APL Calculations [Archive] - Wizards Community

APL Calculations [Archive] - Wizards Community

Post/Author/DateTime Post
chrispedersen
02-02-06, 10:53 AM Some modules have round to the nearest apl.
Others say round UP.

Aka.. 11.4 rounds to either 11 or 12. I think the current LGCS defers to the module. Could this be standardized in the LGCS, and have the lgcs and not the module be authoritative?

Chris
jboerj
02-02-06, 11:28 AM Seconded. Especially since it seemed like at one point mods had different versions of the boiler plate running around?
dr_who
02-02-06, 01:45 PM Additionally, the reference to "standard rounding rules" specifically says that any x.5 rounds up. While this is technically correct for measured numbers (for which the precision is known to some degree), character levels are pure whole numbers and therefore x.5000 is EXACTLY halfway between x and x+1. This can and will arise often because of the way legal parties are put together.

For example, consider a six-member party made up of the following character levels: 3,4,5,5,5,5. This makes an APL 5.5 party after adding one for the 6 person table. If they are playing a regional or meta-regional module and have plenty of smart people, then they are probably OK rounding up to 6. However, if they have no straight casters, they are playing a Core scenario whose blurb mentions something about constructs and elementals, and the third level character really doesn't want to take an xp hit, why shouldn't they be allowed to play APL 4 (round 5.5 down to 5 and then bump down to APL4)?

By "standard rounding rules" the LGCS refers to rounding numbers whose precision is less than .001. However, since character levels are always whole numbers, I think parties should be allowed to choose which way their APL rounds if they wind up with x.5.
Shaudius
02-02-06, 02:27 PM Rounding rules can be tricky, and I think beyond the scope of most LG player knowledge. A number such as 5.54 rounds up to 6, whereas a number such as 5.47 rounds down to 5(no double rounding). This becomes especially tricky at numbers such as 5.50 and 6.50, one would think that 5.50 would round up to 6, and 6.50 would round up to 7, but this is not the case. In order to prevent rounding bias one always rounds to the nearest EVEN number, thus 5.50 becomes 6 and 6.50 also becomes 6. This is only the case if the remainder is exactly 5, if the remainder is something like 5.53 then it rounds up. So if a party of 6 averages to 7.50 they round up to 8, and not down to 7. So they don't have the option of playing 6 or 8 they must play 8.

I do agree however that the rounding rules need to be specified in the LGCS instead of in indiviudal modules, as this point causes much confusion.
redgamer
02-02-06, 02:35 PM No you round normally. LG doesn't create its own math for rounding. If your rounded APL is an odd number you can play either the APL 1 above or 1 below. If you rounded APL is even your have to play that APL.
Britt
02-02-06, 02:44 PM In order to prevent rounding bias one always rounds to the nearest EVEN number
Based on my math experience, that is only one method for avoiding rounding bias. You could just as easily say that you always round to the nearest odd number. I believe that a rule stating that >=.50 rounds up and <.50 rounds down avoids bias as well, but I could be wrong there. In any case, the bias introduced is so small as to be inconsequential to gamers. Most people are taught to round up at .50, so why increase complexity by introducing unneeded mathematics?
Shaudius
02-02-06, 03:01 PM Thats ultimately just the thing. There is really no such thing as "standard rounding rules". The standard rounding rules that one is taught in grade school(and the most familar to people) is not the standard that is applied in academic settings, chemistry classrooms, physics classrooms, engineering classrooms.

The most common standard in those setting is the rounding to nearest EVEN interger. So it could be implied that the LGCS means the always rounding up convention, but this is certainly not the standard rounding rule.
chrispedersen
02-02-06, 03:12 PM some modules say round up

aka 1.1 --> 2

and some modules say round to nearest
1.1 --> 1.

And it isn't theoretical -- I compared like a dozen modules from the same year and found 3 different wordings on the boilerplate.

C
Britt
02-02-06, 03:16 PM Yes, I agree, there is discrepancy between the boilerplates. I'm not sure when it happened, but at some point the old front matter snuck into some templates and stayed. I got a new boilerplate from the Circle a while back. I'll double-check that what it says is what they want.
redgamer
02-02-06, 03:18 PM Certaintly the boilerplate need to be standardize. I just asked someone from each of the four settings Shaudius mentioned and none of them have ever heard of rounding to the nearest even integer.
Britt
02-02-06, 03:20 PM Certaintly the boilerplate need to be standardize. I just asked someone from each of the four settings Shaudius mentioned and none of them have ever heard of rounding to the nearest even integer.
I've heard of it before. Some friends of mine in academia have had this very discussion before. Rounding is really fairly arbitrary. As long as you use a consistent rule, it really doesn't matter that much.
dr_who
02-02-06, 03:31 PM I've heard of it before. Some friends of mine in academia have had this very discussion before. Rounding is really fairly arbitrary. As long as you use a consistent rule, it really doesn't matter that much.

As one of those people "in academia" (finishing physics PhD thesis at this very moment) I cannot argue with almost all of the posts above. My point has been missed, however. Currently, the LGCS says that .5 rounds up. There is no ambiguity in that, and I don't think it needs clarification. My suggestion is that we change it so that a .5000.... is left up to the table to choose. The example that I gave is a very real and, in my experience, relatively common situation. Under the current rules you can make an APL 6 table with no character lvl 6 or higher. Unfortunately, this means certain doom in those scenarios which cater to the most powerful characters in the campaign. The only place it could become an issue is at a gameday or con where you cannot control your party make-up but are forced to play up because of the current rounding system presented in the LGCS.
Britt
02-02-06, 03:36 PM If the justification is that someone joining your table might force you to the next APL because you landed on x.5, all this does is change it to x.5001. Previously, as long as said person did not push you over x.4999, you played down. Moving it doesn't really change anything other than the likelihood. You might be right, though, that it is far more likely to get x.5 than to get x.5001 or something like that. I really don't know the calculations, but guessing I would say that x.5 is far more common.

As for whether or not that's fair, I have no idea :)
dr_who
02-02-06, 03:39 PM Good point about the percentages. I haven't done any calculations on how often this will make a difference; I'm only speaking from experience (it has happened thrice in the recent past and we regretted having to play up).
MerricB
02-02-06, 04:18 PM You are never going to get a situation where the fraction is 0.5001. Never, ever, at a LG table. It's purely simple maths where the divisor is either 4, 5 or 6.

The fractional components can be:
At 4 players: 0.00; 0.25; 0.50; 0.75
At 5 players: 0.00; 0.20; 0.40; 0.60; 0.80
At 6 players: 0.00; 0.17; 0.33; 0.50; 0.66; 0.83

Cheers!
Britt
02-02-06, 04:23 PM Good point. :)
Timlagor
02-03-06, 03:41 AM My preference for X.5 is to give the players the choice.

In fact, I'd like to see the rounding rule removed completely -just let players choose the APL freely using the calculations as only a guideline.
qstor
02-03-06, 09:30 AM My preference for X.5 is to give the players the choice.

In fact, I'd like to see the rounding rule removed completely -just let players choose the APL freely using the calculations as only a guideline.

No, then people would be playing down all the time to the lowest APL where the PCs would get full xp and gold.

There's the option to play up and only suicidal players choose that option :)

Mike M.
JohnduBois
02-03-06, 09:36 AM At higher APL's, though, the rewards for being "suicidal" are certainly present, as the gp/xp ratio is higher.

Plus, everyone in Furyondy knows that playing up is ALWAYS safe with a Radiant Servant on your side... :rolleyes:

Post/Author/DateTime	Post
chrispedersen 02-02-06, 10:53 AM	Some modules have round to the nearest apl. Others say round UP. Aka.. 11.4 rounds to either 11 or 12. I think the current LGCS defers to the module. Could this be standardized in the LGCS, and have the lgcs and not the module be authoritative? Chris
jboerj 02-02-06, 11:28 AM	Seconded. Especially since it seemed like at one point mods had different versions of the boiler plate running around?
dr_who 02-02-06, 01:45 PM	Additionally, the reference to "standard rounding rules" specifically says that any x.5 rounds up. While this is technically correct for measured numbers (for which the precision is known to some degree), character levels are pure whole numbers and therefore x.5000 is EXACTLY halfway between x and x+1. This can and will arise often because of the way legal parties are put together. For example, consider a six-member party made up of the following character levels: 3,4,5,5,5,5. This makes an APL 5.5 party after adding one for the 6 person table. If they are playing a regional or meta-regional module and have plenty of smart people, then they are probably OK rounding up to 6. However, if they have no straight casters, they are playing a Core scenario whose blurb mentions something about constructs and elementals, and the third level character really doesn't want to take an xp hit, why shouldn't they be allowed to play APL 4 (round 5.5 down to 5 and then bump down to APL4)? By "standard rounding rules" the LGCS refers to rounding numbers whose precision is less than .001. However, since character levels are always whole numbers, I think parties should be allowed to choose which way their APL rounds if they wind up with x.5.
Shaudius 02-02-06, 02:27 PM	Rounding rules can be tricky, and I think beyond the scope of most LG player knowledge. A number such as 5.54 rounds up to 6, whereas a number such as 5.47 rounds down to 5(no double rounding). This becomes especially tricky at numbers such as 5.50 and 6.50, one would think that 5.50 would round up to 6, and 6.50 would round up to 7, but this is not the case. In order to prevent rounding bias one always rounds to the nearest EVEN number, thus 5.50 becomes 6 and 6.50 also becomes 6. This is only the case if the remainder is exactly 5, if the remainder is something like 5.53 then it rounds up. So if a party of 6 averages to 7.50 they round up to 8, and not down to 7. So they don't have the option of playing 6 or 8 they must play 8. I do agree however that the rounding rules need to be specified in the LGCS instead of in indiviudal modules, as this point causes much confusion.
redgamer 02-02-06, 02:35 PM	No you round normally. LG doesn't create its own math for rounding. If your rounded APL is an odd number you can play either the APL 1 above or 1 below. If you rounded APL is even your have to play that APL.
Britt 02-02-06, 02:44 PM	In order to prevent rounding bias one always rounds to the nearest EVEN number Based on my math experience, that is only one method for avoiding rounding bias. You could just as easily say that you always round to the nearest odd number. I believe that a rule stating that >=.50 rounds up and <.50 rounds down avoids bias as well, but I could be wrong there. In any case, the bias introduced is so small as to be inconsequential to gamers. Most people are taught to round up at .50, so why increase complexity by introducing unneeded mathematics?
Shaudius 02-02-06, 03:01 PM	Thats ultimately just the thing. There is really no such thing as "standard rounding rules". The standard rounding rules that one is taught in grade school(and the most familar to people) is not the standard that is applied in academic settings, chemistry classrooms, physics classrooms, engineering classrooms. The most common standard in those setting is the rounding to nearest EVEN interger. So it could be implied that the LGCS means the always rounding up convention, but this is certainly not the standard rounding rule.
chrispedersen 02-02-06, 03:12 PM	some modules say round up aka 1.1 --> 2 and some modules say round to nearest 1.1 --> 1. And it isn't theoretical -- I compared like a dozen modules from the same year and found 3 different wordings on the boilerplate. C
Britt 02-02-06, 03:16 PM	Yes, I agree, there is discrepancy between the boilerplates. I'm not sure when it happened, but at some point the old front matter snuck into some templates and stayed. I got a new boilerplate from the Circle a while back. I'll double-check that what it says is what they want.
redgamer 02-02-06, 03:18 PM	Certaintly the boilerplate need to be standardize. I just asked someone from each of the four settings Shaudius mentioned and none of them have ever heard of rounding to the nearest even integer.
Britt 02-02-06, 03:20 PM	Certaintly the boilerplate need to be standardize. I just asked someone from each of the four settings Shaudius mentioned and none of them have ever heard of rounding to the nearest even integer. I've heard of it before. Some friends of mine in academia have had this very discussion before. Rounding is really fairly arbitrary. As long as you use a consistent rule, it really doesn't matter that much.
dr_who 02-02-06, 03:31 PM	I've heard of it before. Some friends of mine in academia have had this very discussion before. Rounding is really fairly arbitrary. As long as you use a consistent rule, it really doesn't matter that much. As one of those people "in academia" (finishing physics PhD thesis at this very moment) I cannot argue with almost all of the posts above. My point has been missed, however. Currently, the LGCS says that .5 rounds up. There is no ambiguity in that, and I don't think it needs clarification. My suggestion is that we change it so that a .5000.... is left up to the table to choose. The example that I gave is a very real and, in my experience, relatively common situation. Under the current rules you can make an APL 6 table with no character lvl 6 or higher. Unfortunately, this means certain doom in those scenarios which cater to the most powerful characters in the campaign. The only place it could become an issue is at a gameday or con where you cannot control your party make-up but are forced to play up because of the current rounding system presented in the LGCS.
Britt 02-02-06, 03:36 PM	If the justification is that someone joining your table might force you to the next APL because you landed on x.5, all this does is change it to x.5001. Previously, as long as said person did not push you over x.4999, you played down. Moving it doesn't really change anything other than the likelihood. You might be right, though, that it is far more likely to get x.5 than to get x.5001 or something like that. I really don't know the calculations, but guessing I would say that x.5 is far more common. As for whether or not that's fair, I have no idea :)
dr_who 02-02-06, 03:39 PM	Good point about the percentages. I haven't done any calculations on how often this will make a difference; I'm only speaking from experience (it has happened thrice in the recent past and we regretted having to play up).
MerricB 02-02-06, 04:18 PM	You are never going to get a situation where the fraction is 0.5001. Never, ever, at a LG table. It's purely simple maths where the divisor is either 4, 5 or 6. The fractional components can be: At 4 players: 0.00; 0.25; 0.50; 0.75 At 5 players: 0.00; 0.20; 0.40; 0.60; 0.80 At 6 players: 0.00; 0.17; 0.33; 0.50; 0.66; 0.83 Cheers!
Britt 02-02-06, 04:23 PM	Good point. :)
Timlagor 02-03-06, 03:41 AM	My preference for X.5 is to give the players the choice. In fact, I'd like to see the rounding rule removed completely -just let players choose the APL freely using the calculations as only a guideline.
qstor 02-03-06, 09:30 AM	My preference for X.5 is to give the players the choice. In fact, I'd like to see the rounding rule removed completely -just let players choose the APL freely using the calculations as only a guideline. No, then people would be playing down all the time to the lowest APL where the PCs would get full xp and gold. There's the option to play up and only suicidal players choose that option :) Mike M.
JohnduBois 02-03-06, 09:36 AM	At higher APL's, though, the rewards for being "suicidal" are certainly present, as the gp/xp ratio is higher. Plus, everyone in Furyondy knows that playing up is ALWAYS safe with a Radiant Servant on your side... :rolleyes: