Answers.Body: <p>Given the new requirements, I tried to do a calculation. I couldn't find one on the internet suitable for this task, but <a href="https://wismuth.com/elo/calculator.html" rel="noreferrer">this one</a> suggests that for <em>one game</em> between a 2150 and a 2450 player, the following probabilities hold (from the standpoint of the weaker player):</p>
  
  <pre><code>win   4.5%
  loss 75.1%
  draw 20.4%
  </code></pre>
  
  <p>To get a score of 4.5 or more, which is needed to score a TPR of at least 2450, the following results work:</p>
  
  <pre><code>5 or more wins              (0.0023%)
  4 wins, and 1 or more draws (0.0434%)
  3 wins, and 3 or more draws (0.0842%)
  2 wins, and 5 or more draws (0.0490%)
  1 win,  and 7 or more draws (0.0045%)
              9 draws         (0.0001%)
  -------------------------------------
                               0.1835%
  </code></pre>
  
  <p>(you need some combinatorics to get the percentages)</p>
  
  <p>So he will succeed once every 545 tournaments, on average.</p>
  
  <p><s>It will depend on the strength of the opposition. To take two extremes: if your opponents all have a rating of 1000, you'll always win but never be able to get a TPR of 2450 (9/9 gives a TPR of +700). Conversely, if you're playing nine Stockfishes/Houdinis, rated 3300, you'll score 0/9 but that would give you a TPR of 2600. So the probability you're looking for can be 0%, 100% and everything in between.</s></p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-12-10T14:54:47.727Z
Answers.Text: Let's assume average rating of opposition is 2450 and we score 50% for this question.  And yes I believe you also have to play 5 titled players including 3 IM's to be eligible for the IM norm.  There may also be federation requirements of the opponents as well, but I'm not sure of those rules.
Answers.UserDisplayName: AS3Noob
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-12-10T15:23:41.080Z
Answers.Text: I'm not down voting you, but you should know your examples are very poor and have no bearing on the question. Here are two quotes from the FIDE Title Regulations: "IM performance is ≥ 2450 performance against opponents with average rating ≥ 2230" and "1.42 The following are not included: ... 1.42b Games against computers."
Answers.UserDisplayName: Brian Towers
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-12-10T15:26:01.403Z
Answers.Text: @BrianTowers the problem was that the question was ill-defined to begin with, and could have all possible outcomes. Now that its scope has been narrowed by the OP, I could provide a reasonable calculation of the probability.
Answers.UserDisplayName: Glorfindel
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Answers.CreationDate: 2016-12-10T15:34:46.337Z
Answers.Text: I like your edit :-). Have an up vote. Yes, somebody who normally plays at 2150 level is a very long way away from an IM norm. Browning: "A man's aim should exceed his grasp, else what's a heaven for?"
Answers.UserDisplayName: Brian Towers
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-04T10:26:45.167Z
Answers.Text: This must depend on how much the person's rating have been increasing relative to number of rated games played and K.  (Practically everyone who is highly commited to getting norms will be underrated)
Answers.UserDisplayName: Ian Ringrose
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Answers.CreationDate: 2016-12-10T13:27:50.963Z
Answers.LastActivityDate: 2016-12-10T15:24:26.380Z
Answers.LastEditDate: 2016-12-10T15:24:26.380Z
Answers.UserDisplayName: Glorfindel
Body: <p>What is the expected probability that someone rated 2150 will have a performance rating of 2450 over a 9 round tournament and earn an IM norm?</p>
  
Tags: <rating><performance>
Title: FIDE norm chance expectation calculation question
ThreadText: # FIDE norm chance expectation calculation question
  
  (Asked by: username_0 on 2016-12-10)
  
  What is the expected probability that someone rated 2150 will have a performance rating of 2450 over a 9 round tournament and earn an IM norm?
  
  **Tags:** rating, performance
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2016-12-10. Score: 6 | Accepted answer
  
  Given the new requirements, I tried to do a calculation. I couldn't find one on the internet suitable for this task, but [this one](https://wismuth.com/elo/calculator.html) suggests that for *one game* between a 2150 and a 2450 player, the following probabilities hold (from the standpoint of the weaker player):
  
  ```
  win   4.5%
  loss 75.1%
  draw 20.4%
  
  ```
  
  To get a score of 4.5 or more, which is needed to score a TPR of at least 2450, the following results work:
  
  ```
  5 or more wins              (0.0023%)
  4 wins, and 1 or more draws (0.0434%)
  3 wins, and 3 or more draws (0.0842%)
  2 wins, and 5 or more draws (0.0490%)
  1 win,  and 7 or more draws (0.0045%)
              9 draws         (0.0001%)
  -------------------------------------
                               0.1835%
  
  ```
  
  (you need some combinatorics to get the percentages)
  
  So he will succeed once every 545 tournaments, on average.
  
  ~~It will depend on the strength of the opposition. To take two extremes: if your opponents all have a rating of 1000, you'll always win but never be able to get a TPR of 2450 (9/9 gives a TPR of +700). Conversely, if you're playing nine Stockfishes/Houdinis, rated 3300, you'll score 0/9 but that would give you a TPR of 2600. So the probability you're looking for can be 0%, 100% and everything in between.~~
  
  > **Comments:**
  > **username_0**: Let's assume average rating of opposition is 2450 and we score 50% for this question.  And yes I believe you also have to play 5 titled players including 3 IM's to be eligible for the IM norm.  There may also be federation requirements of the opponents as well, but I'm not sure of those rules.  
  > **username_2**: I'm not down voting you, but you should know your examples are very poor and have no bearing on the question. Here are two quotes from the FIDE Title Regulations: "IM performance is ≥ 2450 performance against opponents with average rating ≥ 2230" and "1.42 The following are not included: ... 1.42b Games against computers."  
  > **username_1**: @username_2 the problem was that the question was ill-defined to begin with, and could have all possible outcomes. Now that its scope has been narrowed by the OP, I could provide a reasonable calculation of the probability.  
  > **username_2**: I like your edit :-). Have an up vote. Yes, somebody who normally plays at 2150 level is a very long way away from an IM norm. Browning: "A man's aim should exceed his grasp, else what's a heaven for?"  
  > **username_3**: This must depend on how much the person's rating have been increasing relative to number of rated games played and K.  (Practically everyone who is highly commited to getting norms will be underrated)  
  
  ---
  
  