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Thread: FORMULA DISCUSSION

  1. #1
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    FORMULA DISCUSSION

    FORMULA DISCUSSION

    Some facts:
    - The bot calculates the scores.
    - The bot is developed by qan.
    - qan used formulas provided by Ogron.
    - I have never seen the formulas.
    - People keep sending me questions about whether dollar values are correct.
    - I'm starting to think we should make new formulas that are: easier to understand why you got the score you got; simpler and therefore less error prone.
    - I think the current formulas should be made public.

    My observations as a player:
    - Jav/Wb: it's very harsh when your dollar value is lower than your Kills.
    - Jav/Wb: there should be more correlation between kills and dollar value. I think there's a win bonus skewing things based on how close the result is.
    - Jav: TKing is severely punished, some TKing is unavoidable. (if someone catches your bomb it's not your fault.)
    - Terr: generally OK.
    - Shark: it's near impossible to get a good score unless you win.
    - Shark: TeKs are too highly rewarded, and encourages TKing which...
    - Shark: TKing is severely punished, some TKing is unavoidable.
    - Shark: RPD is the most important stat IMO and this doesn't seem so important based on current scores.
    - Spider: the win bonus is much too big. an elite spider on the losing team gets a similar score to a trash spider on the winning team.
    - We don't want the situation where you must win 20 games to qualify (i.e. if you win half the time, you need to play 40 games).


    It's easy to complain about formulas, but how many people are actually prepared to try and make better ones?

    Well, I decided to try...


    WARBIRD / JAV

    MAX(0, ((K-TK)*2) ) + (WIN ? 5 : 0)

    Notes:
    - Dollar value should never be less than $0.
    - The main part of the score is based on Kills (with TKs removed in Jav) multiplied by 2.
    E.g. 5 kills = $10, 10 kills = $20, 15 kills = $30, 20 kills with 5 TKs = $30.
    - Plus a bonus of $5 if you win the game.


    BASE

    Notes:
    - Dollar value should never be less than $0.
    - Each ship has it's own formula, providing a range from $0 (trash performance) to $30 (elite performance).
    - Each ship score is comparable, so multi-ship doesn't favor some ships over others.
    - Every ship gets $3 per TeK.
    - Every ship gets $5 if you win the game.

    TERR

    MAX(0, MIN(30, (1-(D/TP))*30 ) ) + (TeK*3) + (WIN ? 5 : 0)

    Notes:
    - The main part of the score is based on deaths per minute.
    E.g. in a 20 minute game: 1 death = $28; 7 deaths = $19; 15 deaths = $7.

    SHARK

    MAX(0, MIN(30, (RPD-2)*30 ) ) + (TeK*3) + (WIN ? 5 : 0)

    Notes:
    - The main part of the score is based on RPD.
    E.g. RPD 3.0 = $30; RPD 2.7 = $21; RPD 2.4 = $12.

    SPIDER

    MAX(0, MIN(30, ((((30*60)/TP)*K)/120)*30 ) ) + (TeK*3) + (WIN ? 5 : 0)

    Notes:
    - Kills are pro-rated up to 30 minutes, so you aren't forced to make it a longer game to get more kills.
    - Camping is not rewarded.
    - The main part of the score is based on Kills.
    E.g. in a 22 minute game, 100 kills = $30; 75 kills = $25; 50 kills = $17.
    Last edited by Rab; 09-23-2017 at 11:11 AM.

  2. #2
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    Looks great, I know I appreciate the time you took to lay out a simple formula for us and put great emphasis on whatever formula they decide to use to make it known public. I do have a few gripes with your formula, so I will get right to it.

    WB - I would like to see $ not only for getting kills, but WHO you kill. If Iron Survivor (Rated 10 for this instance) kills IxaDor (Rated 5 for this instance) he only gets $2 (example $ for this instance). Now if IxaDor kills Iron Survivor, IxaDor gets $2 PLUS 2 times the deficit in his skill to Iron Survivors skill, making it $12 (example $ for this instance, 2x Deficit is likely way too much). So an under skilled player gets more when killing a skilled player. This also helps prevent players (not going to name names) from going after players they know are weaker to pad scores in hopes for less blowouts matches and some added fairness to this "all inclusive" league. This would have to use ratings of some kind though and as you brought up in another thread, a way to implement new ratings every season would be a must for this to be fair and I hope they do it regardless of this thread post, static/mysterious ratings aren't fair to up and coming players or those who trained with new ships since.

    JAV- Looks pretty good just one thing I see is that TK's should be punished, though not as harshly as it is now that I agree. Already this season some people (not naming names) tk'd me just to tk me because they don't like me (lol.) and it was nice to have the punishment attached of them losing $. Removing it or near removing it (as you have suggested here) worries me. I just think taking it down a peg or two would do. I just want fair competition, in all leagues.

    BASE - Like your idea for Shark and Terrier, well done. Spider though I do not like at all honestly as I think it would encourage people to "pad kills" verse play as a team and go for the objective. The amount of kills you have to have for decent money in spider is also worrisome. 100 kills for $30? I can think of a handful of current spids who can do this, majority of them are lucky to go over 50. Spider is already punishment for many of us because 90% of the current basers are forced to play in this ship while "pro's" get to play in Terrier/Shark. I am not sure what the best way to go about this but your current proposal to me seems way to extreme.

    Other than that, I am happy. Just really happy someone is trying to make things transparent here because already the money you earn from matches has been incredibly inconsistent, for instance in wb week 1 I was 9-10 and this week I go 10-10 but I made more money for the 9-10 (something like $4 more) and both those games were losses, so it wasn't a win bonus either. I would, like yourself, be very interested to know exactly what is going on here with these formulas and ratings that unfortunately dictate the outcome of the game based on your performance. Anyways, a pleasure as always Rab, glad to have you here offering up more ideas for us to discuss and think about. Even if nothing comes of it, I think it's great for the zone and these leagues to always be looking at perfecting them. Take care my friend.

    -IxaDor

  3. #3
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    Bumping to see if more people want to comment on this.
    I think TSLB scores for terr and shark are measuring the wrong things, the spider scores are the only ones that make any sense.
    I'd like to see them changed for next season.
    It should be done in such a way that the scores are comparable between ships, and then using Overall for qualification purposes, so people feel free to play any ship without their qualification suffering.

  4. #4
    Leland
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    thank you
    Leland

  5. #5
    zeebu 'DUMPTRUCK' johnson Zeebu's Avatar
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    in wb and jav its a good start but not all kills should be weighted evenly. killing a person that sucks should be worth less than killing someone who is good. base it on the rating when entering the game to avoid any circular references and stuff and there you go.

    im not sure how to give a weighted system to base


    1996 Minnesota State Pooping Champion

  6. #6
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    I agree about points per kill in jav and wb being rating-based. It already is implemented that way, so we can leave it alone - I'm mainly talking about base now. I don't see any need for weighting in base.

    I know the spider kills-per-minute looks high but it isn't. The rate of 120 kills per 30 minute (4 kpm) does represent a strong round for a spider. That's about what spiders like skyforger and Henry get. cripple can get 5+ kpm.

    The way the spider kpm formula works is it calculates your kpm as a fraction of the 4kpm target, then multiplies $30 by that. So if you get 4kpm ($30*1.0) you get $30. If you get 2kpm ($30*0.5) you get $15. Then your TeK and Win bonuses are added to that.

    The dollar value of the Spider kpm component is capped at $30 to remain comparable with Terr (where 0 deaths gets you $30) and Shark (where 3.0 rpd gets you $30). If the Spider kpm target is too low then too many players would hit the cap, and if everyone's routinely hitting $30 it doesn't help differentiate good players from bad. If the Spider kpm target is too high then good spider scores are too low compared to good terr and shark scores.

  7. #7
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    Do people agree in principle that these are the things we should measure:
    - Terr: deaths per minute
    - Shark: RPD
    - Spider: kills per minute
    - All ships: bonus for TeKs, bonus for Win

    Atm I think Sharks are being scored on their kills, which is just bullshit IMO. I'd like for the actual formulas to be posted and explained in this thread, so people can see how bullshit they are.

    And do people agree in principle that scores should be comparable and Overall should be used for qualification?

  8. #8
    Registered User skyforger's Avatar
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    Quote Originally Posted by Rab View Post
    Do people agree in principle that these are the things we should measure:
    - Terr: deaths per minute
    - Shark: RPD
    - Spider: kills per minute
    - All ships: bonus for TeKs, bonus for Win

    Atm I think Sharks are being scored on their kills, which is just bullshit IMO. I'd like for the actual formulas to be posted and explained in this thread, so people can see how bullshit they are.

    And do people agree in principle that scores should be comparable and Overall should be used for qualification?

    Agree with a reservation. Kills for sharks/terrs should still affect the rating, but wayy less than it seems to be now. Reason being it still helps the team a bit, though, it is not essential to be an asset to the team in those ships. The main measurable things you have underlined correctly, I believe.

    Would add picking up greens as a tiny contribution to all ships rating, but slightly more weight for sharks. Could be done on a prorated to 30 min basis similar to your spider kills method. Don't know if technically feasible to calc it (seems it is, since green no's in the extended game reports).

  9. #9
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    Quote Originally Posted by skyforger View Post
    Kills for sharks/terrs should still affect the rating, but wayy less than it seems to be now.
    How small? $1 per 10 kills?

    Quote Originally Posted by skyforger View Post
    Would add picking up greens as a tiny contribution to all ships rating, but slightly more weight for sharks. Could be done on a prorated to 30 min basis similar to your spider kills method. Don't know if technically feasible to calc it (seems it is, since green no's in the extended game reports).
    I think this is double-measuring.
    Spiders - greens give full charge, which is included in kills per minute already.
    Sharks - greens give repels, which is included in rpd already.
    Terrs - greens give ports, which is included in deaths per minute already. ;; but also give bursts, which is covered by including kills to some extent as per your other point.
    There is indirect benefit, i.e. a green you collect as a spider might benefit your terr more than you - this is already covered by the win bonus.

  10. #10
    Registered User skyforger's Avatar
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    Probably has to be prorated to 30 mins like other kills. Not really sure about the formula but probably not more than 5$-7$ bonus for the upper end of kill count.

    Good point about the greens. Scrap that idea.

  11. #11
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    Updated terr and shark formulas with a small bonus for kills, at a rate of $1 per 10 kills:


    TERR


    MAX(0, MIN(30, ((1-(D/TP))*30)+(K/10) ) ) + (TeK*3) + (WIN ? 5 : 0)

    Notes:
    - The main part of the score is based on deaths per minute.
    E.g. in a 20 minute game: 1 death = $28; 7 deaths = $19; 15 deaths = $7.

    SHARK

    MAX(0, MIN(30, ((RPD-2)*30)+(K/10) ) ) + (TeK*3) + (WIN ? 5 : 0)

    Notes:
    - The main part of the score is based on RPD.
    E.g. RPD 3.0 = $30; RPD 2.7 = $21; RPD 2.4 = $12.
    Last edited by Rab; 04-11-2018 at 07:13 AM.

  12. #12
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    I have put these formulas into a spreadsheet and added some sample game data, so we can compare the scores they produce to the scores from the current formula.

    Link: https://docs.google.com/spreadsheets...it?usp=sharing

    I'm not really happy with these scores, but now it's in a spreadsheet I can tune it. Gotta do something else now, but I'll revisit this later / tomorrow.

  13. #13
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    CHANGES

    Win Bonus
    - $5 for a win and $0 for a loss was too harsh on the losing team. We want to avoid the scenario where your 10 qualifying scores must be wins.
    - Win bonus changed to $1.
    - Added a time component. Up to $3 depending how much time your team gets.

    TeK Bonus
    - $3 for a TeK is too high.
    - Changed to $1

    Spider
    - KPM Scores were too generous, re-tuned from 4 kpm to 4.8 kpm as the target.
    - Rewritten formula to be easier to understand. The formula was somehow wrong and my math-fu is weak, so I simplified it. The number 4 represents kills per minute. 4.8 kpm is worth $30, 2.4 kpm is worth $15.

    Terr
    - Rewritten formula to be easier to understand. The number 0.1 represents deaths per minute. 0.15 dpm is worth $30, 0.3 dpm is worth $15.
    - Added #DIV/0 catch if no deaths.

    Shark
    - RPD part of score too generous. Tuned such that 3.1 = $30, 2.2 = $0.


    UPDATED FORMULAE

    Terr
    MAX(0, MIN(30, ((1/(((IF(D = 0, 0.01, D))/TPMin)/0.15))*30)+(K/10) )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    Shark
    MAX(0, MIN(30, (((RPD-2.2)/(3.1-2.2))*30)+(K/10) )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    Spider
    MAX(0, MIN(30, ((K/TP)/4.8)*30 )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)


    UPDATED SPREADSHEET

    https://docs.google.com/spreadsheets...it?usp=sharing
    Last edited by Rab; 04-11-2018 at 10:17 AM.

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    Notes:
    - Need to subtract TKs for shark

  15. #15
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    CHANGES

    Shark
    - Excluded TKs from K bonus: (K/10) becomes ((K-TK)/10). TKs aren't punished because they can be accidental or even worth it in context.


    UPDATED FORMULAE

    Terr
    MAX(0, MIN(30, ((1/(((IF(D = 0, 0.01, D))/TPMin)/0.15))*30)+(K/10) )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    Shark
    MAX(0, MIN(30, (((RPD-2.2)/(3.1-2.2))*30)+((K-TK)/10) )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    Spider
    MAX(0, MIN(30, ((K/TP)/4.8)*30 )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)


    UPDATED SPREADSHEET

    Added yesterday's 2 games to the bottom as there were some dodgy scores I noticed.

    https://docs.google.com/spreadsheets...it?usp=sharing

  16. #16
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    I've been asked to explain a bit more about how the formulas work, what the constants are, etc. So here goes...

    APPROACH

    Think of the formulas as:
    (A) + (B)
    Where
    (A) = Ship-specific stuff
    (B) = Ship-neutral stuff

    (A) produces a score from $0 to $30
    (B) may allow the score to rise above $30

    This approach allows for scores between ships to be comparable, dependent on how (A) is tuned.


    FORMULAE

    The full formulae are:

    Terr
    MAX(0, MIN(30, ((1/(((IF(D = 0, 0.01, D))/TPMin)/0.15))*30)+(K/10) )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    Shark
    MAX(0, MIN(30, (((RPD-2.2)/(3.1-2.2))*30)+((K-TK)/10) )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    Spider
    MAX(0, MIN(30, ((K/TP)/4.8)*30 )) + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    (B) for all ships is:

    + (TeK*1) + IF(Win,1,0) + ((TFor/TTarget)*3)

    (A) is therefore:

    Terr
    MAX(0, MIN(30, ((1/(((IF(D = 0, 0.01, D))/TPMin)/0.15))*30)+(K/10) ))

    Shark
    MAX(0, MIN(30, (((RPD-2.2)/(3.1-2.2))*30)+((K-TK)/10) ))

    Spider
    MAX(0, MIN(30, ((K/TP)/4.8)*30 ))

    I will remove the MIN and MAX to simplify and discuss (remember that those limits exist).


    DETAILS

    Each ship's (A) component should produce a number between $0 and $30.
    This is achieved by devising a fraction between 0.00 and 1.00 and multiplying $30 by it.


    Terr
    ((1/(((IF(D = 0, 0.01, D))/TPMin)/0.15))*30) +(K/10)

    The objective is to base most of the score on deaths-per-minute (dpm), with a small addition for kills.

    This part is just division-by-zero error protection: IF(D = 0, 0.01, D)
    If the player has zero deaths, a dpm of 0.01 is assumed, which is so low it produces the maximum score.
    I'll re-state the formula with this simplified out:

    ((1/((D/TPMin)/0.15))*30) +(K/10)

    This part calculates dpm: (D/TPMin), e.g. 1 death in a 10 minute game is 0.1 dpm.
    The constant 0.15 is a dpm target required to get the full $30.
    If the player has 0.1 dpm, then 0.1/0.15 = 0.67.
    If the player has 1 dpm, then 1/0.15 = 6.67.
    Dividing 1 by this number inverts it (as higher dpm is bad):
    1/0.67 = 1.49
    1/6.67 = 0.149
    Multiply that by $30 and you get a sensible number between $0 and $30. $30 is achievable but not too easy.

    This part represents a small bonus for kills at a rate of $1 per 10 kills: (K/10)
    E.g. a terr who gets 40 kills will get a $4 bonus.
    Note this is still part of (A), which is capped at $30, otherwise terr scores could theoretically be higher than spider or shark scores.


    Shark
    (((RPD-2.2)/(3.1-2.2))*30) +((K-TK)/10)

    The objective is to base most of the score on RPD, with a small addition for kills.

    The constant 2.2 represents an RPD which should produce $0.
    E.g. if your RPD is 2.2 then 2.2-2.2 = 0; 0*$30 = $0.

    The constant 3.1 represents and RPD which should produce $30.
    E.g. (3.1 - 2.2)/(3.1 - 2.2) = 1.0; 1.0*$30 = $30.

    The kill bonus is the same concept as for terr, but with TKs removed.


    Spider
    ((K/TP)/4.8)*30

    The objective is to base most of the score on kills-per-minute (kpm).

    This part represents kpm: (K/TP)
    E.g. 70 kills in a 15 minute game is: 70/15 = 4.67kpm
    E.g. 30 kills in a 15 minute game is: 30/15 = 2kpm

    The constant 4.8 represents the kpm which should yield $30.
    E.g. 4.8/4.8 = 1; 1*$30 = $30
    E.g. 4/4.8 = 0.83; 0.83*$30 = $25
    E.g. 3/4.8 = 0.625; 0.625*$30 = $19
    E.g. 2/4.8 = 0.42; 0.42*$30 = $13
    Last edited by Rab; 04-12-2018 at 03:55 AM.

  17. #17
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    VISUALISATION

    I noticed when writing my previous post that Shark has a lower bound (i.e. 2.2 RPD is considered shit, as opposed to 0.0), but there's no equivalent lower bound for Spider or Terr. So I decided to try and visualise a range of scores to see if the ships are balanced throughout the range.

    I put in a line called "Ideal" which is what I'm aiming for. In this scenario a terrible score gets $0 and a strong score gets $30.

    I have created 10 theoretical players for each ship, their name is like a rating, 10 = noob, 100 = vet. I have made up scores that represent what these players might achieve, and calculated the dollar values accordingly.

    I charted all of this so we can see how closely it tracks the ideal.

    Shark tracks very well, Terr and Spider less so.

    I think with a bit more tuning I can get it much closer. I'll attempt that next.


    VISUALISATION SPREADSHEET

    https://docs.google.com/spreadsheets...it?usp=sharing

  18. #18
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    Observation

    K-TK for shark can result in the TKs being punished.

    E.g.
    10 kills and 0 TKs: (10-0)/10 = $1
    0 kills and 10 TKs: (0-10)/10 = -$1

    I haven't really formed an opinion on whether this matters yet, just pointing it out.

    Edit: Observation 2

    The shark numbers in the visualisation don't match the calculated dollar values.
    However, the outcome is the same.
    Last edited by Rab; 04-12-2018 at 07:16 AM.

  19. #19
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    CHANGES

    All ships:
    - Increased TeK bonus from $1 to $2
    - Increased Win bonus from $1 to $2

    Terr
    - Better way of calculating dpm based on visualisation chart.
    - New constant 0.6 represents dpm which should result in $0.
    - Changed kill bonus rate to $1 every 15 kills.

    Spider
    - Better way of calculating kpm based on visualisation chart.
    - New constant 1.35 represents a kpm which should result in $0.
    - New constant 5.10 represents a kpm which should result in $30.

    Shark
    - Changed lower const from 2.2 to 2.3.


    UPDATED FORMULAE

    Terr
    MAX(0, MIN(30, (((0.6-(D/TP))/0.6) *30)+(K/15) )) + (TeK*2) + IF(Win,2,0) + ((TFor/TTarget)*3)

    Shark
    MAX(0, MIN(30, (((RPD-2.3)/(3.1-2.3)) *30)+((K-TK)/10) )) + (TeK*2) + IF(Win,2,0) + ((TFor/TTarget)*3)

    Spider
    MAX(0, MIN(30, (((K/TP)-1.35)/(5.10-1.35)) *30 )) + (TeK*2) + IF(Win,2,0) + ((TFor/TTarget)*3)


    UPDATED SPREADSHEET

    Added column to show the difference between the two dollar values.

    https://docs.google.com/spreadsheets...it?usp=sharing


    UPDATED VISUALISATION

    Adjusted some of the player stats to better reflect real games.

    https://docs.google.com/spreadsheets...it?usp=sharing

  20. #20
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    Getting to the point where I'm changing things and making it worse, so I think it's time to stop.

    How does everyone feel about this as a final product?


    CHANGES

    Spider
    - Reverted change of constant from 5.1 back to 4.8.


    UPDATED FORMULAE

    Terr
    MAX(0, MIN(30, (((0.6-(D/TP))/0.6) *30)+(K/15) )) + (TeK*2) + IF(Win,2,0) + ((TFor/TTarget)*3)

    Shark
    MAX(0, MIN(30, (((RPD-2.3)/(3.1-2.3)) *30)+((K-TK)/10) )) + (TeK*2) + IF(Win,2,0) + ((TFor/TTarget)*3)

    Spider
    MAX(0, MIN(30, (((K/TP)-1.35)/(4.8-1.35)) *30 )) + (TeK*2) + IF(Win,2,0) + ((TFor/TTarget)*3)


    UPDATED SPREADSHEET

    https://docs.google.com/spreadsheets...it?usp=sharing


    UPDATED VISUALISATION

    https://docs.google.com/spreadsheets...it?usp=sharing

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