149 lines
8.1 KiB
Markdown
149 lines
8.1 KiB
Markdown
---
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layout: post
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title: Unfair fixtures!
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categories: ["ideas", "cricket"]
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---
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[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
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a double round robin followed by a double eliminator with the top 4 teams to decide the ultimate winner - modelled after the well recognized
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"Group Stage followed by Playoffs" format.
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**Group Stage**
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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
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there are less number of teams, the fixture could include a double round robin instead, where each team plays against every other team
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twice.
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Let us assume that there are a total of 8 teams in the tournament.
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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.
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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
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the number of matches played by each team, which is 14 times 8 = 112.
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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
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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
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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
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total number of games is actually half of the above figure which is **56**.
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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
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of this as the winner of the tournament.
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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
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to use to set up as many close games as possible.
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**The Playoffs**
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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.
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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
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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
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double round robin group stage. But hey... there could be "upsets".
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A better alternative for playoffs follows..
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Consider this setup for the top 4 seeded teams.
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- Game 1: Team 1 plays against Team 2.
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- Game 2: Team 3 plays against Team 4.
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- Game 3: Winner of Game 1 plays against Winner of Game 2.
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- Game 4: Loser of Game 1 plays against Loser of Game 2. Loser of this game is eliminated.
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- Game 5: Winner of Game 4 plays against Loser of Game 3.
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- Game 6: Winner of Game 5 plays against Winner of Game 3.
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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
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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
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go out on a single freak loss after playing the entire group stage properly. This format - is called a **double-eliminator**
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since each team needs to lose twice to leave the tournament.
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But most importantly, we now have mitigated the possibility of upsets!
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> 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.
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Each game generates a winner and a loser who plays subsequently, or generates a winner and eliminates the other team. At the end of
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the round where only a winner is generated, we would need a corresponding winner from another game to pair up in the next round.
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This is only possible if halving the total number of teams after every such stage still leaves a number of teams that is divisible by 2.
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**What does IPL do?**
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IPL generally runs a double round robin for the Group stage and then a funky partial double eliminator for the Playoffs as follows.
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- Game 1: Team 1 vs Team 2.
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- Game 2: Team 3 vs Team 4. Loser is eliminated.
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- Game 3: Winner of Game 2 vs Loser of Game 1.
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- Game 4: Winner of Game 3 vs Winner of Game 1.
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The top 2 teams get 2 chances. The bottom 2 teams are eliminated on their first loss. Pretty sure that the organizers would simply
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explain this unfairness away by saying that the top teams are better than the bottom two and deserve more chances than the bottom
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teams.
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Traditionally there are 8 teams. That means 56 group stage matches and 4 playoff games resulting in a total of 60 games. This format
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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.
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IPL 2023 had 10 teams. If the organizers did what they normally do, the tournament would have ended up even more crazy -
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10 teams double round robin = 90 games in the group stage.
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4 teams "funky" partial double eliminator = 4 games in the playoffs.
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A total of 94 games with 90 games in the group stage!!
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The only reason the organizers do this is because more matches - especially those that are guaranteed to take place without eliminations
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(basically all group stage games) are money making machines - stadium tickets, and advertisements. The fairness of the fixtures isn't even
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the 10th most important thing in this context.
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Surprisingly though, IPL 2023 did something less crazy with 10 teams, the group stage had 70 games. And the playoffs 4.
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70!??
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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.
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How did each team play a fractional number of games against the other?
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**More Teams = More Unfairness**
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To figure this out, I started investigating the fixtures more deeply. Unfortunately, the organizing committee simply has a PDF file containing
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the list of fixtures. That is not an easy format for anyone interesting in doing data analysis. Therefore, I took a detour trying to
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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
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[here](https://github.com/cool-mist/ipl-data)).
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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
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of them more than once as there are only 9 other teams.
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I picked a team at random - Mumbai Indians, and looked at the games they have played.
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They have played 2 games against the following teams and 1 game with the remaining teams. This means 5 times 2 plus 4 = 14.
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- Gujarat Titans
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- Royal Challengers Bangalore
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- Punjab Kings
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- Sunrisers Hyderabad
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- Chennai Super Kings
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I picked up another team - Delhi Capitals, and they played the same type of games, exactly 2 games against the same 5 teams above.
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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
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above. The other Group 2 is
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- Rajasthan Royals
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- Lucknow Super Giants
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- Delhi Capitals
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- Kolkata Knight Riders
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- Mumbai Indians
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Each team played a single game against members of the same group, and 2 games against the opposite group.
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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,
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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
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anything in this volatile tournament where players switch sides every year.
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**A Fairer Alternative**
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I propose below, a fairer alternative to the above nonsense, for 10 teams.
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- A single round robin group stage for a total of 45 games.
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- Eliminate the bottom 2 teams. A proper double elimination with the top 8 teams for a total of 14 games.
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This brings the total number of games to 59! 1 Less than what IPL has been doing with 8 teams previously.
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If required, we can throw in another game to identify the 3rd place in the playoffs as well to round it up to 60.
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(The double eliminator for 8 teams with an optional 3rd place playoff is shown below).
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