$Id: README.scores,v 1.5 2001/02/23 02:34:09 ahn Exp $

                      Continuous Scoring System
                       Momentum Scoring System

Dave Ahn <ahn@genocide.netrek.org>


Continuous Scoring and Momentum Scoring are new systems for
determining the on-going and final score of a league game.  The old
system uses an absolute planet count of 11-8-1 for the winning
condition.  It has worked fine for many years, but some players argue
that it favors the use of a passive strategy to stash a large number
of armies for a last minute push before end-game.  The consequence is
that the first 1/2 to 2/3 of a clue game can often be boring and
somewhat meaningless.  Continuous Scoring and Momentum Scoring
attempt to address these problems by using the on-going state of the
entire game to determine the winning condition instead of just the
final planet count.  Whether these new systems are better than the
old...only time will tell.

**** Continuous Scoring ****

This system works by tallying the points for each team at every tick.
One point is worth one pair of armies on a planet, capped at 2 points
per planet:

	Army count	Points awarded
	----------	--------------
	0		0
	1-2		1
	3+		2

The INL robots runs at 10 ticks per second, so points are computed 10
times each second.  This point sum is multiplied by a weight factor so
that a weak score at the beginning of the game (from poor play such as
losing the base+25 at opening) can be more easily offset by improved
play at the end of the game.  The weight factor is exponential and
ranges from 1.0 to 2.0.  The formula for the weight at each tick
is:

	weight = exp(time) - (0.71828183 * time)
	time = range from 0.0 to 1.0, from start to end (regulation)

If the game goes to OT, the weight stays capped at 2.0.

The total number of points awarded at each tick for each team is:

	total = SUM(all planets owned by the team,
		   (weight * MINMAX(0, 2, points_for_each_planet))

For example, given weight = 1.0 and the team owns 2 planets, each with
2 and 5 armies, the points given to the team at that tick would be
(1.0 * 1) + (1.0 * 2) = 3 points.  If the team owns 10 planets, each
with 17 armies (such as at the beginning of a clue game), it would get
(1.0 * 2) * 10 = 20 points that tick.

Because these point scores are hard to interpret (what is a score of
12345 vs 12344?), the continuous scores are presented in
planet-normalized fashion.  A continuous score of 1.0 means that a
team has owned the equivalent of 1 planet.  Since the score is
weighted, 1.0 is not exactly 1 planet.  A running score of 9.23 - 8.01
means that the winning team has averaged about 9.23 planets while the
losing team has averaged about 8.01 planets.  The normalization
formula is:

	cont_score = total_points / (weighted_total_ticks * 2)

The continuous score is announced in regular intervals during the
game.  A player can also get the current score by sending the word
"SCORE" to himself.  The announcement looks something like:

	INL->ALL  Planet count: FED - ROM: 12 - 6 - 2 [FED]
	INL->ALL  Continuous score: FED - ROM: 10.12 - 9.01 [tied]
	INL->ALL  SCORE: FED is winning by planet count [tie break]

Each score is followed by the winning team under that scoring system.
Here, FED is winning by planet count.  Continous score is tied.  If
the game were to end immediately, FED would win by the planet count
tie breaker.  Please see the WINNING CONDITIONS section below on how
to interpret these messages.

**** Momentum Scoring ****

Momentum Scoring was first proposed by Doug Pitters to help address
some of the problems with continuous scoring.  In continuous scoring,
a team that is down by a large margin for most of the game would have
little real chance of staging a comeback.  A team could lose the game
despite being up by planet count.  Momentum scoring uses both the
planet count and continuous score to add additional time to the game
until a winner can be determined.


**** WINNING CONDITIONS ****

The INL robot now supports three different winning conditions.  The
first is the traditional 11-8-1 planet count win.  The second is based
on the new continuous scoring system.  The third is the momentum
scoring system.  The default is to use the NORMAL scoring mode based
on planet count.  However, both captains may switch to the CONTINUOUS
scoring mode using the command "SCOREMODE" during pre-game.

NORMAL scoring mode:
	At the end of regulation, 11-8-1 planet count by either team
	WINS the game.

	Otherwise, game goes into sudden death overtime.

	In overtime, the first team to get 11-8-1 WINS the game.

	The score announcements should indicate "winning by planet
	count" or something similar.

CONTINUOUS scoring mode:
	At the end of regulation, either team with a continuous score
	lead of 2.0 or more WINS the game regardless of planet count.

	Otherwise, if continuous scores are within 2.0 of each other,
	then the planet count is considered.  If the planet count is
	11-8-1 or greater, then the team with the higher planet count
	WINS.  This is called "tie breaker win"

	Otherwise, the game goes into sudden death overtime.

	In overtime, the first team to get 11-8-1 WINS the game.
	Continuous scores are tallied and announced during OT, but
	they do not affect the winning condition.

	The score announcements should indicate "winning by continuous
	score" or something similar.

MOMENTUM scoring mode:
	Score         Team A       Team B
	-------       ------       ------
	Continuous    WIN          loss       Team A WINS.
	Planets       WIN          loss

	Continuous    TIE          TIE        Team A WINS.
	Planets       WIN          loss

	Continuous    WIN          loss       Team A WINS.
	Planets       TIE          TIE

	Continuous    TIE          TIE        Game goes to regular OT
	Planets       TIE          TIE        Whoever gets 11-8-1 wins.

	Continuous    WIN          loss       Game goes to EXTRA TIME.
	Planets       loss         WIN

	In the first EXTRA TIME mode, all ships are oblierated like
	sudden death OT.  Exactly 5 minutes are added, and game play
	resumes.  At the end of 5 minutes, the above rules are used to
	determine the winner. If the game is tied by rule 5, then an
	additional 5 minutes of EXTRA TIME are added.  Up to 15
	minutes (3 rounds of EXTRA TIME) are allowed. If no winner
	emerges at the end, whoever has the higher continuous score
	WINS if conditions 1-4 are not met.  Note that EXTRA TIME is
	not sudden death.


**** PROBLEMS ****

There are two major issues with continuous scoring.  The first is to
fine tune the parameters of the system so that a team that is losing
the game can reasonably come back to win the game.  The current
weighting system should help with this, but it will need adjustment.

The other is interpreting the scores for decision-making.  Given a
score of 11.00 and 9.51, what does the winning team have to do to
ensure a win with 5 minutes left in regulation?  Because the scores
are weighted and summed over time, the answer is not clear.  I am
thinking about adding a planet-minute count to the announcements.  For
example, "ROM needs 1.25 planet-minutes to win." would mean that ROM
would have to own 1.25 planets (5 armies worth) for at least 1 full
minute to meet the winning condition.  But ROM would also be able to
own 2.50 planets worth for 0.5 minutes to meet the winning condition.
This code has not yet been added, so suggestions are welcome.

The major issue with momentum scoring is that it is even more
complicated to interpret than continuous scoring alone.

Continuous scoring and momentum scoring require Vanilla Server 2.9pl6
or higher.

That's it.
Dave
