that, competitor A would be doing the same to regain the throne. And a lot more elaborate algorithms would emerge.

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