$Id: README.scores,v 1.1 2005/03/21 05:23:34 jerub Exp $ Continuous Scoring System Momentum Scoring System Dave Ahn 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. Continuous 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 obliterated 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