Towards an Elo-style rating system for BattleTech

Roger Burton West

Table of Contents

1 Scoring games

1.1 Basic scoring formula

In a game where sides A and B fight each with the objective of destroying the other, the score for side A is:
SA = BsAs(Ae + Bs − Be)
where Asis side A’s total starting BV, Aeis A’s ending BV, and similarly for side B.
Larger games have larger score values. This is deliberate, both to encourage larger games to be played and because the larger the game the less overall effect luck is likely to have.

1.2 Damaged units

Since nobody wants to go to the trouble of calculating exact BVs for damaged units:
A unit that has made it off a friendly board edge (either by fleeing during the game or by the opposing commander accepting an offer to retreat) has its BV halved.

1.3 Objectives

Objectives are rated with a BV-scale number, agreed before the match starts. For example:

2 Calculating ratings

Each player starts with a rating of 1,000.
For each game, calculate the expected score based on the size of the battle and the ratings of the two players. KA is the total of any objective points available only to that side and not already included in AS; K*is the total of objective points available to any side and not already included in AS.
EA = 11 + 10(RB − RA400)(AS + BS + KA + K*2)
The difference between the actual score and the expected score, divided by 20 and rounded to the nearest integer, equals the change in rating.
RA = RA + int(SA − EA20 + 0.5)