Answers.Body: <p>Group of SPs and then average evaluation (rounded to 4 decimal places):</p>
  <ol>
  <li>RKRXXXXX - 0,1900</li>
  <li>RKXRXXXX - 0,1906</li>
  <li>XRKRXXXX - 0,1878</li>
  <li>XXXXXRKR - 0,2017</li>
  <li>RXKRXXXX - 0,1867</li>
  <li>Whole of Chess960 - 0.1801</li>
  <li>Whole of Chess90 - 0.1913</li>
  <li>Whole of Chess870 - 0.1790</li>
  </ol>
  <p>Therefore,</p>
  <p>(0.1913-0.1790)/0.1790 = 0.06871508379 ~ <strong>6.87%, almost 7%.</strong></p>
  <hr />
  <p><strong>Remarks</strong>:</p>
  <ol>
  <li><p>Chess960 has a higher evaluation than chess870, but only by (0.1801-0.1790)/(0.1790) = 0.00614525139 ~ 0.6%.</p>
  </li>
  <li><p>Chess90 and each of its 5 SP groups have an average evaluation higher than the average evaluation of both chess960 and chess870.</p>
  </li>
  <li><p>SP 518 is 0.22, which is higher than each of the 8 evaluations.</p>
  </li>
  </ol>
  <hr />
  <p>In case you want to verify for yourself, here are my google sheet codes for the 5 SP groups of chess90:</p>
  <ol>
  <li>RKRXXXXX - <code>=IF(LEFT(B2;3)=&quot;RKR&quot;;1;0)</code></li>
  <li>RKXRXXXX - <code>=IF(AND(LEFT(B2;2)=&quot;RK&quot;;MID(B2;4;1)=&quot;R&quot;);1;0)</code></li>
  <li>XRKRXXXX - <code>=IF(MID(B2;2;3)=&quot;RKR&quot;;1;0)</code></li>
  <li>XXXXXRKR - <code>=IF(RIGHT(B2;3)=&quot;RKR&quot;;1;0)</code></li>
  <li>RXKRXXXX - <code>=IF(AND(LEFT(B2;1)=&quot;R&quot;;MID(B2;3;2)=&quot;KR&quot;);1;0)</code></li>
  </ol>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-20T19:55:11.143Z
Answers.Text: Are those differences meaningful though? What's the difference between a +0.18 position and a +0.20 one?
Answers.UserDisplayName: David
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-20T20:32:57.740Z
Answers.Text: @BCLC This percentage doesn't tell the whole picture or even close: there's a 200% difference between +0.01 and +0.03 but they're hardly distinguishable as chess engine evaluations. A better way would be to hypothesis test. (That said, it's an interesting question you ask and have started analysing.)
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-21T09:08:24.983Z
Answers.Text: @David anyway where did you get 0.18 and 0.20 ? i computed/calculated a 7% difference '(0.1913-0.1790)/0.1790 = 0.06871508379 ~ 6.87%, almost 7%' i.e. a chess90 SP is 7% more powerful for white compared to a chess870 SP Edit: Ah you mean XXXXXRKR and chess870 ?
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T00:49:31.210Z
Answers.Text: Alright, call it 0.1913 and 0.1790 then. Same point applies
Answers.UserDisplayName: David
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T06:10:19.307Z
Answers.Text: @David well i guess maybe not so meaningful based on comment of Mobeus Zoom
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T11:42:02.690Z
Answers.Text: @MobeusZoom even with hypothesis testing, a statistically significant difference is not the same as a practically relevant one. You could get a statistically significant result just by adding more and more possible starting positions, no matter how tiny the average difference is. But that wouldn't make the actual difference more relevant
Answers.UserDisplayName: David
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T14:33:17.177Z
Answers.Text: @David and MobeusZoom how would i do a hypothesis test here? hypothesis testing sounds more relevant for those computer chess winning percentages than for theoretical evaluations. like here i just have 2 numbers 0.1913 and 0.1790. hypothesis testing seems to be more for like having much more data to have a sample size n. looks like sample size is just 2 points here idk.
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T18:53:23.923Z
Answers.Text: @David It is up to BCLC, not you, how he wishes to define sufficient advantage to be "relevant" in characterising the positions. I don't see his post suggesting that a computer-judged advantage is irrelevant if it doesn't translate to significantly disparate practical results. Given the metric for advantage is BCLC's choice, the point is only regarding the methodology.
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T18:54:41.160Z
Answers.Text: @BCLC The sample size is much greater than 2. You want to compare sets of positions (of size 90 and 870) if I'm not mistaken.
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T19:39:01.993Z
Answers.Text: @MobeusZoom ok so what is the/a right way to compare the 90 points vs the 870 points ? Edit: Ah wait i think i remember: you mean null hypothesis test that average mean of 1 set is less than or is unequal to or whatever the mean of the other set? but these 90 and 870 are not exactly 'samples' of 'things'....they are the actual things. afaiu, hypothesis testing assumes there's like a real 'thing' and then the data we have are samples of the real things
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-23T20:33:13.910Z
Answers.Text: @MobeusZoom Update: https://stats.stackexchange.com/questions/561590/can-you-do-hypothesis-testing-when-instead-of-a-sample-size-you-have-actual
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-18T18:15:08.547Z
Answers.LastActivityDate: 2023-02-11T09:53:57.377Z
Answers.LastEditDate: 2023-02-11T09:53:57.377Z
Answers.UserDisplayName: BCLC
Body: <p><a href="https://chess.stackexchange.com/questions/37082/how-many-chess960-positions-exist-in-which-castling-on-1-side-does-not-require-m">Here</a>, it is shown 90 of 960 positions involve having to move a rook on 1 side in order to castle on the other side (unless the rook is somehow captured or something). These 90 positions come from 18 rearrangements/permutations/combinations/whatever from each of 5 groups of starting positions (SPs)</p>
  <ol>
  <li>RKRXXXXX</li>
  <li>RKXRXXXX</li>
  <li>XRKRXXXX</li>
  <li>XXXXXRKR</li>
  <li>RXKRXXXX</li>
  </ol>
  <p>Based on the <a href="https://docs.google.com/spreadsheets/d/1JVT6_ROOlCTtMmazzBe0lhcGv54rB6JCq67QOhaRp6U/edit#gid=0" rel="nofollow noreferrer">Sesse evals for the 960 SPs</a> (see <a href="https://chess.stackexchange.com/questions/37673/why-dont-these-statistics-disprove-whites-supposed-larger-practical-advanta/37682#37682">here</a> also) or based on other similar sources (such as practical instead of theoretical statistics like win rate eg <a href="http://www.computerchess.org.uk/ccrl/404FRC/opening_report_by_white_score.html" rel="nofollow noreferrer">this (computer chess)</a> [again see <a href="https://chess.stackexchange.com/questions/37673/why-dont-these-statistics-disprove-whites-supposed-larger-practical-advanta/37682#37682">here]</a>), what is white's increased advantage in chess90 compared to chess870?</p>
  <p>Note 1: This can't be vacuous. If white actually has a bigger advantage in chess870 compared to chess90, then the answer is simply negative.</p>
  <p>Note 2: I'm answering below for the sesse evals. I have yet to answer or receive an answer for the computer chess statistics.</p>
  
Tags: <chess-variants><statistics><castling><mathematics><chess960>
Title: What is white's increased advantage in chess90 as compared to chess870? (Chess960 can be split into 2 subsets, chess90 and chess870)
ThreadText: # What is white's increased advantage in chess90 as compared to chess870? (Chess960 can be split into 2 subsets, chess90 and chess870)
  
  (Asked by: username_0 on 2021-12-18)
  
  [Here](https://chess.stackexchange.com/questions/37082/how-many-chess960-positions-exist-in-which-castling-on-1-side-does-not-require-m), it is shown 90 of 960 positions involve having to move a rook on 1 side in order to castle on the other side (unless the rook is somehow captured or something). These 90 positions come from 18 rearrangements/permutations/combinations/whatever from each of 5 groups of starting positions (SPs)
  
  1. RKRXXXXX
  2. RKXRXXXX
  3. XRKRXXXX
  4. XXXXXRKR
  5. RXKRXXXX
  
  Based on the [Sesse evals for the 960 SPs](https://docs.google.com/spreadsheets/d/1JVT6_ROOlCTtMmazzBe0lhcGv54rB6JCq67QOhaRp6U/edit#gid=0) (see [here](https://chess.stackexchange.com/questions/37673/why-dont-these-statistics-disprove-whites-supposed-larger-practical-advanta/37682#37682) also) or based on other similar sources (such as practical instead of theoretical statistics like win rate eg [this (computer chess)](http://www.computerchess.org.uk/ccrl/404FRC/opening_report_by_white_score.html) [again see [here]](https://chess.stackexchange.com/questions/37673/why-dont-these-statistics-disprove-whites-supposed-larger-practical-advanta/37682#37682)), what is white's increased advantage in chess90 compared to chess870?
  
  Note 1: This can't be vacuous. If white actually has a bigger advantage in chess870 compared to chess90, then the answer is simply negative.
  
  Note 2: I'm answering below for the sesse evals. I have yet to answer or receive an answer for the computer chess statistics.
  
  **Tags:** chess-variants, statistics, castling, mathematics, chess960
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_0 on 2021-12-18. Score: 0 | Accepted answer
  
  Group of SPs and then average evaluation (rounded to 4 decimal places):
  
  1. RKRXXXXX - 0,1900
  2. RKXRXXXX - 0,1906
  3. XRKRXXXX - 0,1878
  4. XXXXXRKR - 0,2017
  5. RXKRXXXX - 0,1867
  6. Whole of Chess960 - 0.1801
  7. Whole of Chess90 - 0.1913
  8. Whole of Chess870 - 0.1790
  
  Therefore,
  
  (0.1913-0.1790)/0.1790 = 0.06871508379 ~ **6.87%, almost 7%.**
  
  ---
  
  **Remarks**:
  
  1. Chess960 has a higher evaluation than chess870, but only by (0.1801-0.1790)/(0.1790) = 0.00614525139 ~ 0.6%.
  2. Chess90 and each of its 5 SP groups have an average evaluation higher than the average evaluation of both chess960 and chess870.
  3. SP 518 is 0.22, which is higher than each of the 8 evaluations.
  
  ---
  
  In case you want to verify for yourself, here are my google sheet codes for the 5 SP groups of chess90:
  
  1. RKRXXXXX - `=IF(LEFT(B2;3)="RKR";1;0)`
  2. RKXRXXXX - `=IF(AND(LEFT(B2;2)="RK";MID(B2;4;1)="R");1;0)`
  3. XRKRXXXX - `=IF(MID(B2;2;3)="RKR";1;0)`
  4. XXXXXRKR - `=IF(RIGHT(B2;3)="RKR";1;0)`
  5. RXKRXXXX - `=IF(AND(LEFT(B2;1)="R";MID(B2;3;2)="KR");1;0)`
  
  > **Comments:**
  > **username_1**: Are those differences meaningful though? What's the difference between a +0.18 position and a +0.20 one?  
  > **username_2**: @username_0 This percentage doesn't tell the whole picture or even close: there's a 200% difference between +0.01 and +0.03 but they're hardly distinguishable as chess engine evaluations. A better way would be to hypothesis test. (That said, it's an interesting question you ask and have started analysing.)  
  > **username_0**: @username_1 anyway where did you get 0.18 and 0.20 ? i computed/calculated a 7% difference '(0.1913-0.1790)/0.1790 = 0.06871508379 ~ 6.87%, almost 7%' i.e. a chess90 SP is 7% more powerful for white compared to a chess870 SP Edit: Ah you mean XXXXXRKR and chess870 ?  
  > **username_1**: Alright, call it 0.1913 and 0.1790 then. Same point applies  
  > **username_0**: @username_1 well i guess maybe not so meaningful based on comment of username_2 username_2  
  > **username_1**: @username_2 even with hypothesis testing, a statistically significant difference is not the same as a practically relevant one. You could get a statistically significant result just by adding more and more possible starting positions, no matter how tiny the average difference is. But that wouldn't make the actual difference more relevant  
  > **username_0**: @username_1 and username_2 how would i do a hypothesis test here? hypothesis testing sounds more relevant for those computer chess winning percentages than for theoretical evaluations. like here i just have 2 numbers 0.1913 and 0.1790. hypothesis testing seems to be more for like having much more data to have a sample size n. looks like sample size is just 2 points here idk.  
  > **username_2**: @username_1 It is up to username_0, not you, how he wishes to define sufficient advantage to be "relevant" in characterising the positions. I don't see his post suggesting that a computer-judged advantage is irrelevant if it doesn't translate to significantly disparate practical results. Given the metric for advantage is username_0's choice, the point is only regarding the methodology.  
  > **username_2**: @username_0 The sample size is much greater than 2. You want to compare sets of positions (of size 90 and 870) if I'm not mistaken.  
  > **username_0**: @username_2 ok so what is the/a right way to compare the 90 points vs the 870 points ? Edit: Ah wait i think i remember: you mean null hypothesis test that average mean of 1 set is less than or is unequal to or whatever the mean of the other set? but these 90 and 870 are not exactly 'samples' of 'things'....they are the actual things. afaiu, hypothesis testing assumes there's like a real 'thing' and then the data we have are samples of the real things  
  > **username_0**: @username_2 Update: https://stats.stackexchange.com/questions/561590/can-you-do-hypothesis-testing-when-instead-of-a-sample-size-you-have-actual  
  
  ---
  
  