Body: <p>I am looking for the right terminology for this problem, so I know what to learn about.</p>
  <p>Imagine a population of 100 people in a town. The town has a sport team with 10 positions that play in competitions, and the town's people join the team when they can randomly. In this sport everybody plays the same position.</p>
  <p>We have a data sheet with all the matches played, including score achieved and the people that formed that particular team. Now we have a big final, and we want to pick the best 10 people for the match. NOT simply the team from the data sheet that scored the higher score, but to pick and choose those members that according the data maximises the chances of getting a high score.</p>
  <p>I am sorry if I do not explain myself well. For example, taking tennis, imagine that 2vs2 matches have been on going for a long time, and although Nadal and Federer have never played together, data would show that putting them in the same team would likely ensure a high score.</p>
  <p>What type of algorithm or technique do I need to find out?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-23T13:35:57.093Z
Comments.Text: It is important to understand how much team play factors such as team cohesion, and skills coverage can affect the result in your imagined game. For something where the team members compete separately with very similar skillset and add results at the end (e.g. running) vs strong player skill coverage (e.g. pub quiz) vs strong team cohesion (e.g. soccer, ignoring player position), you may need different strategies when building your team. A team full of "superstars" may not actually be a good team, depending on the sport
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-23T19:10:25.867Z
Comments.Text: That is the thing, we do not have those details. We have the match score and the team members, and we want to infer whom are the players that will for sure bring a good score based on the data we have.
Comments.UserDisplayName: vtscop
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-23T19:43:37.467Z
Comments.Text: Do you know the nature of the game, in order to use domain knowledge when considering those details?
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-24T07:34:55.780Z
Comments.Text: The game is an example. Imagine a team of lumberjacks working on the forest, for which you only record how many trees they cut in total for that team. If there are a few lumberjacks in a population that cut more trees than the rest, data will show that whenever those individuals are in a team, the team total is higher. I want to find whom those lumberjacks are.
Comments.UserDisplayName: vtscop
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-24T08:43:34.997Z
Comments.Text: I can see what you are getting at. You are better off IMO using a mathematical description of the problem. The analogies with sports are weak, and not realistic - tennis would be a poor example. What you appear want is to find some individual random number distributions with highest expected values, given that you can only observe the results in aggregate. I think that is a known and studied problem.
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-29T12:48:01.837Z
Comments.Text: It occurred to me that a reasonable team sport to use as an example here might be 10-pin bowling (where you only knew aggregate score out of 3000 for each team for some reason - not how team selectors would really do it of course, they'd make a point of collecting individual scores). There should only be a small amount of interplay between individual scores within a team, and for modelling purposes you can reasonably pretend there is none.
Comments.UserDisplayName: Neil Slater
Tags: <machine-learning><terminology><models><algorithm-request>
Title: Which algorithm can find the best combination of players to maximize the chance of getting a high score?
UserDisplayName: vtscop
ThreadText: # Which algorithm can find the best combination of players to maximize the chance of getting a high score?
  
  (Asked by: username_0 on 2022-04-23)
  
  I am looking for the right terminology for this problem, so I know what to learn about.
  
  Imagine a population of 100 people in a town. The town has a sport team with 10 positions that play in competitions, and the town's people join the team when they can randomly. In this sport everybody plays the same position.
  
  We have a data sheet with all the matches played, including score achieved and the people that formed that particular team. Now we have a big final, and we want to pick the best 10 people for the match. NOT simply the team from the data sheet that scored the higher score, but to pick and choose those members that according the data maximises the chances of getting a high score.
  
  I am sorry if I do not explain myself well. For example, taking tennis, imagine that 2vs2 matches have been on going for a long time, and although Nadal and Federer have never played together, data would show that putting them in the same team would likely ensure a high score.
  
  What type of algorithm or technique do I need to find out?
  
  **Tags:** machine-learning, terminology, models, algorithm-request
  
  > **Comments:**
  > **username_1**: It is important to understand how much team play factors such as team cohesion, and skills coverage can affect the result in your imagined game. For something where the team members compete separately with very similar skillset and add results at the end (e.g. running) vs strong player skill coverage (e.g. pub quiz) vs strong team cohesion (e.g. soccer, ignoring player position), you may need different strategies when building your team. A team full of "superstars" may not actually be a good team, depending on the sport  
  > **username_0**: That is the thing, we do not have those details. We have the match score and the team members, and we want to infer whom are the players that will for sure bring a good score based on the data we have.  
  > **username_1**: Do you know the nature of the game, in order to use domain knowledge when considering those details?  
  > **username_0**: The game is an example. Imagine a team of lumberjacks working on the forest, for which you only record how many trees they cut in total for that team. If there are a few lumberjacks in a population that cut more trees than the rest, data will show that whenever those individuals are in a team, the team total is higher. I want to find whom those lumberjacks are.  
  > **username_1**: I can see what you are getting at. You are better off IMO using a mathematical description of the problem. The analogies with sports are weak, and not realistic - tennis would be a poor example. What you appear want is to find some individual random number distributions with highest expected values, given that you can only observe the results in aggregate. I think that is a known and studied problem.  
  > **username_1**: It occurred to me that a reasonable team sport to use as an example here might be 10-pin bowling (where you only knew aggregate score out of 3000 for each team for some reason - not how team selectors would really do it of course, they'd make a point of collecting individual scores). There should only be a small amount of interplay between individual scores within a team, and for modelling purposes you can reasonably pretend there is none.  
  
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  ## 0 answers
  
  