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+---
+layout: post
+title:  Unfair fixtures!
+categories: ["ideas"]
+---
+
+Analyzing the fixtures of recently concluded IPL 2023. Was it set up fairly?
+
+------
+
+[IPL](https://en.wikipedia.org/wiki/2023_Indian_Premier_League) is the biggest cricket event in the world. The format of the game is generally
+a double round robin followed by a double eliminator with the top 4 teams to decide the ultimate winner - modelled after the well recognized
+"Group Stage followed by Playoffs" format.
+
+**Group Stage**
+
+Group Stage is used to seed the teams. A round robin format is when each team plays against every other team. This is pretty good. If
+there are less number of teams, the fixture could include a double roun robin instead, where each team plays against every other team
+twice.
+
+Let us assume that there are a total of 8 teams in the tournament.
+
+Then each team has 7 opponents. Each team has to play each of those 7 teams twice, which means each team would play 14 games.
+In total, the total number of games in the double round robin fixtures is going to be the number of teams in the tournament times
+the number of matches played by each team, which is 14 times 8 = 112.
+
+But not quite, you see out of the 14 games played by team 1, 2 of them are against team 2. We should not make the mistake of counting
+that game again while calculating the total games played by team 2. That is - team 1 vs team 2 is the same as team 2 vs team 1. In the
+above calculation, we have effectively counted each game twice - once as team 1 vs team 2 and once as team 2 vs team 1. Therefore the
+total number of games is actually half of the above figure which is **56**.
+
+At this point, as each team has already played twice against another, I would consider it fair to simply call the top team at the end
+of this as the winner of the tournament. 
+
+But people like watching close games - regardless of the skill level of the players. Under such a premise, the seeding done above could be put
+to use to set up as many close games as possible.
+
+**The Playoffs**
+
+One way to set up the playoff matches is to pick the top teams of the tournament (preferably the top 4) and make them play against each other.
+To make it fairer to the top performing teams, we could pit the top team against the bottom team and pit the second team against the
+second-last team. It is likely that the first two teams are going to go to the finals based on what we might have already seen in the 
+double round robin group stage. But hey... there could be "upsets".
+
+Consider this setup for the top 4 seeded teams.
+
+- Game 1: Team 1 plays against Team 2.
+- Game 2: Team 3 plays against Team 4.
+- Game 3: Winner of Game 1 plays against Winner of Game 2.
+- Game 4: Loser of Game 1 plays against Loser of Game 2. Loser of this game is eliminated.
+- Game 5: Winner of Game 4 plays against Loser of Game 3.
+- Game 6: Winner of Game 5 plays against Winner of Game 3. 
+
+Winner of Game 6 is the winner of the tournament. The final is between a team that has won all its games, against a team
+that has lost exactly one game. If a team loses 2 games, then it is eliminated. This format also ensures that a team doesn't
+go out on a single freak loss after playing the entire group stage properly. This format - is called a **double-eliminator**
+since each team needs to lose twice to leave the tournament.
+
+But most importantly, we now have mitigated the possibility of upsets!
+
+> Note that to run a double-eliminator, one needs a number of teams that can be expressed as an exponent of 2 - 4, 8, 16 and so on.
+Each game generates a winner and a loser who plays subsequently, or generates a winner and eliminates the other team. At the end of
+the round where only a winner is generated, we would need a corresponding winner from another game to pair up in the next round.
+This is only possible halving the total number of teams after every such stage still leaves a number of teams that is divisible by 2.
+
+**What does IPL do?**
+
+IPL generally runs a double round robin for the Group stage and then a funky partial double eliminator for the Playoffs as follows.
+
+- Game 1: Team 1 vs Team 2.
+- Game 2: Team 3 vs Team 4. Loser is eliminated.
+- Game 3: Winner of Game 2 vs Loser of Game 1.
+- Game 4: Winner of Game 3 vs Winner of Game 1.
+
+The top 2 teams get 2 chances. The bottom 2 teams are eliminated on their first loss. Pretty sure that the organizers would simply
+explain this unfairness away by saying that the top teams are better than the bottom two and deserve more chances than the bottom
+teams.
+
+Traditionally there are 8 teams. That means 56 group stage matches and 4 playoff games resulting in a total of 60 games. This format
+is pretty stupid spending more than 90 percent of the games on seeding only to finish off the tournament in a matter of 4 games.
+
+IPL 2023 had 10 teams. If the organizers did what they normally do, the tournament would have ended up even more crazy - 
+
+10 teams double round robin = 90 games in the group stage.
+4 teams "funky" partial double eliminator = 4 games in the playoffs.
+
+A total of 94 games with 90 games in the group stage!!
+
+The only reason the organizers do this is because more matches - especially those that are guaranteed to take place without eliminations
+(basically all group stage games) are money making machines - stadium tickets, and advertisements. The fairness of the fixtures isn't even
+the 10th most important thing in this context.
+
+Surprisingly though, IPL 2023 did something less crazy with 10 teams, the group stage had 70 games. And the playoffs 4.
+
+70!??
+
+How are there 70 games? If each team plays against the other team once, there should be 45 games. If they play twice, there should be 90.
+How did each team play a fractional number of games against the other?
+
+**More Teams = More Unfairness**
+
+To figure this out, I started investigating the fixtures more deeply. Unfortunately, the organizing committee simply has a PDF file containing
+the list of fixtures. That is not an easy format for anyone interesting in doing data analysis. Therefore, I took a detour trying to
+parse and extract out this data in a more machine readable form. That took some time, but it was worth it. (The code is available
+[here](https://github.com/cool-mist/ipl-data)).
+
+Once I had the data in the right format, I could see that each team played exactly 14 games each. Clearly implying that they played atleast some
+of them more than once as there are only 9 other teams.
+
+I picked a team at random - Mumbai Indians, and looked at the games they have played.
+
+They have played 2 games against the following teams and 1 game with the remaining teams. This means 5 times 2 plus 4 = 14.
+
+- Gujarat Titans
+- Royal Challengers Bangalore
+- Punjab Kings
+- Sunrisers Hyderabad
+- Chennai Super Kings
+
+I picked up another team - Delhi Capitals, and they played the same type of games, exactly 2 games against the same 5 teams above.
+
+In fact, by bruteforcing my way through the entire team list, we can see that there have been 2 hidden groups. Group 1 is the group listed
+above. The other Group 2 is
+
+- Rajasthan Royals
+- Lucknow Super Giants
+- Delhi Capitals
+- Kolkata Knight Riders
+- Mumbai Indians
+
+Each team played a single game against members of the same group, and 2 games against the opposite group. 
+
+Somehow, they have made this even less fair than how it already is. To ensure that one side does not get to win too many games in the group stage,
+the two virtual groups above have to be balanced. This balancing is probably done using the results of the previous year, but that doesn't mean
+anything in this volatile tournament where players switch sides every year.
+
+**A Fairer Alternative**
+
+I propose below, a fairer alternative to the above nonsense, for 10 teams.
+
+- A single round robin group stage for a total of 45 games.
+- Eliminate the bottom 2 teams. A proper double elimination with the top 8 teams for a total of 14 games.
+
+This brings the total number of games to 59! 1 Less than what IPL has been doing with 8 teams previously.
+
+If required, we can throw in another game to identify the 3rd place in the playoffs as well to round it up to 60.
+
+(The double eliminator for 8 teams with an optional 3rd place playoff is shown below).
+
+![YouShallNotPass]({{site.base_url | absolute_url}}/images/doubleeliminator.png)
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