The recently introduced Marshal badge is awarded for achieving a flag weight of 749. According to this investigation by marcog (meanwhile confirmed by Wladimir Palant), it takes a mere 10 correct flags to get from 749 to 750, so why isn't the badge awarded for reaching the maximal flag weight of 750?

To make this clear: The original intention was to make 750 an asymptotic limit that can't be reached (except due to rounding errors maybe). If that was the case, then the 749 would make a lot of sense. However, the actual implementation is such that the increase in flag weight is always at least 0.1 for each correct flag on questions and answers. Thus, it turns out that the limit 750 can easily be reached, even without any rounding issues.

Just to point this out before people start telling me: I don't even know what my own flag weight is at the moment.

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    You're nowhere close to getting this badge, so no worries about bias. ;-) – Cody Gray Aug 22 '11 at 13:24
  • Your flag weight on Stack Overflow is 100; its value is not shown, as that is the default value. – kiamlaluno Aug 22 '11 at 14:12
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    @kiamlaluno: Well, I definitely know my flag weight on SO - my activity there is close to 0, so the flag weight had to be 100 :-) But thanks nevertheless. – Hendrik Vogt Aug 22 '11 at 14:16
  • Re-tag this "feature request"? – agf Aug 29 '11 at 16:17

OK, I found some (not quite satisfactory) explanation myself: the Marshal badge was introduced after a bounty was offered for the feature-request New badges for the increased flag-weight. There it was suggested that the badge should be awarded for achieving a flag weight of 749, and this was implemented on 21 August, shortly before the bounty period ended. The suggestion itself is from 11 March and was apparently based on the assumption that 750 is an asymptotic limit that can't be reached, so it made a lot of sense. It became clear only later on that 750 can be reached with 576 correct flags in a row.

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It seems that it was going to be impossible to reach 750, (check out the comment thread on this answer) but someone messed up his rounding...

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    I know that the aim was to make 750 an asymptotic limit. But the thing is that it isn't asymptotic, and the reason for this is not related to rounding. I'll update my question ... – Hendrik Vogt Aug 23 '11 at 9:10
  • @Hendrik If you look at the comments of the second link I posted, you will see that Mark (jokingly?) blames rounding. – John Aug 23 '11 at 15:54
  • @Hendrik the intention was to make 750 impossible. But for whatever reason (will non SE devs ever know?) It was not implemented that way. – John Aug 23 '11 at 15:56
  • Well, because of your answer (and also because of the downvotes to the question) I added another comment to that second link, and I tried to address this rounding business in my question here. I don't know what Marc meant - maybe he was joking, yes. – Hendrik Vogt Aug 23 '11 at 15:57
  • Please see my edit, where I also speculate about the intentions. My only guess about the reason is some math blunder, but I can't possibly tell. – Hendrik Vogt Aug 23 '11 at 15:59
  • @Hendrik I don't understand how my answer doesn't answer your question. I basically said what you later added in your edit. Rounding or not, I think it's pretty clear that it was a math error and that 750 was supposed to be impossible to reach. – John Aug 23 '11 at 16:26
  • Well, what you write in your answer is correct. But it's been official for quite some time that 750 can be reached, and the badge was introduced only 2 days ago. My problem is that the badge fits the originally intended, but not the implemented behaviour of flag weight. I think it should reflect the actual implementation. Otherwise people might still be led to believe that 750 is an asymptotic limit ... – Hendrik Vogt Aug 23 '11 at 16:35
  • @Hendrik Ah I see. In that case, no one except the devs are qualified to answer that. Maybe they intended to correct the math error eventually? – John Aug 23 '11 at 16:38
  • I actually hoped for an answer by the devs. I've already bombarded Marc with comments on this point, but he hasn't reacted so far. See also my 2nd comment to kiamlaluno's answer. – Hendrik Vogt Aug 23 '11 at 16:39
  • @Hendrik In that case, I personally don't think there is a reason, other than [name] said so/wanted it. – John Aug 23 '11 at 16:50

I think the reason is that 750 is, theoretically, the asymptotic limit for the flag weight. If it were not for computer rounding, it should not be a value that is possible to reach.

Now, it could be they are planning to change the code to calculate the flag weight, and they could use code that makes more difficult to reach a flag weight of 750. In this case, I imagine it makes sense not to set a badge for who reaches a flag weight of 750, when that value would (in a possibly close future) be a value impossible (or difficult) to reach. I agree it would be easier to change the badge to be gained from who has a flag weight of 749, instead of 750, but the question would then be: Why don't you set the badge for being gained from who has a flag weight of 749 since the beginning?

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    No, this is not true: please read the links I provided in my question; the formula derived by marcog shows that 750 is reached without any rounding. – Hendrik Vogt Aug 22 '11 at 14:22
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    That doesn't mean they could change the formula to make 750 really an asymptotic value. Also, what reported in that answer is the deducted formula, which could be the formula really applied; even applying that formula, every time you apply it there are values that are rounded, because a computer doesn't keep all the digits after the decimal point. – kiamlaluno Aug 22 '11 at 14:25
  • If they did, then 749 would make a lot of sense. But I don't see it coming; Marc Gravall said they've diddled with that enough. – Hendrik Vogt Aug 22 '11 at 14:27
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    That would also mean "we passed time aimlessly or unproductively, talking about 750 being the asymptotic limit." – kiamlaluno Aug 22 '11 at 14:33
  • I've learned quite some time ago that this asymptotic limit business was wrong. But I have to say that I liked the idea quite a lot! – Hendrik Vogt Aug 22 '11 at 14:47
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    Re "every time you apply it there are values that are rounded": This is true of course, but according to Wladimir's answer it takes only 536 correct flags to get from 500 to 750. Moreover, flag weight is apparently computed with at least 8 digits precision, so rounding won't be relevant here. – Hendrik Vogt Aug 22 '11 at 14:59
  • In fact, the growth is exponential with a below-one base. With a shape similar to the square root function the growth does slow down but it doesn't have any linear asymptotes. It is actually possible to reach any value eventually. So rounding has really nothing to do with it. – Wladimir Palant Aug 24 '11 at 11:30
  • The problem is that you don't see the code they are using, but the results. Do you have any proof that they will never change the code to really give values that tend to 750 without to reach that value? Maybe they are looking at changing that code to really make 750 an asymptotic value, but they don't want to use a computationally expensive code; it could be that task has a low priority. Also, rounding is what makes the difference between 749.9999 and 750.0001. – kiamlaluno Aug 24 '11 at 12:38
  • @Wladimir: Thanks for chiming in here. The shape is actually not so similar to the square root function but to a logarithm. But that doesn't change what you say about the absence of linear (or, rather, horizontal) asymptotes. – Hendrik Vogt Aug 24 '11 at 16:59
  • @kiamlaluno: If the code is changed all the flag weights need to be recalculated anyway. And it makes sense to update the criteria for the badge then. But right now there is no reason it should be 749 rather than 750. – Wladimir Palant Aug 24 '11 at 19:00
  • @Hendrik: I was thinking about the wrong function indeed, what we have there isn't an exponential function at all. But the analysis is still correct, it doesn't have any linear asymptotes - neither horizontal nor otherwise. And any flag weight would be reachable eventually if the devs hadn't capped it at 750. – Wladimir Palant Aug 24 '11 at 19:06
  • @Wladimir Palant I don't see why making such changes when 749 would always be reachable, even if 750 is not a real asymptote. – kiamlaluno Aug 24 '11 at 19:16
  • @kiamlaluno: Why not make them? There is nothing special about 749, flag weight 750 on the other hand is the maximal value that you can reach. Having the badge awarded there makes sense. – Wladimir Palant Aug 24 '11 at 19:26
  • Something that makes sense isn't necessarily something that is implemented; if you look at other badges, there are many values that should have been used in defining them. Does giving the "Good Answer" badge for answers with a score of at least 25 have a special meaning, or is 25 a special value in some way? – kiamlaluno Aug 24 '11 at 19:44

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