Index stat for map sizes

Archived from groups: alt.games.vgaplanets4 (More info?)

At most hostsites there's a pool of maps to choose from for playing.
Usually they are described with the planet count and the rough size of
the galaxy (given in coordinate cornerpoints).
I would like another number or two added to the map descriptions for a
better overview. Something like planet density. To get an idea how far
I have to travel to get from planet to planet. I believe this to be a
very important statistic (beside size and planet count) to judge the
map on its playability, and if warp or hyp engines will be of advantage
(generally speaking).

It could be something simple like planet density:

p=P/A

p: planet density
P: number of Planets
A: area of galaxy

With area as simple as (length)^2 for squares or pi*(radius)^2 for
circles.

p^(-1) would be something like 'space around each planet', and you
could derive a mean distance d between planets from it:

d=2*sqr((pi*p)^(-1))

I know of course that such a description by numbers would be very
general. Some maps have a varying density, some have clusters, and so
forth. But it would at least give a general idea and a better feeling
for a map you have not seen before. And a look at the map (and its
planet distribution) will provide a quick evaluation of the credibility
of the statistics p and d.

To give a few examples:

Echo Cluster (500 planets, 2000 x 2000 square)
p=1.25*10^(-4)
d=101

Blitzkrieg (220 planets, 400 radius circle)
p=4.38*10^(-4)
d=54

YaleLite (252 planets, 2000 radius circle)
p=0.2*10^(-4)
d=252

I think these examples already give a feeling for each (very different)
map, and if you'd want to play a non-hyp race in it. Something I
don't easily get just from a look at the coordinate points or even a
picture (without scale) of the map.

What I want to know now is, would there be enough of a popular demand
for such stats like 'planet density' and 'mean distance' to
convince the map creators and the hostsite administrators to add these
stats to the map descriptions?
24 answers Last reply
More about index stat sizes
  1. Archived from groups: alt.games.vgaplanets4 (More info?)

    I'd love to see this.

    Greg Bahr

    P.S. This is a result of our discussion isn't it?
  2. Archived from groups: alt.games.vgaplanets4 (More info?)

    "Lord Owl" <lord.owl@gmx.de> schrieb im Newsbeitrag news:1112362545.660292.48050@l41g2000cwc.googlegroups.com...

    > forth. But it would at least give a general idea and a better feeling
    > for a map you have not seen before. And a look at the map (and its

    Extend the description and give minimum, maximum, mean and volatility for each map.

    GFM GToeroe
  3. Archived from groups: alt.games.vgaplanets4 (More info?)

    Owl

    Could you state your formulae in more exact maths? If the group could
    agree a programmatic formula then this could be coded from a cut-down
    version of map2ps fairly swiftly. Site admins could then run this over
    ..MAP files when they install them. New maps would be easily handled.
    Indeed maybe I could make map2ps throw off some metrics as a side effect.

    Lord Owl wrote:
    > At most hostsites there's a pool of maps to choose from for playing.
    > Usually they are described with the planet count and the rough size of
    > the galaxy (given in coordinate cornerpoints).
    > I would like another number or two added to the map descriptions for a
    > better overview. Something like planet density. To get an idea how far
    > I have to travel to get from planet to planet. I believe this to be a
    > very important statistic (beside size and planet count) to judge the
    > map on its playability, and if warp or hyp engines will be of advantage
    > (generally speaking).
    >
    > It could be something simple like planet density:
    >
    > p=P/A
    >
    > p: planet density
    > P: number of Planets
    > A: area of galaxy
    >
    > With area as simple as (length)^2 for squares or pi*(radius)^2 for
    > circles.
    >
    > p^(-1) would be something like 'space around each planet', and you
    > could derive a mean distance d between planets from it:
    >
    > d=2*sqr((pi*p)^(-1))
    >
    > I know of course that such a description by numbers would be very
    > general. Some maps have a varying density, some have clusters, and so
    > forth. But it would at least give a general idea and a better feeling
    > for a map you have not seen before. And a look at the map (and its
    > planet distribution) will provide a quick evaluation of the credibility
    > of the statistics p and d.
    >
    > To give a few examples:
    >
    > Echo Cluster (500 planets, 2000 x 2000 square)
    > p=1.25*10^(-4)
    > d=101
    >
    > Blitzkrieg (220 planets, 400 radius circle)
    > p=4.38*10^(-4)
    > d=54
    >
    > YaleLite (252 planets, 2000 radius circle)
    > p=0.2*10^(-4)
    > d=252
    >
    > I think these examples already give a feeling for each (very different)
    > map, and if you'd want to play a non-hyp race in it. Something I
    > don't easily get just from a look at the coordinate points or even a
    > picture (without scale) of the map.
    >
    > What I want to know now is, would there be enough of a popular demand
    > for such stats like 'planet density' and 'mean distance' to
    > convince the map creators and the hostsite administrators to add these
    > stats to the map descriptions?
    >
  4. Archived from groups: alt.games.vgaplanets4 (More info?)

    Lord Owl asks

    >What I want to know now is, would there be enough of a popular demand
    >for such stats like 'planet density' and 'mean distance' to
    >convince the map creators and the hostsite administrators to add these
    >stats to the map descriptions?

    Mean distance would be interesting to me. Because I would understand it.
    Mentioning this is a good idea.

    Density would not be meaningful to me. It is not a very intuitive
    concept to convey for maps - to me, anyway. It would be a number which I
    would ignore.
    --
    Paul Honigmann
  5. Archived from groups: alt.games.vgaplanets4 (More info?)

    The planet density is quite straightforward. Determine the area of the
    map by the given coordinates of its cornerpoints, i.e. A=(length)^2.
    Or, if it is a circle, take half a side as radius R and determine the
    area with pi*R^2. Divide the planet number through the total area, and
    you got some kind of planet density.
    As Paul mentioned below it is something of an abstract value.

    But if you take its reciprocal you get something like average space per
    planet. Imagine a circular area of space of that amount, with the
    planet in its center. Average distance from planet to planet would be
    twice the radius r of such a 'planet-space' circle. To get the
    radius, solve a=pi*r^2.

    A: Area of map
    P: number of planets
    a: space per planet
    d: average distance between planets

    a=A/P, a=pi*r^2

    d=2r=2*sqr(A/(pi*P))

    I am not sure how close this value approximates the real average
    distance between neighbouring planets on a map. Mathematically it
    appears to be sound. Depends a lot on the individual map and its
    homogenity. At the very least it gives you a rough idea ;).
  6. Archived from groups: alt.games.vgaplanets4 (More info?)

    Mean distance is more intuitive for me also. One could take a given
    planet and calculate the mean distance to all other planets. This could
    approximate to something that tells me how a given race would fare in
    running a transport network.

    Map forms do matter though. A clustered map would behave very
    differently than one blob (like Echo). The two cluster extended Yale
    would get a weird metric.

    I can only think to produce a set of mini values based on local mean
    distances using randomly selected planets. Then take the mean and
    std-deviation of the set of figures.

    KlingonKommand wrote:
    > Lord Owl asks
    >
    >> What I want to know now is, would there be enough of a popular demand
    >> for such stats like 'planet density' and 'mean distance' to
    >> convince the map creators and the hostsite administrators to add these
    >> stats to the map descriptions?
    >
    >
    > Mean distance would be interesting to me. Because I would understand it.
    > Mentioning this is a good idea.
    >
    > Density would not be meaningful to me. It is not a very intuitive
    > concept to convey for maps - to me, anyway. It would be a number which I
    > would ignore.
  7. Archived from groups: alt.games.vgaplanets4 (More info?)

    I'm not playing VGAP much any more, but this is such an interesting
    problem to work on that I couldn't resist :)

    I came up with two statistics that I think do a pretty good job of
    describing:
    1) How close planets are on average
    2) How big the area is between clusters of planets

    I call these measurements the "Median Distance Index" (measured in
    lightyears) and the "Boonies Index" (how likely you are to end up "out
    in the boonies").

    Before explaining how I arrived at these numbers, take a look at my
    results (if this doesn't show up formatted correctly, try using a
    fixed-width font. Google's newsgroup reader has a link near the top to
    switch to Fixed-width):

    Map Stars Med Dist Boonies Index
    ============================================
    Yale 1009 67.36 3.24
    Echo 500 60.90 0.17
    Epsilon 688 44.18 11.30
    Stardrift 592 44.15 3.58
    dblossom 400 38.21 2.36
    Snowflake 40 100.00 3.76
    Yalelite 252 139.32 2.55
    QuadraStar 2001 40.01 1.44
    Starburst 420 55.47 36.25
    Phi 500 50.01 3.31

    To compute these figures, the map file is loaded and then a Minimum
    Spanning Tree is constructed from the starmap. The "Median Distance
    Index" is defined as the median edge length of the tree. The "Boonies
    Index" is defined as the difference between the mean and the median
    edge length.

    The "median Distance Index" tells you about how far apart, in
    lightyears, you can expect planets to be.

    A high "Boonies Index" indicates that there are groups of stars which
    are relatively isolated. For example, the Starburst galaxy - which
    consists of several clusters of planets separated by a large distance -
    has the highest Boonies Index.

    Of course, to compute how "warp-friendly" any map is, you'll also need
    to take into account the number of stars, and the overall size... but
    that information is readily available.
  8. Archived from groups: alt.games.vgaplanets4 (More info?)

    Visual aid now available. See pictures of the Minimum Spanning Trees
    for various galaxies:

    http://webpages.charter.net/kgnorris/spanningtrees.png
  9. Archived from groups: alt.games.vgaplanets4 (More info?)

    Wow! That's the difference you get when someone experienced in
    statistics and programming takes care of a problem :). Very elegant
    approach. I dimly remember something vaguely like it from a statistical
    mechanics lecture. Love the pictures :).

    I notice that your average distance is only about 60% of the amount I
    get with my own rather simple method. Hm. I believe the Minimum
    Spanning Tree appears to compute more something like 'average
    distance to the closest planet' than 'average distance to all
    neighbouring planets'. At least in tendency.

    Concerning the Boonies Index, what do you understand under "the
    difference between the mean and the median edge length"? It's
    probably a language thing. I assume 'mean edge length' is the
    average length of a single tree line (make the sum and divide it
    through number of lines), while 'median edge length' is computed
    by, hm, sorting out the extreme ones until you are left with the last
    one right in the middle?
  10. Archived from groups: alt.games.vgaplanets4 (More info?)

    Roger writes
    >Visual aid now available. See pictures of the Minimum Spanning Trees
    >for various galaxies:
    >
    >http://webpages.charter.net/kgnorris/spanningtrees.png

    Very pretty!
    --
    Paul Honigmann
  11. Archived from groups: alt.games.vgaplanets4 (More info?)

    Yes, your understanding of mean and median is correct.

    I did a little more number crunching based on some other types of
    trees, to see if those numbers are helpful in any way. I'm not going
    to try to format these.... import it into Excel if you want to view
    them properly :)

    Map Info,,Minimum Spanning Tree,,,Maximum Spanning Tree,,,Lattice,,,
    Map,Stars,Median,Mean,Diff,Median,Mean,Diff,Median,Mean,Diff
    dblossom,400,38.21,40.57,2.36,102.84,122.74,19.90,66.24,80.72,14.48
    Phi,500,50.01,53.32,3.31,106.94,124.36,17.42,77.32,88.47,11.15
    Epsilon,688,44.18,55.48,11.30,102.18,165.30,63.12,70.18,108.63,38.45
    Stardrift,592,44.15,47.73,3.58,137.59,170.02,32.43,75.29,107.91,32.62
    Echo,500,60.90,61.07,0.17,142.47,165.39,22.92,101.08,112.42,11.34
    Yale,1009,67.36,70.60,3.24,160.12,175.96,15.84,111.51,123.34,11.83
    Starburst,420,55.47,91.72,36.25,383.44,438.23,54.79,115.26,234.69,119.43
    Snowflake,40,100.00,103.76,3.76,202.00,231.39,29.39,158.11,164.58,6.47
    Yalelite,252,139.32,141.87,2.55,340.65,357.90,17.25,219.64,248.65,29.01

    "Minimum Spanning Tree" - Already described.

    "Maximum Spanning Tree" - I don't think this is a real term... but it's
    basically the opposite of the minimum spanning tree. Only edges
    between neighboring stars are eligible.

    "Lattice" - Connects all stars with their neighbors. Stars are
    considered to be "neighbors" if the line between them cannot be cut by
    a shorter line between other stars.

    I may post additional visual aids when I get the chance.
  12. Archived from groups: alt.games.vgaplanets4 (More info?)

    Roger, well done. This is just what was asking for. Someone with
    original ideas and maths skill to write them up cogently. The number
    crunching is a bonus and your numbers give good quick appreciation of
    map character. Comparing my own Yale and Yalelite we see the increase in
    median distance in the thinned out map (making it better for the EE) yet
    the Boonies index is of the same order of magnitude, indicating the
    underlying map stats. Echo with Boonies 0.17 is obviously a totally
    "urban" map.

    I think you have the last word on this. Will you post a list of all maps
    at Drew's for inclusion on his site?

    Everyone else, just stand back in awe for a few minutes.

    Roger wrote:
    > I'm not playing VGAP much any more, but this is such an interesting
    > problem to work on that I couldn't resist :)
    >
    > I came up with two statistics that I think do a pretty good job of
    > describing:
    > 1) How close planets are on average
    > 2) How big the area is between clusters of planets
    >
    > I call these measurements the "Median Distance Index" (measured in
    > lightyears) and the "Boonies Index" (how likely you are to end up "out
    > in the boonies").
    >
    > Before explaining how I arrived at these numbers, take a look at my
    > results (if this doesn't show up formatted correctly, try using a
    > fixed-width font. Google's newsgroup reader has a link near the top to
    > switch to Fixed-width):
    >
    > Map Stars Med Dist Boonies Index
    > ============================================
    > Yale 1009 67.36 3.24
    > Echo 500 60.90 0.17
    > Epsilon 688 44.18 11.30
    > Stardrift 592 44.15 3.58
    > dblossom 400 38.21 2.36
    > Snowflake 40 100.00 3.76
    > Yalelite 252 139.32 2.55
    > QuadraStar 2001 40.01 1.44
    > Starburst 420 55.47 36.25
    > Phi 500 50.01 3.31
    >
    > To compute these figures, the map file is loaded and then a Minimum
    > Spanning Tree is constructed from the starmap. The "Median Distance
    > Index" is defined as the median edge length of the tree. The "Boonies
    > Index" is defined as the difference between the mean and the median
    > edge length.
    >
    > The "median Distance Index" tells you about how far apart, in
    > lightyears, you can expect planets to be.
    >
    > A high "Boonies Index" indicates that there are groups of stars which
    > are relatively isolated. For example, the Starburst galaxy - which
    > consists of several clusters of planets separated by a large distance -
    > has the highest Boonies Index.
    >
    > Of course, to compute how "warp-friendly" any map is, you'll also need
    > to take into account the number of stars, and the overall size... but
    > that information is readily available.
    >
  13. Archived from groups: alt.games.vgaplanets4 (More info?)

    Roger writes

    >400,38.21,40.57,2.36,102.84,122.74,19.90,66.24,80.72,14.48
    >Phi,500,50.01,53.32,3.31,106.94,124.36,17.42,77.32,88.47,11.15
    >Epsilon,688,44.18,55.48,11.30,102.18,165.30,63.12,70.18,108.63,38.45
    >Stardrift,592,44.15,47.73,3.58,137.59,170.02,32.43,75.29,107.91,32.62
    >Echo,500,60.90,61.07,0.17,142.47,165.39,22.92,101.08,112.42,11.34
    >Yale,1009,67.36,70.60,3.24,160.12,175.96,15.84,111.51,123.34,11.83
    >Starburst,420,55.47,91.72,36.25,383.44,438.23,54.79,115.26,234.69,119.43
    >Snowflake,40,100.00,103.76,3.76,202.00,231.39,29.39,158.11,164.58,6.47
    >Yalelite,252,139.32,141.87,2.55,340.65,357.90,17.25,219.64,248.65,29.01

    Clear, concise, and self-explanatory. It reminds me of Jon Nunn's
    classic "111011" post or Peter Chamber's proof that 2 = 1 on Tuesdays.
    Of course in my day we didn't have 1's, we just had zeroes. We need more
    postings like this. Perhaps we can change the name of the NG to
    alt.games.vgaplanets4.binaries ...
    --
    Paul Honigmann
  14. Archived from groups: alt.games.vgaplanets4 (More info?)

    I'll see what I can do. It'll probably be a few days before I can
    scrounge up enough free time to get to all the maps, but I'll post the
    link when I finish.
  15. Archived from groups: alt.games.vgaplanets4 (More info?)

    The final results are in!

    I didn't actually get to *all* of the maps on Drewhead's, but I think I
    covered most of them. And after further analysis, I decided that
    Minimum Spanning Trees, while visually appealing, really aren't all
    that useful :)

    Read the full report (follow map links for pictures) here:
    http://webpages.charter.net/kgnorris/maps/mapinfo.htm

    I decided on a different method for calculating the Boonies Index.
    First of all, I'm just using the basic lattice instead of the minimum
    spanning tree. (i.e., we're considering all connections between each
    planet and its neighbors). The Boonies Index is now defined as the
    average deviation divided by the median.

    Based on the median and the Boonies Index, I determined an overall
    "Warp Unfriendliness" factor. Should be fairly self-explanatory on the
    results page.

    Hope this info is useful!
  16. Archived from groups: alt.games.vgaplanets4 (More info?)

    Whoops, I missed more than a few maps on my first pass... I've updated
    the list with several additions.
  17. Archived from groups: alt.games.vgaplanets4 (More info?)

    Dear newsgroup.

    As L.O. started this thread I was anxious to see the results as it
    could mean that the world of p4 maps finally would get some
    "clarifying".

    I did the nOob test with Rogers table today and guess what happend!

    I tested it with two objects. Both beginners to intermediate (1-2 games
    played). BOTH of them had absolutley no clue at all what this site was
    telling them.

    --> idea: great
    --> concept: great
    --> result: not usefull at all!

    Fabian
  18. Archived from groups: alt.games.vgaplanets4 (More info?)

    8-)

    Ok - good point!

    So the facts are there we just need to find a way to show 'em in a
    manner that is easily accessible (even for new players).

    Fabian
  19. Archived from groups: alt.games.vgaplanets4 (More info?)

    Some simple descriptions for newbies (I'll add this to the site when I
    get the chance):

    First of all, newbies will probably only care about the first five
    columns or so. Everything after that is for the engineer-types who
    like to stare at pages full of numbers. So, here are those first five
    columns:

    1) Map Name
    Self explanatory

    2) Stars
    The number of stars in the map.

    3) Overall Warp Unfriendliness
    This number attempts to describe how warp-drive races will fare on the
    map. It's really not useful for anything accept comparing two maps to
    see which one is more warp-friendly.

    For example, we can see from the list that Troubadour appears to be the
    friendliest map for warp-drive races.

    A more technical explanation is that this number takes into account
    both the median distance between stars and their neighbors, as well as
    whether stars are evenly distributed across the map.

    4) Boonies Index
    This number describes whether stars are evenly distributed or not. A
    high "Boonies Index" indicates that you're more likely to end up "out
    in the boonies." More specifically, maps with a high Boonies Index
    will tend to have dense clusters of stars separated by large gulfs of
    empty space.

    A map with all the stars evenly distributed, so that each star is about
    the same distance from all of its neighbors, would have a very low
    Boonies Index.

    In our chart, anything with a Boonies Index larger than about 0.7 is
    going to have fairly major "clustering" of stars, or large gulfs of
    empty space.

    5) Lattice Median (measured in lightyears)
    The lattice median is just the median distance beween neighboring
    stars. The median, for those who aren't statistics buffs, is just the
    middle value. For example, a lattice median of 120 indicates that most
    stars are about 120 lightyears away from their neighbors.

    Obviously, this is a very important value to consider when choosing a
    map, since it tells you how difficult it will be for warp-drive ships
    to get to their neighboring stars.
  20. Archived from groups: alt.games.vgaplanets4 (More info?)

    Just wanted to say that I appreciate your work very much! Please
    proceed!!

    Fabian
  21. Archived from groups: alt.games.vgaplanets4 (More info?)

    > We see the Boonies index for these two is 0.49 and 0.50. Is > this
    what we expect?

    Yes. The Boonies Index only takes into account the evenness of the
    distribution. Yale and Yalelite have basically the same distribution,
    so the number is virtually the same. As you said, even though Yalelite
    has a lower planet density, the "clustering" is about the same. So...
    perhaps the Boonies Index should be renamed to the Cluster Index or
    something like that?

    A better measurement of planet density is the Median calculation, which
    measures the median distance between neighboring stars.

    Only the the "Overall Warp Unfriendliness" number takes into account
    both density and clustering. And, if you look at the results, Yale
    scores considerably better in that area than Yalelite, due to its
    greater planet density.
  22. Archived from groups: alt.games.vgaplanets4 (More info?)

    All that is needed is a short explanation.

    This great-idea-but-I-am-too-dumb-to-learn-to-understand-it-attitude is
    nothing for VGAP players anyway.

    Lordfire


    "Fabian" <fabs42@yahoo.com> wrote in message
    news:1114081577.411415.67770@z14g2000cwz.googlegroups.com...
    >
    > Dear newsgroup.
    >
    > As L.O. started this thread I was anxious to see the results as it
    > could mean that the world of p4 maps finally would get some
    > "clarifying".
    >
    > I did the nOob test with Rogers table today and guess what happend!
    >
    > I tested it with two objects. Both beginners to intermediate (1-2 games
    > played). BOTH of them had absolutley no clue at all what this site was
    > telling them.
    >
    > --> idea: great
    > --> concept: great
    > --> result: not usefull at all!
    >
    > Fabian
    >
  23. Archived from groups: alt.games.vgaplanets4 (More info?)

    An interesting test of Boonies indexis the pair { Yale, Yalelight }.

    Yalelight is a sub-set of 25% of the stars in Yale, randomly chosen.
    So the overall stats of the stars distribution should only differ in
    terms of density. Not angular distribution or the like.

    We see the Boonies index for these two is 0.49 and 0.50. Is this what we
    expect? Stars in Yalelite are certainly in a lower density cluster. One
    is in sense in a more rural locale. However the 'clustering' is
    certainly about the same.

    Perhaps the term 'Boonies Index' is merely somewhat mis-named?

    Roger wrote:
    > The final results are in!
    >
    > I didn't actually get to *all* of the maps on Drewhead's, but I think I
    > covered most of them. And after further analysis, I decided that
    > Minimum Spanning Trees, while visually appealing, really aren't all
    > that useful :)
    >
    > Read the full report (follow map links for pictures) here:
    > http://webpages.charter.net/kgnorris/maps/mapinfo.htm
    >
    > I decided on a different method for calculating the Boonies Index.
    > First of all, I'm just using the basic lattice instead of the minimum
    > spanning tree. (i.e., we're considering all connections between each
    > planet and its neighbors). The Boonies Index is now defined as the
    > average deviation divided by the median.
    >
    > Based on the median and the Boonies Index, I determined an overall
    > "Warp Unfriendliness" factor. Should be fairly self-explanatory on the
    > results page.
    >
    > Hope this info is useful!
    >
  24. Archived from groups: alt.games.vgaplanets4 (More info?)

    "Clustering Index" I would support.

    Roger wrote:
    >>We see the Boonies index for these two is 0.49 and 0.50. Is > this
    >
    > what we expect?
    >
    > Yes. The Boonies Index only takes into account the evenness of the
    > distribution. Yale and Yalelite have basically the same distribution,
    > so the number is virtually the same. As you said, even though Yalelite
    > has a lower planet density, the "clustering" is about the same. So...
    > perhaps the Boonies Index should be renamed to the Cluster Index or
    > something like that?
    >
    > A better measurement of planet density is the Median calculation, which
    > measures the median distance between neighboring stars.
    >
    > Only the the "Overall Warp Unfriendliness" number takes into account
    > both density and clustering. And, if you look at the results, Yale
    > scores considerably better in that area than Yalelite, due to its
    > greater planet density.
    >
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