Life Isn't Fair to Losers

One of the most contested topics within the Press Gang forums each year when the new Steamroller document comes out is Strength of Schedule (SoS) as the first tiebreaker. Frequently this results in debate, proposals, and discussion, yet each time no one can find a “better” solution to the problem of breaking final standings ties. Additionally, I want to address the second tiebreaker of Control Points and how it favors certain factions and playstyles.

I propose Cumulative-Scoring as the first tiebreaker and Cumulative-SoS as the second. Cumulative scoring is traditionally used in Chess. I am presenting a hybrid of the cumulative scoring system for Warmachine due to the differences between a Chess Swiss tournament and a Warmachine & Hordes Swiss scored tournament.

 

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Strength of Schedule as it Currently Stands

Ties in the final standings of a Steamroller tournament are first broken by using Strength of Schedule (SoS). From the Steamroller 2014 document: “In the case of two players with the same number of tournament points, determine which one ranks higher by calculating strength of schedule. To do this, count the tournament points scored by each opponent of the tied players. The player whose opponents have the highest total score has the best strength of schedule score and earns the higher rank.” Players earn one tournament point for a win and zero for a loss, so it’s fairly easy to find out a player’s tournament Strength of Schedule by adding up all of his opponents’ wins.

One of the biggest issues with Strength of Schedule is that randomization can cause a weaker schedule without any input from the player. He has no control over his opponent selection, only how well he does against the opposing players he faces. Additionally, players who lose early in the tournament face a weaker field artificially improving their position, while their opponents are also facing weaker opponents artificially improving their SoS.

 

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For my first example, I want to compare two 4-2 players at a 64 player event. Player A loses in the first round and then again in the 4th. Player B does not lose until the 5th round and then again in the 6th. However Player B’s first opponent went 0-2 and then dropped from the event.

In the tables below you can see the entire tournament record for the six opponents that played against each of the players. In red (or bold) you can see the six specific games played against the relevant player (Player A or B).

 Player A’s Opponents’ records

Player A Table

 Player A’s overall SoS: 20

Player B’s Opponents’ records

Player B Table

Player B’s overall SoS: 19

In our example Player A has a higher Strength of Schedule than Player B, but Player A played against weaker opponents throughout the event and player B did not lose until he was matched up against players who finished the tournament with a 5-1 record. This exhibits the core issue with drops and with Strength of Schedule. Player B did not choose to be matched up against the dropping Opponent 1-B, nor did he drop an early round loss and place himself against easier opponents early. But now because of the first tiebreaker (SoS) Player A has finished higher. If, in our example, Player B had 1 higher SoS they would be tied and we would have moved on to the second tiebreaker (Control Points) which influences particular play styles and favors control factions that can score in scenario easier possibly favoring Player A once again.

The above example illustrates one of the weaknesses of SOS in a smaller tournament; however the system changes in a “large event”. In “Large-Event Scoring,” as found in the Steamroller appendix, Player B’s SoS would improve because of his first opponents drop. Opponent 1-B would be given 1TP divided by the number of total games (6) to provide a Large Event Strength of Schedule of .17 then that would be added to his other opponents Large Event scores (.33 + .5 + .66 + .83 + .83) giving him a final Strength of Schedule of 3.33, while Player A’s Large Event Scoring is also 3.33. We have already established that Player B played against stronger opponents and depending on his faction or play style may have had a more difficult time scoring Control Points .

 SoSBadLuckBrian

Certainly there are many times when Strength of Schedule gets it right and I have created examples to show the flaws inherent in the system, but these examples are not uncommon. While anecdotal, I am certain that many tournament players can tell you of similar experiences and I have heard many players voice frustration with the existing Strength of Schedule system.

The Cumulative Hybrid System

As an alternate solution, I am suggesting a conglomerate of tiebreaking systems that have been used in chess for many years. Unfortunately, many of the systems proven in chess cannot be directly translated to the Steamroller ruleset because of the prevalence of draws in tournament chess. However, with a small amount of tweaking we can make it work. While this solution does not completely remove the pairing randomization for scoring, it does reduce its impact.

Cumulative-Scoring for tiebreakers is a system wherein each round each player’s current tournament points are added to a cumulative score. Each round his new tournament point value is added to the sum of his previous rounds tournament points. For example in a 4 round tournament where a player goes 3-1 losing his first game but winning all the rest his cumulative score would be 6. We get this score from taking his tournament point total from each round and adding them together (rd1:(0) + rd2:(0+1) + rd3:(0+1+1) + rd4:(0+1+1+1) = 6) A player with the same record (3-1) that won his first three rounds, in theory, played against stronger opponents each round, and lost in the final round to the event winner would have a cumulative score of 9 (rd1:(1) + rd2:(1+1) + rd3:(1+1+1) + rd4:(1+1+1+0) = 9). This system places more emphasis on winning early rounds, staying in the winners’ bracket into later rounds, and not which player you are randomly dealt. In this situation, the player who lost in the final round would be placed higher in the tiebreaks, even if they both lost to the eventual winner, because the player who lost in the final round would have faced a tougher field throughout the tournament.

 SoSDoge

The Cumulative-Scoring system works well in chess because with draws as part of the scoring system players rarely need to move on to secondary tiebreaks. The field spreads itself out wider during the Swiss pairing system. However, in the game of Warmachine a much higher number of players will end up with the same cumulative score because of the lack of granularity in the scoring. This is where the hybrid solution is needed and we must change our second tiebreaker as well. Strength of Schedule has its flaws, but it does have strengths as well. Instead of using pure SoS as a second tiebreaker I propose using Cumulative-Scoring to calculate a Cumulative-Strength of Schedule.

With Cumulative-SoS each player’s opponents’ cumulative scores are added together to create a cumulative Strength of Schedule. Players who won deeper into the tournament create stronger Strength of Schedule for players they have played against. This will give players whose opponents won more games and won games later into the tournament a higher Cumulative-Strength of Schedule.

Once Cumulative-Score and Cumulative-Strength of Schedule have been used as tiebreaks any remaining ties can be broken using additional tiebreaks such as CPs and Army Points Destroyed. Additionally, if necessary, a form of Large Event Scoring could be added to the Cumulative-SoS system, though drops have less effect on players in the Hybrid Cumulative system.

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Summary

The emphasis in competitive Warmachine among the players has been and should be on a player’s skill. Players with higher skill more frequently win into later rounds and this is reflected in the Cumulative-Scoring system. Strength of Schedule conceptually still has merit, but Cumulative-SoS is superior when being used to differentiate ties between players who lose at similar rounds in an event. The Cumulative-Scoring/Cumulative-SoS system works to create a more intuitive final standings system that will better reflect the success of players in the tournament. Standard Strength of Schedule is a poor tiebreaking system. Chess and other forms of Swiss tournaments have used alternatives for a long time, it is time for Warmachine to move on as well.

Addendum: As a follow up I would like to make a few notes about Player A and Player B using the Cumulative system.

Player A’s Cumulative score is 12 and his Cumulative SoS is 65

Player A’s Cumulative score: 0+1+2+2+3+4=12

Player B’s Cumulative score is 18 and his Cumulative SoS is 78 and that includes his first round opponent which had a Cumulative score of 0.

Player B’s Cumulative score: 1+2+3+4+4+4=18

It is interesting to note that Players 1-A and 4-A who both ended the tournament 4-2 and dealt Player A his only losses both end higher in the rankings than him with Cumulative scores of 14 and 15 respectively.

It is also interesting to note that Player 4-B who ended the tournament at 4-2 but lost to Player B has a cumulative score of 17 placing him behind his first loss (Player B).

About the author: Trevor Christensen is a member of the Chain-Attack Trinity, Judge, and former Press Ganger.  His rules insights run every Friday.