Lotusfly Stewnicely

01-21-2003, 01:31 AM

Dear all,

For a little amusement of myself and a few friends, I recently polled my guild's active membership, for their AA scores. We thought it would be interesting to see how each class compared to one another in terms of AA scores. Who gets the AA points? Which classes don't exp? Which classes exp the most?

I know that there are one or two fellow number crunchers out there for whom this might be interesting, and perhaps just for those that are interested in seeing how various classes' AA scores compare to one another, and so I thought that posting it here might prove amusing for some.

I'll direct you to the results, first of all, then I'll quickly describe how to interpret them - not everyone likes statistics! They are pretty self-explanatory in conjunction with the graphs. After that, for the number crunchers, I'll detail the survey's details.

The HTML version lives here (http://www.keepersofthefaith.org/lotusfly/misc/KTF%20AA%20Distribution%2018%20Jan%202003.htm).

<strong>The contents of the web-page</strong>

The web-page contains a lot of numbers. The interesting illustration appears right at the end, so you may wish to skip right to the bottom.

1. Criteria (ignore unless you're an Excel user)

2. The database (ditto)

3. The results by class (interesting numbers)

4. The data used for the graphs (ignore unless you're an Excel user)

5. The graphs!

<strong>Quick Guide to Interpreting the Graphs</strong>

Skip this if you're familiar with distributions. From my guild article:

'For those not used to examining statistics, the curves which you see describe the spread of players in each class across AA points.

'"Tight", peaked curves indicate that the members of that class all have a similar number of AA points. We can look at the curve for clerics and see that they are all tightly clustered about a particular point, indicating that most clerics have similar AA scores. Some have a little higher, some have a little lower, but nothing wildly different. Statistics has been around a long time and so we have a word for everything: this "spikiness" of the curve is called a leptokurtic distribution, fact fans!

'"Flat", spread-out curves indicate that the members of that class have wildly different AA values. We can look at the bard curve and see that it is incredibly flat. This shows us that some bards have very low AA scores, some bards have very high AA scores, and a few have values in between. This is a platykurtic distribution, for the zero people out there that care!

'It's interesting to see how the classes relate to one another. We can see that druids are pretty spread out in their AA but, generally speaking, they tend to have a higher number than some other classes: this means that the druid curve is flat and spread out, but it is shifted to the right of the graph (it has a higher mean, the average).

'In summary: this is just a bit of fun. It's certainly nothing to take too seriously. I've managed to include nearly all of the active members of KTF, but even so, it's still a pretty small number number when analysed by class: we have one necromancer, one beastlord, compared to (say) ten monks in the study.'

You can see the "flatness" / "spikiness" (<em>kurtosis</em>) of the graphs reflected in the standard deviation field of the Results table. Broad, spread, flat graphs have a high standard deviation (bards have 134 AA points deviation), whilst spiky, thin graphs have a low standard deviation (clerics have 35 AA points deviation).

<strong>Statistical Notes</strong>

The survey was conducted on KTF guild-members over a period of one day. The period of survey was brief enough that one can assume that all classes' AA scores are stationary with respect to one another.

The Gaussian distribution is shown, <em>a posteriori</em>, to be a valid representation of the underlying, actual distribution from plotting the raw data points across all classes. Inspection shows that the distribution is approximately Normal.

Using Gaussian distributions to model each of the sub-classes follows a similar assumption: classes are arbitrary divisions, those distributions of higher-sample classes are close to Normal, therefore the argument for the summation of a series of Gaussians is tenable.

Sample size overall is large enough (in the 'ALL' case) for confidence in the distribution. Some classes have low sampled populations: KTF has one active necromancer, and one active beastlord. These, of course, have standard deviation of 0, variance 0. The graph for these two quantities should be a vertical spike reaching P(x) = 1.0, but I've added a standard deviation of 30 for those two classes to allow them to be plotted on the same meaningful scale that the other graphs share, whilst still retaining the notion that they are highly leptokurtic. If you're using the Results table, bear that in mind and set the standard deviation for NEC and BST to 0.

The graphed quantity for ALL is the "Active" line in the Results table, shown below the orange total. The "Total" contains both active and inactive guildmembers; inactivity being defined in the database as Special = -1, activity as Special = 0.

Draw your own conclusions! That's the fun part. ^__))

Toodlepip,

Rebecca

The Lucky Cabbage

For a little amusement of myself and a few friends, I recently polled my guild's active membership, for their AA scores. We thought it would be interesting to see how each class compared to one another in terms of AA scores. Who gets the AA points? Which classes don't exp? Which classes exp the most?

I know that there are one or two fellow number crunchers out there for whom this might be interesting, and perhaps just for those that are interested in seeing how various classes' AA scores compare to one another, and so I thought that posting it here might prove amusing for some.

I'll direct you to the results, first of all, then I'll quickly describe how to interpret them - not everyone likes statistics! They are pretty self-explanatory in conjunction with the graphs. After that, for the number crunchers, I'll detail the survey's details.

The HTML version lives here (http://www.keepersofthefaith.org/lotusfly/misc/KTF%20AA%20Distribution%2018%20Jan%202003.htm).

<strong>The contents of the web-page</strong>

The web-page contains a lot of numbers. The interesting illustration appears right at the end, so you may wish to skip right to the bottom.

1. Criteria (ignore unless you're an Excel user)

2. The database (ditto)

3. The results by class (interesting numbers)

4. The data used for the graphs (ignore unless you're an Excel user)

5. The graphs!

<strong>Quick Guide to Interpreting the Graphs</strong>

Skip this if you're familiar with distributions. From my guild article:

'For those not used to examining statistics, the curves which you see describe the spread of players in each class across AA points.

'"Tight", peaked curves indicate that the members of that class all have a similar number of AA points. We can look at the curve for clerics and see that they are all tightly clustered about a particular point, indicating that most clerics have similar AA scores. Some have a little higher, some have a little lower, but nothing wildly different. Statistics has been around a long time and so we have a word for everything: this "spikiness" of the curve is called a leptokurtic distribution, fact fans!

'"Flat", spread-out curves indicate that the members of that class have wildly different AA values. We can look at the bard curve and see that it is incredibly flat. This shows us that some bards have very low AA scores, some bards have very high AA scores, and a few have values in between. This is a platykurtic distribution, for the zero people out there that care!

'It's interesting to see how the classes relate to one another. We can see that druids are pretty spread out in their AA but, generally speaking, they tend to have a higher number than some other classes: this means that the druid curve is flat and spread out, but it is shifted to the right of the graph (it has a higher mean, the average).

'In summary: this is just a bit of fun. It's certainly nothing to take too seriously. I've managed to include nearly all of the active members of KTF, but even so, it's still a pretty small number number when analysed by class: we have one necromancer, one beastlord, compared to (say) ten monks in the study.'

You can see the "flatness" / "spikiness" (<em>kurtosis</em>) of the graphs reflected in the standard deviation field of the Results table. Broad, spread, flat graphs have a high standard deviation (bards have 134 AA points deviation), whilst spiky, thin graphs have a low standard deviation (clerics have 35 AA points deviation).

<strong>Statistical Notes</strong>

The survey was conducted on KTF guild-members over a period of one day. The period of survey was brief enough that one can assume that all classes' AA scores are stationary with respect to one another.

The Gaussian distribution is shown, <em>a posteriori</em>, to be a valid representation of the underlying, actual distribution from plotting the raw data points across all classes. Inspection shows that the distribution is approximately Normal.

Using Gaussian distributions to model each of the sub-classes follows a similar assumption: classes are arbitrary divisions, those distributions of higher-sample classes are close to Normal, therefore the argument for the summation of a series of Gaussians is tenable.

Sample size overall is large enough (in the 'ALL' case) for confidence in the distribution. Some classes have low sampled populations: KTF has one active necromancer, and one active beastlord. These, of course, have standard deviation of 0, variance 0. The graph for these two quantities should be a vertical spike reaching P(x) = 1.0, but I've added a standard deviation of 30 for those two classes to allow them to be plotted on the same meaningful scale that the other graphs share, whilst still retaining the notion that they are highly leptokurtic. If you're using the Results table, bear that in mind and set the standard deviation for NEC and BST to 0.

The graphed quantity for ALL is the "Active" line in the Results table, shown below the orange total. The "Total" contains both active and inactive guildmembers; inactivity being defined in the database as Special = -1, activity as Special = 0.

Draw your own conclusions! That's the fun part. ^__))

Toodlepip,

Rebecca

The Lucky Cabbage