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CrabEatOff #1 Posted Jan 31 2013 - 17:09

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The weighted and normalized formulas are a project spearheaded by Praetor77 and members of this forum. A summary written by Praetor can be read here http://www.koreanran...ciency-formula/

The full development and communication regarding it can be read here : http://forum.worldof...ciency-formula/

However, this thread is meant to help de-mystify the components of the formula itself, and debunk some myths.

Limitations
First, lets discuss the limitations of WoT API stats and the ratings derived from them. First, formulas can only be created from stats that are made available via the official WoT website. Efficiency depends on those same stats. Everything WoT-news computes is off those same stats. More information on YOUR history is available from the cached dossier file, but unless everyone starts mass uploading those (which will never happen), then the official website stats are THE source for data.

What isn't in WoT website stats?
Normalized Experience (XP) - theoretically WG could keep track of experience based on whether a user had a premium account or not, and then either remove the premium bonus OR give all standard account users the bonus (for stats purposes) to normalize XP across users. This would be a good comparison as there are a number of factors which aren't accounted for in other stats.

Some of those relevant factors (from http://wiki.worldoft...nce_and_Credits)
  • Spotting an enemy tank for the first time
  • Inflicting critical (module/crew) damage
  • Killing blow
  • Close combat bonus
  • Completed base capture
  • Team performance factor
and most importantly
  • Damage Upon Detection - Damage done to targets you are spotting yourself, by tanks who are not spotting them themselves
The latter is the bread and butter of light tanks (LTs) and of front line fighters. The other bonuses are relatively small compared to the latter. But it is the most noticeably missing in all rating calculations, and it particularly screws over LTs.


Per tank anything - the website cannot tell you damage per tank, spots per tank, etc. This information lives in your dossier and somewhere on the WG servers. If you use a dossier parsing tool (there are several web based and one local), you can obtain this information on your per tank performances.

Implications of limitations

If you play a lot of light tanks (I'm looking at you Tazilon) you will get lower WN6 than someone with same games played in MTs or HTs. This because LTs depend on DUD to get their XP and credits, and generally do lower damage per game at the same tier. A very good LTer will finish off a lot of wounded targets, spot a lot of targets, and win a lot of games, so the effect of not having DUD included will be slightly mitigated. But for example, a tier 7 LT might average 1500+ dpg, but that is still 500 less than a very good HT at the same tier might be doing, so holding spots, frags and wins, the HT would still have a much higher WN6.

Per Praetor

Quote

scouts are VERY badly measured by WN. Sadly. If we had avg damage scouted we cuold do better, but the stat is not available.... still, I enjoy playing scouts a lot and will continue to do so... unlike others, I consider WN as a tool to use with XVM to know APPROXIMATELY how good a player is. I don´t consider it to be more than that. I don´t care if my rating drops for playing scouts, I love them! :D


SPGs also cause issues, as their tiers are not lined up with the rest of tanks! They do much more damage than their tier value would indicate for a HT, MT or TD. This is a known limitation of the formulas. Extensive programming (parsing the website stats for SPG counts and adjusting their tier) COULD fix this, but the problem will go away when the SPGs tiers are stretched to match (per the latest ASAP with SerB). For now...we deal with it. Who care about SPG players stats anyways, amirite?!?!?

Some statistical limitations: When measuring a population, its not going to be possible to put every single person on the scale and have the scale make sense. Again, returning to a notable outlier, Tazilon and his 20k+ VK2801 games. This massive number of games means his average tier played is 5.35, which is lower than is "generally expected" for someone with 28k total games. For example, it is lower than MY average tier, at a mere 6500 games. It takes longer to move through higher tier tanks, and so you end up with more weight at 6+. Because WN6 is designed to measure the population relative to each other, some assumptions have to be made about the habits of the general population. Most players don't play 20k games in any single class or tier below 8, let alone 20k in a single tier 5. If someone plays 10k games in the MS-1....outlier! Takeaway: population ratings cannot account for every outlier.

The Formula
With those limitations in mind, lets examine the formula, piece by piece. WN stands for Weighted and Normalized,

Quote

WN6 formula:
(1240-1040/(MIN(TIER,6))^0.164)*FRAGS
+DAMAGE*530/(184*e^(0.24*TIER)+130)
+SPOT*125
+MIN(DEF,2.2)*100
+((185/(0.17+e^((WINRATE-35)*-0.134)))-500)*0.45
+(6-MIN(TIER,6))*-60

Would like to highlight that MIN() means the number capped at that value, so MIN(TIER, 6) means avg tier capped at 6, (so player avg tier is used if it is lower than 6, otherwise 6 is used) and MIN(DEF,2.2) means defense is capped at 2.2.

Praetor did a good job of explaining the MIN(X,Y) portion, so I won't go over that. Frags, damage, spots and defense are per battle, not absolute counts. Tier and winrate are for the entire account history, or for the period in question.

Frags
(1240-1040/(MIN(TIER,6))^0.164)*FRAGS

Here is your frags factor. Note that tier is accounted for, by taking the min of either tier played or 6. Praetor et al found that frags were a very important factor in predicting player skill. However "although frags is a much more sound statistic, we decided to give them equal weight to avoid kill farming"

A Note on Scales:
For those not accustomed to reading these types of formulas...these random numbers 1240, 1040, 0.164 may seem arbitrary. And the fact is...they ARE arbitrary. The scale of WN6 is itself arbitrary, as are many other familiar scales, Efficiency, SAT scores, and IQ. Without going into a long discussion of scaling (which I would love to do, because I am pedant), lets just say that statisticians create these scales so that persons can be compared to each other, and that the scale is simply accepted as convention. The scale could be from 0-100, but isn't because then it would look like percentages. It could be from 0-1600 like the old SAT or 0-2400 like the new one. The scale is bounded only by the amount of damage available in a game. It can run from the negatives into over 3000 points. However, in practice it has the following values based on the population percentages:

Quote

Praetor, I combed for like 10 mins to find the scale, but couldn't, can you post it to this thread please, so I can insert? Thanks! -Crab

So the coefficients or random numbers simply help normalizescores into a familiar bell curve, and stick generally to the convention of ranges which the Efficiency guys chose, and has become familiar to the WoT community.

Damage
+DAMAGE*530/(184*e^(0.24*TIER)+130)

After frags, we add in damage, which is again normalized using the mathematical constant e. In laymans terms, e helps us turn the distribution of the scores into a bell curve. As with frags, tier is taken into account, and constants are added, multiplied and divided to weight and normalize damage relative to the other components of the score, and to put the population in right order.

Spots
+SPOT*125

Finally! something simple. Every game (except those MM bugged out 7 player games) there are 15 opponents, at every tier. So a spot is ostensibly worth the same at tier 1 as tier 10. There is no tier factor in this portion of the formula.

Defense
+MIN(DEF,2.2)*100

Defense points, capped at 2.2 per game times 100. As with spots, there are the same number of cap and defense points needed at tier 1 and tier 10, so no tier factor.

A Note on Cap and Defense Points
Investigations by the WNX team found that they could not find a correlation between cap points and player skill. Of course there was some subjectivity in who is "skilled", however among players generally known to be among the best in the game, cap points can vary as much as 1.5 to 4.5 per game! However defense points tend to rise with player skills. Very poor players will have below 0.5 per game, while better players will see 1.5 or more (up to and over 2). This bears out, in that suicide rushers never see the end of the game, and aware players will return to base to reset, or to destroy enemies trying to defend cap on Encounter modes.

Capping IS a winning condition however. But because it became so well known that Efficiency was most easily manipulated by capping, the data has become biased towards capping. Capping also takes less skill than eliminating the enemy team. This isn't to say that you shouldn't cap to win, if capping is your best chance. WIN ALWAYS. But making it work across the population wasn't working. Again, this can effect LTs, as often times the best thing they can do is drive real fast and cap out, but....limitations.

You can dispute this with the creators, but not with me, I am just explaining the formula. Their conclusions are evidence based, so if you want to pick this fight, bring large volumes of data!

Winrate
+((185/(0.17+e^((WINRATE-35)*-0.134)))-500)*0.45

Praetor explained this best, from the link above

Quote

having 48% wins leads this term to have a value of 0. This term is an S-curve, which rewards winrates above 48%, but using winrate as a proxy to reward intangible skills like map awareness, knowing when to track tanks which leads to team kills, protecting arty from scouts, etc. All these lead to team wins but dont show anywhere else. Nevertheless, this term accounts for 0-8% of total WN6 score

To view an S-curve: http://en.wikipedia....igmoid_function

So as your win-rate goes above 48% (the population average), you get bonuses to your WN6, up to a point, at which point the contribution levels off. Similarly, players lose WN6 points for being below the population average, but again only to a point. I do not know those inflection points aka the point where it begins to contribute less, but its probably in the massive working thread.

Flat tier penalty
+(6-MIN(TIER,6))*-60

This one is for you UMB! If your minimum tier is 6 or greater, this value is 0. If your average tier played is 5, you lose 60 WN6 points. If its 4, you lose 120. A tier 1 only player will lose 360 points off their WN6. This is perhaps the most inelegant portion of the WN6 formula, buuuuuuuuuut, discussion pedotankers is also inelegant. Pedotankers, by the stats, show more skill relative to their peers, because their peers are worse than the general population. Again this is a limitation of trying to compare portions of the population to each other. The pedotankers do something aberrant and thus we get aberrant results. This knocks them down a few points. Your average player should be showing above tier 6 by around 5k games played though.

Example

Using my monthly stats from http://mywotstats.co...w/1002554374/NA (thank you stumpjumper8)

Tier   7.6
Frag/g 1.57
Dmg/g 1837.44
Spot/g 1.75
WR   73.2
Def /g  1.11

Which results in these WN6 point values

Frag/g 730
Dmg/g 767
Spot/g 219
WR   111
Def /g  248
Tier 0

Total   2074 (rounding, etc)

Questions & Answers

Post 'em, and I will try to answer. You might even get Praetor et al to join in. This post is already too long.

TL;DR
Spoiler                     

Edited by CrabEatOff, Feb 01 2013 - 01:04.


SeanPwnery #2 Posted Jan 31 2013 - 17:12

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Props for explaining it... the average player's head might explode though with all the maths involved.  :Smile_ohmy:

Blackhorse_Six #3 Posted Jan 31 2013 - 17:15

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Ok, where do you go to view or DL WN6 ?

CrabEatOff #4 Posted Jan 31 2013 - 17:19

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View PostBlackhorse_Six, on Jan 31 2013 - 17:15, said:

Ok, where do you go to view or DL WN6 ?

Its not a downloadable per se. You can enable it in ingame XVM-stats.

Per Verilogus

Quote

grab xvm test 2 along with the new executable package and change "eff" to "wn" in the config.

You can view ratings on mywotstats, wotlabs, and noobmeter

BeastMode707 #5 Posted Jan 31 2013 - 17:19

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View PostBlackhorse_Six, on Jan 31 2013 - 17:15, said:

Ok, where do you go to view or DL WN6 ?
It has been added to Wotlabs.net

Wraith27 #6 Posted Jan 31 2013 - 17:28

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Damn, Crab...fine work here.  I came back from a business trip last week and saw a WN6 attached to my sig, and had NO idea what the heck it was.  Your masters thesis fixed that, +1.

The only thing I would suggest is to smooth the flat tier penalty.  I agree with the concept, but hate big 'buckets' for sections of the population...I suggest going one decimal in the average tier.  Instead of a 60 point difference between 4.9 and 5.0 (which is effectively 4 and 5), you would have a 6 point difference.  It smooths out the data.

DarthRegis #7 Posted Jan 31 2013 - 17:29

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+1 for Spoiler summary.

CAMN #8 Posted Jan 31 2013 - 17:31

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View PostBlackhorse_Six, on Jan 31 2013 - 17:15, said:

Ok, where do you go to view or DL WN6 ?

Here you go: http://www.noobmeter.../Blackhorse_Six

For you it's 1318 ;)

Your average tier is weighting you down by a lot I guess.

And thanks for the nerdgasm Crab, so many numbers to look at  :Smile_great:

Edited by CAMN, Jan 31 2013 - 17:33.


Blackhorse_Six #9 Posted Jan 31 2013 - 17:32

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View PostCAMN, on Jan 31 2013 - 17:31, said:

Here you go: http://www.noobmeter.../Blackhorse_Six

For you it's 1318 ;)

Thankyou ...

Is that Good or Bad?

CrabEatOff #10 Posted Jan 31 2013 - 17:32

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View PostWraith27, on Jan 31 2013 - 17:28, said:

Damn, Crab...fine work here.  I came back from a business trip last week and saw a WN6 attached to my sig, and had NO idea what the heck it was.  Your masters thesis fixed that, +1.

The only thing I would suggest is to smooth the flat tier penalty.  I agree with the concept, but hate big 'buckets' for sections of the population...I suggest going one decimal in the average tier.  Instead of a 60 point difference between 4.9 and 5.0 (which is effectively 4 and 5), you would have a 6 point difference.  It smooths out the data.

My masters thesis was a survival analysis of some biostat data. Much drier, but prettier graphs.

It is 6 points between 4.9 and 5.0!

(6-MIN(TIER,6))*-60

(6-5)*-60 = -60

+(6-4.9)*-60 =-66

CrabEatOff #11 Posted Jan 31 2013 - 17:33

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View PostBlackhorse_Six, on Jan 31 2013 - 17:32, said:

Is that Good or Bad?

As soon as I locate the values for the scale, I will insert them. Average is like 850 though, so you are doing pretty good.

Garbad #12 Posted Jan 31 2013 - 17:34

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Its better than efficiency, but still has serious issues, including:

- win rate capped at 65%, despite people proving they can solopub well beyond that
- not adequately scoring scouts/mediums, overrating td/arty
- no way to include exp/game (admittedly tricky)
- no way to value tactical skill, but far the most important part of the game

Its an ok rough guide, and better than efficiency to be sure, but hardly gospel. I still think comparing tank to tank played recently with a large sample size under the same circumstances comparing win rate, dpg, exp/game, and kdr is the only truly reliable comparison.

Blackhorse_Six #13 Posted Jan 31 2013 - 17:37

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View PostCrabEatOff, on Jan 31 2013 - 17:33, said:

As soon as I locate the values for the scale, I will insert them. Average is like 850 though, so you are doing pretty good.

That's cool, Thanks.

I don't pay alot of attention to it because I spend alot of ammo on Recon-by-Fire and Suppression.

Edit: ... Wow ... Unicum ... Really? ... LOL ... Well then, I'd better get serious ...

dualmaster333 #14 Posted Jan 31 2013 - 17:38

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Wow, so much magic!  Or math.  Pretty much the same thing, right?


Nice summary.  I'm glad to see my efficiency and WN6 put me at about the same spot - I guess I wasn't farming cap points too excessively?

CrabEatOff #15 Posted Jan 31 2013 - 17:40

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View PostGarbad, on Jan 31 2013 - 17:34, said:

Its better than efficiency, but still has serious issues, including:

- win rate capped at 65%, despite people proving they can solopub well beyond that
- not adequately scoring scouts/mediums, overrating td/arty
- no way to include exp/game (admittedly tricky)
- no way to value tactical skill, but far the most important part of the game

Its an ok rough guide, and better than efficiency to be sure, but hardly gospel. I still think comparing tank to tank played recently with a large sample size under the same circumstances comparing win rate, dpg, exp/game, and kdr is the only truly reliable comparison.

There is no replacement for dossier analysis taking into account history and maturation effects and I wouldn't every try to say otherwise. WN6 is just the best juggling of the website stats we've got, and loads better than efficiency.

Just like you wouldn't use the SAT alone to admit someone into your undergraduate program, don't use WN6 alone. Every facet matters.

Besides I addressed all those concerns! And this post definite was not aimed at you Garbad. You can read a formula, and know about measurement and stats. But I guess we can never have enough caveats.

CAMN #16 Posted Jan 31 2013 - 17:40

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View PostBlackhorse_Six, on Jan 31 2013 - 17:37, said:

That's cool, Thanks.

I don't pay alot of attention to it because I spend alot of ammo on Recon-by-Fire and Suppression.

Either way, you wouldn't be able to see if you are good or bad with this formula. Since you have over 5k battles with your Tetrach and 5k more with your M2. It's the pedotanker thing that Crab posted about.

Wraith27 #17 Posted Jan 31 2013 - 17:42

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View PostCrabEatOff, on Jan 31 2013 - 17:32, said:

My masters thesis was a survival analysis of some biostat data. Much drier, but prettier graphs.

It is 6 points between 4.9 and 5.0!

(6-MIN(TIER,6))*-60

(6-5)*-60 = -60

+(6-4.9)*-60 =-66

Nice!  I was too lazy to drop numbers into it to check.  Now I have to drag mine up out of the yellow (I hate yellow).

Mourneblade #18 Posted Jan 31 2013 - 17:46

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My head hurts lol

Garbad #19 Posted Jan 31 2013 - 17:50

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View PostCrabEatOff, on Jan 31 2013 - 17:40, said:

Besides I addressed all those concerns! And this post definite was not aimed at you Garbad.
Nor am I upset -- I'm generally ranked in the top 25 in every metric anyone has every come up with. Whether I am ranked #5 or #15 or #100 means nothing to me. Its just that people need to realize these rankings need a liberal dash of salt.

Blackhorse_Six #20 Posted Jan 31 2013 - 17:51

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View PostCAMN, on Jan 31 2013 - 17:40, said:

Since you have over 5k battles with your Tetrarch and 5k more with your M2. It's the pedotanker thing that Crab posted about.

Oh, Here we go ...

This is the argument you Tier Ten E-peeners always use to compensate for your never having been a tanker in the Real World, so you falsely inflate your own egos with meaningless crap about cartoon tanks.

I play what I enjoy, which is the reason for the game - Entertainment.

I do so without apology to you or anyone else.

Deal with it, Prive ...  :Smile_sceptic: