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Edgecase

So you want to maximize your Free XP gain...

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Obviously, having more bonuses is good, and playing more games will get you more Free XP, but did you know you can get more Free XP out of the same flags and camos by stacking them right?

With Missouri reportedly leaving the store in a few patches and a 3x First Win XP weekend going on, there's never been a better time for a quick refresher on how Free XP works, and the best way to maximize your Free XP gains!

TL;DR;F yo math:

Spoiler
  • Stack all +XP and +FXP on a 300% win day for best results. All other slots should help get the best Base XP you can.
  • The best [non-rare] combo currently available is Type 59 camo with all possible +XP and +FXP flags
    • If you can't get that camo but have flags, pick the camo with the most +XP
  • There is no trick to commander XP; it doesn't matter when you use CXP bonuses. Do it some other time.

:cap_look:Update! Since the time of this original post, WG has released three new extra rare camos: Spring Sky, Asian Lantern, and Mosaic. Because these camos are basically equal to or better than Type 59 in every way, they obviously take the top spot if you have them.

For FXP stacking, they go in this order: Spring Sky > Mosaic > Asian Lantern = Type 59 > everything else.


1. How Free XP is calculated

First, there's a basic equation that dictates the amount of FXP you gain in a battle. It's got a little algebra in it, but we'll break down the important parts in a second:

Free XP = Earned XP * [5% of (100% + Sum of XP bonuses)] * (100% + Sum of Free XP bonuses)

That is: FXP = XP * 0.05 * (1+XP_bonuses) * (1+FXP_bonuses)

  • Earned XP here is either Base XP if you're on a regular account, or Base XP * 1.5 if you're on a premium account.
  • All XP bonuses are summed together, no matter where they come from.
    • They're then added on top of the basic 100% XP multiplier (the normal XP with no bonuses)
  • All FXP bonuses are summed together, no matter where they come from.
    • These are also added on top of a basic 100% multiplier (the normal FXP with no bonuses)

There are three main things to notice about this equation.

  1. All the XP bonuses get summed up.
  2. All the FXP bonuses get summed up.
  3. The two sums then get multiplied.

#3 is where our opportunity to optimize comes in, because it's a multiplier instead of just a sum.

Explainer: Additive vs. Multiplicative bonuses

Spoiler

Some bonuses are added together. Others are multiplied. The differences aren't important when there's only one bonus, but once you start "stacking" multiple bonus effects, bonuses that multiply get way stronger. That's because muliplicative bonuses compound each other's effects -- the bonuses make each other bigger. Additive bonuses don't do that.

Here's some examples showing how this works:

  • One "50% bonus" effect on 1000 points
    • Additive: 1000 + 500 = 1500 points
      • 500 comes from (1000 * 50%), which is a "50% bonus"
    • Multiplicative: 1000 * 1.5 = 1500 points
      • 1.5 comes from (100% + 50%), which is "50% bonus"
  • Two "50% bonus" effects on 1000 points
    • Additive: 1000 + 500 + 500 = 2000 points
    • Multiplicative: 1000 * 1.5 * 1.5 = 2250 points
  • Two "100% bonus" effects on 1000 points
    • Additive: 1000 + 1000 + 1000 = 3000 points
    • Multiplicative: 1000 * 2.0 * 2.0 = 4000 points

Multiplicative effects beat out additive effects in two different ways: when there are more bonuses, and when the bonuses are bigger.


2. How to maximize Free XP gain

You may remember a geometry problem from back in school where you need to find the maximum amount of area you can enclose with a certain length of fencing. Yeah, I hated that problem too. But, the answer ends up being a square, because after all the give-and-take between length and width of the fenced area, you get the best results from multiplying two as-large-as-possible numbers together. It turns out we have basically the same situation here.

We get the best FXP by putting together the numbers that give us the biggest value of (1+XP_bonus) * (1+FXP_bonus). Obviously, you get more if you have more XP bonuses, and you get more if you have more FXP bonuses. That's like having more fence length to work with. BUT, there's also the compounding effect -- the "square fence" element, if you will. We'll get the best results from having the most fence AND balancing the "length" and "width" whenever we have to make tradeoffs.

In Warships-ese, that means stacking as many XP bonuses as possible, as many FXP bonuses as possible, and if we have to made a tradeoff (like an XP camo vs. an FXP camo), we pick the one that brings our overall XP and FXP numbers closer to balance.

Short example:

Spoiler

Q: Suppose you have 200% XP and 100% FXP bonuses already, and have to pick a camo. Would you get better results from a +50% XP camo or a +50% FXP camo?

A: The FXP camo would be better in this case.

  • If you take the XP camo:
    • (100% + 250%) XP multiplier
    • (100% + 100%) FXP multiplier
    • 350% * 200% = 700% FXP total
  • If you take the FXP camo:
    • (100% + 200%) XP multiplier
    • (100% + 150%) FXP multiplier
    • 300% * 250% = 750% FXP total

Since the tradeoff amount is equal here, the "square fence effect" means that balancing the numbers closer together produces the best result.

Not all tradeoffs are this easy, of course. The +50% FXP camo would break even vs. a +75% XP camo in this example (both produce 750% FXP total).

Thankfully, WG has made this pretty easy for us in most cases, because the available FXP bonuses are huge percentages (e.g. Papa Papa = 300%), while the available XP bonuses are small percentages (e.g. Equal Speed Charlie London = 50%). That means our "square fence" decisions almost always favor making the regular XP side longer.

In fact, as soon as you throw the Papa Papa (+300% FXP) and Ouroboros flags (+777% FXP) into the mix, +XP% camos just win all the time. My clanmate @Special_Kay ran some numbers to confirm that this is the case for all the high-earning camos:

Spoiler

soffice.bin_2017-12-22_06-13-02.png

For instance, even with the tempting 250% FXP bonus on "This Is Your Day, Commander", it gets beaten by "Frosty Fir Tree" (100% XP, 50% FXP). That's entirely due to the "square fence" effect -- the FXP side of the fence is so long after Papa Papa and Ouroboros that adding to it doesn't matter much at all compared to adding to the XP side. In fact, that 250% FXP bonus almost breaks even with plain old Type 6 camo's 100% XP bonus on a 300% first-win day, and loses to it on any other day, even a 200% day!

So, at the end of the day, your best choice for loadout is:

  • Type 59 Camo (+200% XP)
  • All 5 economic flags that affect XP and/or FXP
    • Equal Speed Charlie London (+50% XP)
    • Papa Papa (+300% FXP)
    • Red Dragon (+100% XP)
    • Ouroboros (+777% FXP)
    • Hydra (+50% XP, +250% FXP)
  • Play on a +300% first-win XP day

If you don't want to shell out for Type 59, your best other options are (in order of decreasing gain): Frosty Fir Tree, Storm Wind, This Is Your Day Commander

If you're missing several items, you'll need to use the formula to figure out which combination gives you the best results:

(100% + sum of XP bonuses) * (1+ sum of FXP bonuses)

Note that this only takes up 5 of your signal flag slots. Use the other three to help you get the highest Base XP possible (I recommend Juliet Charlie as a start).

Thanks again to @Special_Kay for doing all the spreadsheet work!


3. Maximizing Commander XP gain

Commander XP gain, as it turns out, has no trick to maximizing it. Commander XP bonuses are all additive, and it literally doesn't matter when you use them. It also doesn't matter whether you have XP or FXP bonuses active at the time, as they do not affect each other. This seems counterintuitive, but it makes sense once you look at the equation for Commander XP gain:

Commander XP = Earned XP * (100% + Sum of XP bonuses) + Earned XP * (Sum of Commander XP bonuses)

Commander XP = Earned XP * (100% + Sum of XP bonuses + Sum of Commander XP bonuses)

CXP = XP * (1 + XP_bonuses + CXP_bonuses)

The big takeaway here is simply that this equation is all additive. Since there are no multipliers, there is no compounding effect, and therefore there is no benefit (or penalty) for stacking. You simply get a percent of your Earned XP when you use the bonus, regardless of what else is going on.


TL;DR: It was at the top of the post.

Thanks for reading, and happy earning, Commanders!

Edited by Edgecase
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Good stuff right here!

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Thank you @Edgecase, it's posts like these that keep me reading the forums and a welcome relief from the countless "Nerf/Buff/When is XXX arriving?" threads that got endlessly repeated here.

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2 hours ago, Akeno017 said:

Experience camos give more free exp than free exp camos..?

 

Mind. Blown.

The new years free exp camo is rather worthless in this regard with its +200% free exp

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OP forget to add "have a high win rate".

 

The most important part of not wasting exp consumables is to have good games. So grab 2 other purples, get into T10 battle, and farm away. Oh you don't know any purples? awwww that's too bad, enjoy mediocre exp farm wasting expensive consumables.

 

The point here is that without a good win rate, all that consumables are just going to waste.

Edited by NeutralState
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32 minutes ago, Vader_Sama said:

The new years free exp camo is rather worthless in this regard with its +200% free exp

Not worthless, only if your trying to min-maxx fxp rewards, which most probably cant do. Its still good.

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7 minutes ago, Akeno017 said:

Not worthless, only if your trying to min-maxx fxp rewards, which most probably cant do. Its still good.

I don't see myself using up 600+ of these camos 

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24 minutes ago, Vader_Sama said:

I don't see myself using up 600+ of these camos 

I don't see myself ever having 600+ camos.

 

This doest change the fact that most wont have hundreds of papas and ouroburos. Its still a good camo.

Edited by Akeno017

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1 hour ago, NeutralState said:

OP forget to add "have a high win rate".

 

The most important part of not wasting exp consumables is to have good games. So grab 2 other purples, get into T10 battle, and farm away. Oh you don't know any purples? awwww that's too bad, enjoy mediocre exp farm wasting expensive consumables.

Triple unicum divisions do win more, but many times the base xp is lower than a double division. Just have to carry a bit harder than a 3 man div.

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I think it works:

MXEwD0P.jpg

Think what the totals would have been if this had been a really good game!

Next game (1,980 base XP):

0BWhAXj.jpg

Edited by desmo_2

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Really great Edgecase! +1

One small addition to your comprehensive analysis - If you happen to have the Tirpitz w/ its Tarnanstrich special cammo from the Santa's Convoy Missions from 2016, it yields a straight 100% Free XP bonus. 

I've just been putting JUST the Ouroboros flag (+777%) & the Papa Papa flag (+300%) on the Tirp playing a reasonably small number of Ranked games (23 total so far) and have been yielding 20-30K FXP per day (3 play days).

Edited by hangglide42

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11 minutes ago, hangglide42 said:

One small addition to your comprehensive analysis - If you happen to have the Tirpitz w/ its Tarnanstrich special cammo from the Santa's Convoy Missions from 2016, it yields a straight 100% Free XP bonus.

Interesting thing about the way the math stacks up: If you earn ~10% more Base XP in T10s than T8s (due to the higher tier in general), it would more than offset that bonus. While it's not a direct comparison (due to different rates of Premium and camo ownership), T10s in general appear to earn between 20-40% more XP per game on average than their T8 counterparts. So if you happen to own higher-tier ships and don't have a lot of time to play each day, it's worth taking that into account.

 

19 minutes ago, hangglide42 said:

I've just been putting JUST the Ouroboros flag (+777%) & the Papa Papa flag (+300%) on the Tirp playing a reasonably small number of Ranked games (23 total so far) and have been yielding 20-30K FXP per day (3 play days).

Just remember that you're getting a much better use out of those on the First Win than the subsequent ones. If you're short on signals and trying to be efficient, you can run them until your first win then swap them out. :Smile_coin:

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4 minutes ago, Edgecase said:

Interesting thing about the way the math stacks up: If you earn ~10% more Base XP in T10s than T8s (due to the higher tier in general), it would more than offset that bonus. While it's not a direct comparison (due to different rates of Premium and camo ownership), T10s in general appear to earn between 20-40% more XP per game on average than their T8 counterparts. So if you happen to own higher-tier ships and don't have a lot of time to play each day, it's worth taking that into account.

 

 

Hey Edgecase! - Totally understand & agree w/ what you're suggesting - What I really appreciated about your post is that you broke down exactly the mechanisms and the details of the flags/cammos etc. that could be stacked to maximize FXP gain and why, for players to apply to their own situation.   I find what you did really useful because it allows a player like myself to tailor the flag/cammo usage to fit my particular play requirements - i.e. it lets me make decisions on "efficiency" of flag/cammo usage based on play goals/play time necessities (i.e. not only to maximize FXP gains, but other factors as well)

Here are my own parameters and why I gave the Tirpitz example:

  • I currently have all the T10 ships in port (many of the T6-9 ships too) and only have the Pan-Asian line to complete unlocking (currently at T8 Hsienyang & just finished upgrading her fully)
  • I just started dabbling in CV play & have T4-5s in port, mainly practicing in Co-op before subjecting Random players to my CV play - but the near term goal w/ CVs is just so I can accomplish missions that require playing all 4 ship classes (previously, I had been blocked from fully completing these by the CV tasks) - so grinding CV lines is a low priority.
  • Since the grinds have more or less completed & due to the holidays, much of my play has focused on Ranked at T8 & completing the Pan-Asians
  • I do intend to get the Musashi when she comes out in Feb
  • I do intend to fully unlock any new ship lines in 2018
  • I mainly use FXP for 2 purposes:
    • Unlocking FXP ships (Missouri, Nelson, Musashi)
    • Bypassing certain stock configurations of tech tree ships, if too painful - Since I have a deep interest in history, I actually want to play each ship in the tech tree a fair number of games each w/o FXPing past them

Applying your info to my situation allowed me to make the following tradeoffs for "efficiency" of flag usage which is actually a key consideration for me. In my case, Free XP generation is not the only priority.  The Commander's XP gains and XP gains are part of my decision when to apply enough of what flag type.  In other words, I don't want to expend flags which has a 100% XP bonus on a ship that is only going to put that into an Elite Ship XP pool, when it could be used to grind the USN Cruiser Split or French BBs.  In my case, the tradeoff comes down to "what's the most efficient expenditure (i.e. what is enough) of the flags/cammos sufficient to more quickly reach my in-game goals".

  • I'm mainly playing Ranked so the TIrpitz w/ flags that only has FXP bonuses gives a sufficient yield at 20-30K FXP a day w/o expending flags which have additional bonuses such as XP.  I currently have 641K FXP collected so about a week's play (which will happen anyway since the Ranked season is the length it is) w/ these flags in Ranked should easily get me to the 750-800K necessary w/o using flags/cammos which could be used for 2018's new tech tree lines.
  • The current 200% 1st win bonus stacked nicely w/ the Type 59 Cammo which helped me do the 3 upgrades to the Pan-Asian T8 painlessly in a few games - After the 1st win, I switch to the Frosty Fir which has the 100% XP bonus, 50% FXP bonus, 125% Commanders XP bonus to continue grinding that line.
  • I do have 6 19-pt captains that are playable on 37 different ships to "farm Elite Commander XP" - when applicable, I use the Commander boosting cammos

The above strategy allows me to complete the ship goals/grinds in a reasonable, normal play cycle while ensuring I have sufficient numbers of the nice bonus flags/cammos for helping w/ the new grinds coming in 2018 (i.e. where XP and Commander's XP bonuses take priority & FXP collection is secondary).

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sofer watt ees wurth... think....think... lightbulb... 

 

We need those stupid buttons to demount, mount signals... checkboxes, SOMETHING more than we currently have. thank you. 

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In short, run free XP flags and ship XP camo, supplementing the latter with ship XP-boosting flags, special-event first-win bonuses and premium time wherever possible.

It works - I loaded up on the flags like this on a 200% day when I still had a Warspite XP boost mission left to run. The results were... impressive to say the least. I've never had XP returns in the five figures before (I did have a pretty reasonable win).

 

In retrospect I should have been willing to spend a lot more flags and camo while I had those XP boost missions (there were only 25 of them, and I had that many flags to spend). Those buying premium ships, please note.

 

I'm just 35,000 free XP away from the Nelson, thanks to a couple of very nice container prizes (a CCT container raffled by @Lord_Zath which served up 100K FXP, and a 50K supercontainer). That's worth burning flags for. Or spamming the hell out of my Anshan (which gives double the usual FXP anyway).

Edited by Ensign_Cthulhu

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