Answers.Body: <p>The first chess rating system, the Ingo system used in Germany, had very different numbers because in that system <em>lower is better</em>.  So the ratings there have no relevance to the current scale used by modern rating systems.</p>
  <p>The second chess rating system, the Harkness system used by USCF starting in 1950, already is calibrated almost the same as modern rating systems.  In the <a href="http://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1950/1950_11_2.pdf" rel="noreferrer">original USCF announcement of the rating system</a> it clearly says Class D below 1500, Class C between 1500-1700, Class B 1700-1900, Class A 1900-2100, Expert 2100-2300 and Master 2300-2500.  This is the same as current ratings but shifted by 100 points.  Acording to <a href="https://en.wikipedia.org/wiki/Chess_title#Master" rel="noreferrer">Wikipedia</a>, the Harkness system caused ratings to deflate which forced them to both move the rating cutoffs down by 100 points and to switch to Elo.  So Elo was originally calibrated to match the ratings of Harkness but adjusted down by 100.  Unfortunately I can't find any sources about how Harkness chose his calibration.  So unless someone has access to Harkness's private letters or similar sources, it is unlikely that we'll get a definitive answer.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-03-22T16:31:24.787Z
Answers.Text: There may be further details in Harkness's book "Official Chess Handbook" 1967, if anyone has a copy.
Answers.UserDisplayName: Noah Snyder
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Answers.Text: It seems plausible to speculate that Harkness wanted the typical range of ratings to be 1500-2500, because a thousand points is a nice round number and this way it's unlikely that people will have negative ratings.
Answers.UserDisplayName: Noah Snyder
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Answers.LastActivityDate: 2021-03-22T16:33:11.373Z
Answers.LastEditDate: 2021-03-22T16:33:11.373Z
Answers.UserDisplayName: Noah Snyder
Answers.Body: <p>I found a reference in a 1993 <a href="http://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1993/1993_07.pdf" rel="nofollow noreferrer">Chess Life</a> article about Arpad Elo to one possible motivation of Harkness. GM Andy Soltis wrote (emphasis mine):</p>
  <blockquote>
  <p>Harkness's system resembled the Ingo, but used four digits and a top rating of about 2600. (Why four digits and not five? Or three? The English and Germans got along well with fewer digits than us. Today a typical British club player gets a rating of about 50 and the best Brits never reach 300. <strong>Harkness felt fewer digits would leave too many players with the same rating.</strong>)</p>
  </blockquote>
  <p>And the article says this about Elo basing his scale on Harkness's:</p>
  <blockquote>
  <p>Elo decided to keep the Harkness structure, which postulated 2000 as the typical rating of &quot;a strong club player.&quot; Later, Elo said it would have made more sense to place that level at 1000 — but that would mean some weak players would approach minus numbers.</p>
  </blockquote>
  
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Answers.CreationDate: 2021-06-26T22:53:30.373Z
Answers.Text: This might be the closest we will get to an answer. So the order of magnitude of the ratings was to guarantee that ratings were unique enough after rounding, and making the average high enough was done so that people didn't get negative ratings. So I guess it's a bit like local end-of-primary-school test scales here, which were between 550 and 650 - "obscure" the scale so people don't get their feelings hurt too much when they are on the low end of the scale.
Answers.UserDisplayName: TMM
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Answers.CreationDate: 2021-06-27T12:56:42.623Z
Answers.Text: I think that was the intent. As it turns out, some very weak players would approach minus numbers anyway, except we don't allow it - FIDE simply won't rate anyone under 1000, and the USCF has an absolute floor of 100.
Answers.UserDisplayName: D M
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Answers.UserDisplayName: D M
Answers.Body: <p>The Glicko and Glicko-2 systems <em>require</em> that new players be given the rating of 1500 as one of the axioms. This is not to mimic existing systems, but simply to ensure the maths works out correctly (since Glicko and Glicko-2 don't just look at absolute rating differences between the players.)</p>
  <p>Although the rating gain/loss for both players in a single game is not zero-sum, over a large playerbase and large number of games the mean rating of the entire playerbase will not vary significantly from 1500 (assuming no shenanigans).</p>
  <p>The Elo rating system does not impose such a requirement.</p>
  <p>Reading material:</p>
  <ul>
  <li><a href="https://lichess.org/page/rating-systems" rel="nofollow noreferrer">https://lichess.org/page/rating-systems</a> (simple explainer)</li>
  <li><a href="http://www.glicko.net/glicko.html" rel="nofollow noreferrer">http://www.glicko.net/glicko.html</a> (Dr Glickman's site explaining his system)</li>
  </ul>
  
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Answers.Text: Now wait. Glickman's paper may specify 1500, but if you look at the context it says "If the player is unrated, set the rating to 1500 and the RD to 350. These are default reasonable choices". Starting at 1500 is no more than that: a default reasonable choice, and *not* a requirement. People can and do use other values; for example chess.com uses Glicko and doesn't start everyone at 1500.
Answers.UserDisplayName: D M
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Answers.Text: The maths works out equally correctly if I scale all the calculations by a factor 10, or translate all ratings afterwards by -1500. There is no magic property of 1500 that makes the system work.
Answers.UserDisplayName: TMM
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Answers.Text: @TMM if you multiply all ratings by 10 the expected scores will change drastically since the rating differences are not the same. 
  However, you can indeed add a constant term to all ratings and nothing would change. There's nothing special about 1500.
Answers.UserDisplayName: koedem
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Answers.Text: I think for this answer to be more valuable, a little more detail on why 1500 is a special number for Glicko would be needed. As it, it hints that there is a reason, but gives no followup.
Answers.UserDisplayName: Grade 'Eh' Bacon
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Answers.Text: ONLY multiplying all the ratings by a scalar causes issues, in ELO and Glicko; however, if one wanted to rescale ELO (by 10x), you can do this by scaling ratings and k-factors by a factor of 10 AND adjusting the constant Q to be the 10th root of its current value.  This would create an identical rating system, 10x.  The only difference being the precision of rounding when ratings are calculated each period.  Analogously, Glicko can be scaled 10x using the exact same adjustments, to r, q, RD (aka K), and the winprob formula.  The scale isn't perfect, but its a reasonable 10x rating system.
Answers.UserDisplayName: DongKy
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Answers.Text: These are all comments completely unrelated to my original question. I know how maths works and I know that in the "worst case" one could just publish rating a*X+b while doing all internal computations with rating X, making the rating system equally valid while scaling/translating all outputs. The question is not about whether scaling/translating is possible; it is about observing that (1) 1500 (or 1200, or 1800, or whatever) is not some magical number (especially not for Elo's system), so (2) why was a number of this order of magnitude chosen as the baseline? Why not 10? Why not 100000?
Answers.UserDisplayName: TMM
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Answers.Text: @TMM I mean, the comments are for exactly that, discussions about the post that aren't necessarily answers to the original question, otherwise one would write an answer, not a comment. As for why that magnitude, why not? Ingo or to this day ECF ratings have different rating ranges. You have to pick some range and so someone made it this range. I don't think there's much more to it.
Answers.UserDisplayName: koedem
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Answers.Text: @koedem One could indeed ask the same question about ECF, and I'm sure there is some motivation to those choices as well. Like how Celsius needed to put some anchors and put them at the freezing and boiling points of water, or how Kelvin uses the same scale as Celsius and normalizes at absolute zero. The "mean" or "initial rating" is a free parameter that does not necessarily affect performance, and it's just a matter of taste. So I'm just wondering why it's not a "rounder" number like 0, 100, 1000, etc.
Answers.UserDisplayName: TMM
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Answers.UserDisplayName: Remellion
Body: <p>Although there is some variation in rating systems (in chess), most systems put the starting value and the mean of all users somewhere around 1500. Some pools are higher, some are lower, but most have their means somewhere in the 1200-1800 range. As ratings only have relative meaning within their respective pools, scaling or translating all ratings within a pool will not make the rating system any less effective for assessing relative strength. So my question is: what is the historical reason that the means are usually in the 1200-1800 range? Which &quot;natural&quot; parameter choices led to these means? And why not e.g. 100, or around 0, with positive and negative ratings?</p>
  <p>For newer rating systems that aim to replace older systems, I suppose the mean is just a consequence of trying to mimic the previous system as well as possible. Say Glicko replacing Elo, or Elo replacing whatever was before that. I've tried some digging, but some historical works are behind paywalls and I am unable to find the historical, initial motivation for parameters choices that led to these averages in the 1200-1800 range.</p>
  <p>Any pointers to relevant (freely available) literature explaining this choice would be appreciated!</p>
  <p><strong>Edit</strong>: As pointed out, not all systems start out at 1500, and averages for e.g. USCF or FIDE ratings may not be exactly 1500. My question is specifically why, historically, someone chose approximately 1500 as the average or starting value (and not any other value), and who was the one that made this deliberate choice (rather than making the average be in the 1000-2000 range to mimic other systems). Maybe the initial choice was just &quot;let's put beginner ratings at 1000&quot; and the 1500ish mean followed from that, that's possible too; I'm just wondering what ultimately led to the 1500ish mean of many rating pools.</p>
  <p>(If anyone has access to Elo's original book, maybe they could look up what motivated Elo to use something like 1500 as the baseline.)</p>
  <p><strong>Edit 2</strong>: While the formulas of the Glicko system may somehow incorporate 1500 as a &quot;special&quot; initial choice, observe that the Elo system is the predecessor and <em>clearly</em> does not need 1500 as the baseline. And surely Elo didn't choose 1500 as baseline only because Glicko would later &quot;need&quot; 1500 as the baseline.</p>
  <p>So perhaps to make it more clear that I am not looking for tangential discussions about whether the 1500 value for Glicko is necessary, let me ask the closely related question to my original question: why did Elo use initial parameter choices that led to ~1500 as baseline? (That answer might be &quot;because the predecessor to Elo used 1500 as baseline&quot; so digging further may be necessary, but all discussions about Glicko's subsequent choices are irrelevant to this question about the historical motivation of Elo and its predecessors.)</p>
  <p><strong>Edit 3</strong>: As pointed out in the comments, sources suggest the Elo system was designed to give similar ratings/rating chances as the Harkness system used previously. So to find the answer to this question one has to answer the question: why did the Harkness system have/lead to 1200-1800ish rating averages?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-16T19:46:00.983Z
Comments.Text: I might be wrong but, I would challenge the assumption that most systems put the starting value at 1500. lichess does this. Chess.com does not. uscf, fide, do not have a starting value.
Comments.UserDisplayName: CognisMantis
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-17T03:47:19.203Z
Comments.Text: Yes, not every system does this, but most notably Elo did this which was later adopted in many places. Also I believe Chess.com uses a lower starting value to compensate for inflation, and stays relatively close to the 1500 mean of other systems. Historically someone must have thought at some point "let's take 1500 as starting value!" and I'm wondering who it was and why they chose 1500.
Comments.UserDisplayName: TMM
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-17T12:20:16.993Z
Comments.Text: Actually, chess.com allows users to start from 800 to 1800 when the user creates their account.
Comments.UserDisplayName: CognisMantis
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-17T20:37:19.990Z
Comments.Text: Re edit 2, Glicko does not need 1500 as baseline. Glicko does not care at all what the baseline is, you could do identical maths if you started at 0 or any other number. I guess Glickman chose 1500 for your above reason, that it seems to be a common starting point.
Comments.UserDisplayName: koedem
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Comments.CreationDate: 2021-02-17T21:06:27.973Z
Comments.Text: @koedem That edit was in response to some other comments here, arguing that 1500 is special. I agree that's not the case, which is why I wrote "need" rather than need. Either way it's an off-topic discussion. (I also removed the glicko-tag because historically Glicko succeeded Elo and so the historical motivation for Elo's choices won't be found in subsequent work by Glickman.)
Comments.UserDisplayName: TMM
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-18T02:36:28.443Z
Comments.Text: https://chess.stackexchange.com/a/2702/12629 indicates that Elo ratings were designed to give similar ratings to the previous Harkness system. (And, of course, many ratings are the way they are to be similar to Elo ratings.) I don't know whether the book referenced in that answer says how Harkness chose the numbers he did.
Comments.UserDisplayName: D M
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-18T20:07:40.253Z
Comments.Text: Yes, I assume that switching from Harkness to Elo only involved changing the formulas for subsequent calculations, without resetting all ratings, so then the question is: why were the rating averages in the Harkness system in the 1200-1800 range?
Comments.UserDisplayName: TMM
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-20T02:25:05.003Z
Comments.Text: Check out http://chessforallages.blogspot.com/2017/10/the-harkness-system-explained.html - I don't see the answer, but it says which Chess Life issues explained the Harkness system, and maybe one of them has the answer, if someone has access to those really old magazines?
Comments.UserDisplayName: D M
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-20T03:35:12.230Z
Comments.Text: btw, the average rating of active chess.com members is around 900 right now, just as an aside. It use to be around 1200, but during 2020, chess.com had a large influx of beginer chess players...
Comments.UserDisplayName: CognisMantis
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-02-21T19:36:20.397Z
Comments.Text: Harkness described his system in detail in a series of articles for chess life in 1952.  You may find those articles here:  http://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1952/1952_All.pdf @DM.  There is no initial default rating, initial ratings of unrated players are calculated after the first tournament is over based on the ratings of the other participants
Comments.UserDisplayName: Michael West
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Comments.CreationDate: 2021-02-21T21:23:41.387Z
Comments.Text: @MichaelWest Thank you very much. Unfortunately, in those articles, I was unable to find any mention of why Harkness chose the scale that he did, or of how he calculated the *first* tournament he rated, where nobody had a prior rating to use.
Comments.UserDisplayName: D M
Tags: <rating><history><elo>
Title: Historical motivation for the 1200-1800ish rating average
ThreadText: # Historical motivation for the 1200-1800ish rating average
  
  (Asked by: username_0 on 2021-02-16)
  
  Although there is some variation in rating systems (in chess), most systems put the starting value and the mean of all users somewhere around 1500. Some pools are higher, some are lower, but most have their means somewhere in the 1200-1800 range. As ratings only have relative meaning within their respective pools, scaling or translating all ratings within a pool will not make the rating system any less effective for assessing relative strength. So my question is: what is the historical reason that the means are usually in the 1200-1800 range? Which "natural" parameter choices led to these means? And why not e.g. 100, or around 0, with positive and negative ratings?
  
  For newer rating systems that aim to replace older systems, I suppose the mean is just a consequence of trying to mimic the previous system as well as possible. Say Glicko replacing Elo, or Elo replacing whatever was before that. I've tried some digging, but some historical works are behind paywalls and I am unable to find the historical, initial motivation for parameters choices that led to these averages in the 1200-1800 range.
  
  Any pointers to relevant (freely available) literature explaining this choice would be appreciated!
  
  **Edit**: As pointed out, not all systems start out at 1500, and averages for e.g. USCF or FIDE ratings may not be exactly 1500. My question is specifically why, historically, someone chose approximately 1500 as the average or starting value (and not any other value), and who was the one that made this deliberate choice (rather than making the average be in the 1000-2000 range to mimic other systems). Maybe the initial choice was just "let's put beginner ratings at 1000" and the 1500ish mean followed from that, that's possible too; I'm just wondering what ultimately led to the 1500ish mean of many rating pools.
  
  (If anyone has access to Elo's original book, maybe they could look up what motivated Elo to use something like 1500 as the baseline.)
  
  **Edit 2**: While the formulas of the Glicko system may somehow incorporate 1500 as a "special" initial choice, observe that the Elo system is the predecessor and *clearly* does not need 1500 as the baseline. And surely Elo didn't choose 1500 as baseline only because Glicko would later "need" 1500 as the baseline.
  
  So perhaps to make it more clear that I am not looking for tangential discussions about whether the 1500 value for Glicko is necessary, let me ask the closely related question to my original question: why did Elo use initial parameter choices that led to ~1500 as baseline? (That answer might be "because the predecessor to Elo used 1500 as baseline" so digging further may be necessary, but all discussions about Glicko's subsequent choices are irrelevant to this question about the historical motivation of Elo and its predecessors.)
  
  **Edit 3**: As pointed out in the comments, sources suggest the Elo system was designed to give similar ratings/rating chances as the Harkness system used previously. So to find the answer to this question one has to answer the question: why did the Harkness system have/lead to 1200-1800ish rating averages?
  
  **Tags:** rating, history, elo
  
  > **Comments:**
  > **username_1**: I might be wrong but, I would challenge the assumption that most systems put the starting value at 1500. lichess does this. Chess.com does not. uscf, fide, do not have a starting value.  
  > **username_0**: Yes, not every system does this, but most notably Elo did this which was later adopted in many places. Also I believe Chess.com uses a lower starting value to compensate for inflation, and stays relatively close to the 1500 mean of other systems. Historically someone must have thought at some point "let's take 1500 as starting value!" and I'm wondering who it was and why they chose 1500.  
  > **username_1**: Actually, chess.com allows users to start from 800 to 1800 when the user creates their account.  
  > **username_2**: Re edit 2, Glicko does not need 1500 as baseline. Glicko does not care at all what the baseline is, you could do identical maths if you started at 0 or any other number. I guess Glickman chose 1500 for your above reason, that it seems to be a common starting point.  
  > **username_0**: @username_2 That edit was in response to some other comments here, arguing that 1500 is special. I agree that's not the case, which is why I wrote "need" rather than need. Either way it's an off-topic discussion. (I also removed the glicko-tag because historically Glicko succeeded Elo and so the historical motivation for Elo's choices won't be found in subsequent work by Glickman.)  
  > **username_3**: https://chess.stackexchange.com/a/2702/12629 indicates that Elo ratings were designed to give similar ratings to the previous Harkness system. (And, of course, many ratings are the way they are to be similar to Elo ratings.) I don't know whether the book referenced in that answer says how Harkness chose the numbers he did.  
  > **username_0**: Yes, I assume that switching from Harkness to Elo only involved changing the formulas for subsequent calculations, without resetting all ratings, so then the question is: why were the rating averages in the Harkness system in the 1200-1800 range?  
  > **username_3**: Check out http://chessforallages.blogspot.com/2017/10/the-harkness-system-explained.html - I don't see the answer, but it says which Chess Life issues explained the Harkness system, and maybe one of them has the answer, if someone has access to those really old magazines?  
  > **username_1**: btw, the average rating of active chess.com members is around 900 right now, just as an aside. It use to be around 1200, but during 2020, chess.com had a large influx of beginer chess players...  
  > **username_4**: Harkness described his system in detail in a series of articles for chess life in 1952.  You may find those articles here:  http://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1952/1952_All.pdf @DM.  There is no initial default rating, initial ratings of unrated players are calculated after the first tournament is over based on the ratings of the other participants  
  > **username_3**: @username_4 Thank you very much. Unfortunately, in those articles, I was unable to find any mention of why Harkness chose the scale that he did, or of how he calculated the *first* tournament he rated, where nobody had a prior rating to use.  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_5 on 2021-03-22. Score: 6
  
  The first chess rating system, the Ingo system used in Germany, had very different numbers because in that system *lower is better*. So the ratings there have no relevance to the current scale used by modern rating systems.
  
  The second chess rating system, the Harkness system used by USCF starting in 1950, already is calibrated almost the same as modern rating systems. In the [original USCF announcement of the rating system](http://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1950/1950_11_2.pdf) it clearly says Class D below 1500, Class C between 1500-1700, Class B 1700-1900, Class A 1900-2100, Expert 2100-2300 and Master 2300-2500. This is the same as current ratings but shifted by 100 points. Acording to [Wikipedia](https://en.wikipedia.org/wiki/Chess_title#Master), the Harkness system caused ratings to deflate which forced them to both move the rating cutoffs down by 100 points and to switch to Elo. So Elo was originally calibrated to match the ratings of Harkness but adjusted down by 100. Unfortunately I can't find any sources about how Harkness chose his calibration. So unless someone has access to Harkness's private letters or similar sources, it is unlikely that we'll get a definitive answer.
  
  > **Comments:**
  > **username_5**: There may be further details in Harkness's book "Official Chess Handbook" 1967, if anyone has a copy.  
  > **username_5**: It seems plausible to speculate that Harkness wanted the typical range of ratings to be 1500-2500, because a thousand points is a nice round number and this way it's unlikely that people will have negative ratings.  
  
  ---
  
  ### Answer by username_3 on 2021-06-24. Score: 2
  
  I found a reference in a 1993 [Chess Life](http://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1993/1993_07.pdf) article about Arpad Elo to one possible motivation of Harkness. GM Andy Soltis wrote (emphasis mine):
  
  > Harkness's system resembled the Ingo, but used four digits and a top rating of about 2600. (Why four digits and not five? Or three? The English and Germans got along well with fewer digits than us. Today a typical British club player gets a rating of about 50 and the best Brits never reach 300. **Harkness felt fewer digits would leave too many players with the same rating.**)
  
  And the article says this about Elo basing his scale on Harkness's:
  
  > Elo decided to keep the Harkness structure, which postulated 2000 as the typical rating of "a strong club player." Later, Elo said it would have made more sense to place that level at 1000 — but that would mean some weak players would approach minus numbers.
  
  > **Comments:**
  > **username_0**: This might be the closest we will get to an answer. So the order of magnitude of the ratings was to guarantee that ratings were unique enough after rounding, and making the average high enough was done so that people didn't get negative ratings. So I guess it's a bit like local end-of-primary-school test scales here, which were between 550 and 650 - "obscure" the scale so people don't get their feelings hurt too much when they are on the low end of the scale.  
  > **username_3**: I think that was the intent. As it turns out, some very weak players would approach minus numbers anyway, except we don't allow it - FIDE simply won't rate anyone under 1000, and the USCF has an absolute floor of 100.  
  
  ---
  
  ### Answer by username_6 on 2021-02-17. Score: 1
  
  The Glicko and Glicko-2 systems *require* that new players be given the rating of 1500 as one of the axioms. This is not to mimic existing systems, but simply to ensure the maths works out correctly (since Glicko and Glicko-2 don't just look at absolute rating differences between the players.)
  
  Although the rating gain/loss for both players in a single game is not zero-sum, over a large playerbase and large number of games the mean rating of the entire playerbase will not vary significantly from 1500 (assuming no shenanigans).
  
  The Elo rating system does not impose such a requirement.
  
  Reading material:
  
  * <https://lichess.org/page/rating-systems> (simple explainer)
  * <http://www.glicko.net/glicko.html> (Dr Glickman's site explaining his system)
  
  > **Comments:**
  > **username_3**: Now wait. Glickman's paper may specify 1500, but if you look at the context it says "If the player is unrated, set the rating to 1500 and the RD to 350. These are default reasonable choices". Starting at 1500 is no more than that: a default reasonable choice, and *not* a requirement. People can and do use other values; for example chess.com uses Glicko and doesn't start everyone at 1500.  
  > **username_0**: The maths works out equally correctly if I scale all the calculations by a factor 10, or translate all ratings afterwards by -1500. There is no magic property of 1500 that makes the system work.  
  > **username_2**: @username_0 if you multiply all ratings by 10 the expected scores will change drastically since the rating differences are not the same.  However, you can indeed add a constant term to all ratings and nothing would change. There's nothing special about 1500.  
  > **username_7**: I think for this answer to be more valuable, a little more detail on why 1500 is a special number for Glicko would be needed. As it, it hints that there is a reason, but gives no followup.  
  > **username_8**: ONLY multiplying all the ratings by a scalar causes issues, in ELO and Glicko; however, if one wanted to rescale ELO (by 10x), you can do this by scaling ratings and k-factors by a factor of 10 AND adjusting the constant Q to be the 10th root of its current value.  This would create an identical rating system, 10x.  The only difference being the precision of rounding when ratings are calculated each period.  Analogously, Glicko can be scaled 10x using the exact same adjustments, to r, q, RD (aka K), and the winprob formula.  The scale isn't perfect, but its a reasonable 10x rating system.  
  > **username_0**: These are all comments completely unrelated to my original question. I know how maths works and I know that in the "worst case" one could just publish rating a*X+b while doing all internal computations with rating X, making the rating system equally valid while scaling/translating all outputs. The question is not about whether scaling/translating is possible; it is about observing that (1) 1500 (or 1200, or 1800, or whatever) is not some magical number (especially not for Elo's system), so (2) why was a number of this order of magnitude chosen as the baseline? Why not 10? Why not 100000?  
  > **username_2**: @username_0 I mean, the comments are for exactly that, discussions about the post that aren't necessarily answers to the original question, otherwise one would write an answer, not a comment. As for why that magnitude, why not? Ingo or to this day ECF ratings have different rating ranges. You have to pick some range and so someone made it this range. I don't think there's much more to it.  
  > **username_0**: @username_2 One could indeed ask the same question about ECF, and I'm sure there is some motivation to those choices as well. Like how Celsius needed to put some anchors and put them at the freezing and boiling points of water, or how Kelvin uses the same scale as Celsius and normalizes at absolute zero. The "mean" or "initial rating" is a free parameter that does not necessarily affect performance, and it's just a matter of taste. So I'm just wondering why it's not a "rounder" number like 0, 100, 1000, etc.  
  
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