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Gunslinger Lt Math

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  • Gunslinger Lt Math

    Hello Everyone!

    It's that time again. Winter is around the corner, and the holidays are creeping up on us. But most exitingly, the UE overlords have blessed us with a new Lt to do math with... Gunslinger. So lets see if we can determine if Gunslinger is right for you. Here I will post all of my math and reasoning, but if you want, you can simply skip to the results and discussion section to see my data and thoughts on the matter. Hope you find this helpful!

    Equations

    So, the math on this Lt is pretty strait forward. First, he gives you a reduction in the amount of time between tokens in EvE, as well as a chance for 4 bonus tokens at the start of the war. The equations go as thus:

    Time reduction:

    1+S=t

    Here, S is the star level of Gunslinger, and t is the time reduced between tokens in seconds. However, we will be using the unit of minutes in the calculations, so keep in mind 1 second=1/60 minutes.

    The equation for getting four extra tokens at the start is:

    12+2S=B

    Here B is the bonus chance in percent (%). And of course, S is still the star level.

    So for example, if you had a 3 star Gunslinger, you would get a reduction time of 1+3=4 seconds, and a bonus token chance of 12+2(3)=18%.

    Math

    So, first, we need to know what each bonus does for you separately at each level, then we can add them together (for the sake of simplicity, I am using an armory with a three minute base token generation time, but if you want to redo any particular calculation, just use my equations with your armory's reduction time). Also, at the start of the war, you begin with 10 tokens, but because I am calculating tokens generated by the Lt, these are irrelevant.

    So we will take the time we get, divide it by a reduced token-per-unit-time to fund the number of tokens you will receive:

    1 star=120/[3-(2/60)]=40.45 tokens
    2 star=120/[3-(3/60)]=40.68 tokens
    3 star=120/[3-(4/60)]=40.91 tokens
    4 star=120/[3-(5/60)]=41.14 tokens
    5 star=120/[3-(6/60)]=41.38 tokens
    6 star=120/[3-(7/60)]=41.62 tokens
    7 star=120/[3-(8/60)]=41.86 tokens
    8 star=120/[3-(9/60)]=42.11 tokens
    9 star=120/[3-(10/60)]=42.35 tokens

    Note that the base amount of tokens is 40, meaning that the 1 star generates 0.45 (40.45-40.00) tokens per war. However, that number makes no sense in this context, and therefore, all token values will be rounded down as follows:

    1 star=40.45 tokens=0 tokens
    2 star=40.68 tokens=0 tokens
    3 star=40.91 tokens=0 tokens
    4 star=41.14 tokens=1 token
    5 star=41.38 tokens=1 token
    6 star=41.62 tokens=1 token
    7 star=41.86 tokens=1 token
    8 star=42.11 tokens=2 tokens
    9 star=42.35 tokens=2 tokens

    Next, we need to know what the bonus tokens will do. For simplicity, I am showing this as the average result of getting the bonus. Therefore if you have a 20% chance of getting 4 tokens, you average 0.2*4=0.8 extra tokens per war. They are given as follows:

    1 Star=0.14*4=0.56 tokens/war
    2 Star=0.16*4=0.64 tokens/war
    3 Star=0.18*4=0.72 tokens/war
    4 Star=0.20*4=0.80 tokens/war
    5 Star=0.22*4=0.88 tokens/war
    6 Star=0.24*4=0.96 tokens/war
    7 Star=0.26*4=1.04 tokens/war
    8 Star=0.28*4=1.12 tokens/war
    9 Star=0.30*4=1.20 tokens/war

    This means together you get:

    1 Star=0+0.56=0.56 tokens/war
    2 Star=0+0.64=0.64 tokens/war
    3 Star=0+0.72=0.72 tokens/war
    4 Star=1+0.80=1.80 tokens/war
    5 Star=1+0.88=1.88 tokens/war
    6 Star=1+0.96=1.96 tokens/war
    7 Star=1+1.04=2.04 tokens/war
    8 Star=2+1.12=3.12 tokens/war
    9 Star=2+1.20=3.20 tokens/war

    Results:

    Here is the result of the above calculations (repeating the results without calculations for the sake of organization).

    1 Star=0.56 tokens/war
    2 Star=0.64 tokens/war
    3 Star=0.72 tokens/war
    4 Star=1.80 tokens/war
    5 Star=1.88 tokens/war
    6 Star=1.96 tokens/war
    7 Star=2.04 tokens/war
    8 Star=3.12 tokens/war
    9 Star=3.20 tokens/war

    These value are how many extra tokens you should expect to generate on average per war, given a 3 minute base token recharge time.

    Discussion:

    This math was very, very interesting. On average, you can expect anything from 0.56-3.2 tokens/war while using this Lt. However, because of the nature of token generation, there are large spikes in average tokens generated between certain levels of this Lt. Notably from stars 3->4 and 7->8. This is where enough time elapses for one to actually get the full extent of the time reduction bonus from the Lt (note that this will change if you have an armory with a different base recharge time than 3 minutes). Looking at stars 1-3, you only get extra tokens if you get the bonus 4 at the beginning of the war. First looking at the Lt, he looks great, but now it is quite clear that this aspect of his effect is rather underwhelming overall. If you are a player who insists that this Lt is worth it, then you will want to simply level him to 4 star for the bonus.

    Notably, sometimes this bonus results in more tokens than calculated because reapers and players with Layla can sometimes generate more tokens with the extra token they are given. Also, this effect can be amplified by cloning it. However, I doubt this effect is strong enough to take priority in cloning in general, and that is assuming players have the necessary Lts to clone an ability. So most of the time, the vanilla numbers given above will be what you actually get. However, I concede that other facts can increase the token amounts slightly.

    Even though this Lt may not be great for use during wars, he still has some application. You can treat him like Centurion in that you just equip him right before war, and let his power take effect. So in this case, if you have a 1 star Gunslinger, you just equip him at the start of the wars so that you get a 14% chance at 4 extra tokens, then you swap him out for a stronger Lt. In this respect, he is actually pretty useful, and you don't have to worry too much about adjusting your chairs to fit Gunslinger in.

    So in summary, the time reduction on tokens is mostly useless before star level 4, so if you are going to use him all war, you will want to get him to at least 4 star. But he also has the benefit of simply being an Lt that you put in immediately before a war, and he will occasionally pay out very highly.

    Thank you guys for your time, and no matter how you feel about Gunslinger, at least now you have data to make an informed decision.

    Until next time,
    -PerpleX
    Last edited by PerpleX; 12-10-2015, 03:57 AM. Reason: Grammar

  • #2
    Re: Gunslinger Lt Math

    Nice work PerpleX!
    Come join us
    on the official
    Underworld Empire Discord Server
    https://discord.gg/ThdmzmJ

    Comment


    • #3
      Re: Gunslinger Lt Math

      Originally posted by Porcinette
      Excellent Calculation.

      Your math is based on a 120mn EvE.

      Is is safe to divide your results by 120 and multiply by 15, 30, 45, 60, 75, 90, 105 to get an idea how many tokens extra for shorter EvEs?
      So, the values for the token generated at the start will always stay constant no matter what. So multiplying those by a constant would be incorrect.

      Also, the time-dependent part of the equation has a significant amount of round error. So, you would need to multiply the war times by the numbers before they were rounded, and then round again afterwards. Basically you would have to redo the entire calculation for shorter wars unfortunately. I wouldn't even feel confident saying that the multiplication would give you a close guess because of so many different factors.
      Last edited by PerpleX; 12-08-2015, 06:35 AM.

      Comment


      • #4
        Re: Gunslinger Lt Math

        Nice math, thanks.
        48BE8B

        Comment


        • #5
          Re: Gunslinger Lt Math

          The way I see it, he is perfect to use in a pre-war health setup, but basically useless to have seated during war. There are many LTs who give a better bonus, be it as bonus dmg, chance to get free token (Layla), or other. Not many would care to switch him in and out between each hit. Thats a lot of work for a very tiny bonus.

          Overall, I like him for his pre-war setup bonus, and for the artwork.

          Comment


          • #6
            Re: Gunslinger Lt Math

            This tells me that the next level on empire upgrades are coming in the next few months. At 2:30 token regen, the equation here changes enough to make it much more interesting.

            Comment


            • #7
              Re: Gunslinger Lt Math

              Good job! Very useful and clarifying! Thank you!

              Now I wonder if you add Envy (or another "cloning" LT), you have a chance to get 4 tokens from Gunslinger and another 4 tokens from Envy? (with far less probability of course...)
              Or will just improve Gunslinger's chances to give 4 tokens?...

              Comment


              • #8
                Re: Gunslinger Lt Math

                Originally posted by LLL View Post
                Good job! Very useful and clarifying! Thank you!

                Now I wonder if you add Envy (or another "cloning" LT), you have a chance to get 4 tokens from Gunslinger and another 4 tokens from Envy? (with far less probability of course...)
                Or will just improve Gunslinger's chances to give 4 tokens?...
                Unfortunately one can only determine this through experience. If you do it and ever get 8 tokens at once, then you know it is the former, but otherwise, you would need a table of data to determine the latter. However, in either case, the average tokens generated at the start of war increases by a factor of 3/2.
                Last edited by PerpleX; 12-10-2015, 03:51 AM.

                Comment


                • #9
                  Re: Gunslinger Lt Math

                  Originally posted by Dr death View Post
                  This tells me that the next level on empire upgrades are coming in the next few months. At 2:30 token regen, the equation here changes enough to make it much more interesting.
                  This could be the case, but it also tells me that maybe he isn't a good Lt. If you think about it, the job of the creators at phoenix age is to create something that will sell very well, and not give us to much real value. This way, they keep up demand for new Lts.

                  They may have just made the text look very appealing, but in actuality it isn't that great. However, this is a really pessimistic approach to the Lt creation process. I guess it depends if you want to see the glass half-empty or half-full.

                  Comment


                  • #10
                    Re: Gunslinger Lt Math

                    God Tier Black Market Lts (Huge impact): Acceptable Black Market Lts (Somewhat impactful): Vomit Inducing Black Market Lts (none/minimal impact):
                    Centurion (2013)
                    Envy (2015)
                    Hotwire (2013)
                    Scorpion (2013)
                    Anson (2014)
                    Rocket (2014)
                    Miss Conduct (2014)
                    Brutus (2014)
                    Edge (2014)
                    Joaquin (2015)
                    Layla (2015)
                    Gunslinger (2015)
                    Trix (2013)
                    Malina (2013)
                    Victoria Vanderblit (2014)
                    Gunner (2015)
                    Seven (2013)
                    Eve Armstrong (2012?)
                    Fleur (post nerf) (2015)
                    Yokozuna (2015)
                    Buster (2013)
                    Nightshade (2013)
                    Ghost (2013)
                    Tony (2013)
                    Total Count: 5

                    By Year:
                    2013 - 3
                    2014 - 1
                    2015 - 1
                    Total Count: 11

                    By Year:
                    2013 - 2
                    2014 - 5
                    2015 - 4
                    Total Count: 8

                    By Year:
                    2013 - 5
                    2014 - 0
                    2015 - 2

                    2012 - 1?
                    Insignia Upgrade Chances
                    -Under Construction-
                    Chances of upgrading to : (Success/Attempts)
                    Level 2: 100% (26/26)
                    Level 3: 100% (26/26)
                    Level 4: 96% (25/26)
                    Level 5: 96% (25/26)
                    Level 6: 81% (23/28)
                    Level 7: 80% (23/27)
                    Level 8: 74% (23/30)
                    Level 9: 73% (19/26)
                    Level 10: 69% (12/18)
                    Level 11: 60% (12/21)
                    Level 12: 38% (12/34)
                    Level 13: 39% (12/27)
                    Level 14: 35% (12/36)
                    Level 15: 29% (12/36)

                    Comment


                    • #11
                      Re: Gunslinger Lt Math

                      Originally posted by Simplyawsomex View Post
                      God Tier Black Market Lts (Huge impact): Acceptable Black Market Lts (Somewhat impactful): Vomit Inducing Black Market Lts (none/minimal impact):
                      Centurion (2013)
                      Envy (2015)
                      Hotwire (2013)
                      Scorpion (2013)
                      Anson (2014)
                      Rocket (2014)
                      Miss Conduct (2014)
                      Brutus (2014)
                      Edge (2014)
                      Joaquin (2015)
                      Layla (2015)
                      Gunslinger (2015)
                      Trix (2013)
                      Malina (2013)
                      Victoria Vanderblit (2014)
                      Gunner (2015)
                      Seven (2013)
                      Eve Armstrong (2012?)
                      Fleur (post nerf) (2015)
                      Yokozuna (2015)
                      Buster (2013)
                      Nightshade (2013)
                      Ghost (2013)
                      Tony (2013)
                      Total Count: 5

                      By Year:
                      2013 - 3
                      2014 - 1
                      2015 - 1
                      Total Count: 11

                      By Year:
                      2013 - 2
                      2014 - 5
                      2015 - 4
                      Total Count: 8

                      By Year:
                      2013 - 5
                      2014 - 0
                      2015 - 2

                      2012 - 1?
                      Since you gave no context as to where this is from, are we to assume this is your personal assessment of the Lt?

                      Comment


                      • #12
                        Re: Gunslinger Lt Math

                        Originally posted by KingKong
                        I would like to shift Ar least Layla to left hand side. Centurion can now be shifted to acceptable as health insignias have reduced his "must have" importance.
                        good point, centurion used to be one of the most wanted lts due to his bonus, but that has subsided after the introduction of insignias. Due to the important role EvE plays in the game Layla is quite a difference maker.


                        Originally posted by PerpleX View Post
                        Since you gave no context as to where this is from, are we to assume this is your personal assessment of the Lt?
                        To a certain extent yes, the effectiveness and impacts of their abilities are based on a combination of the overall feedback of the community (post nerf fleur, the desire for a lady vice lite lt etc..) and my observations on the usage of these blackmarket lts in the game.
                        Insignia Upgrade Chances
                        -Under Construction-
                        Chances of upgrading to : (Success/Attempts)
                        Level 2: 100% (26/26)
                        Level 3: 100% (26/26)
                        Level 4: 96% (25/26)
                        Level 5: 96% (25/26)
                        Level 6: 81% (23/28)
                        Level 7: 80% (23/27)
                        Level 8: 74% (23/30)
                        Level 9: 73% (19/26)
                        Level 10: 69% (12/18)
                        Level 11: 60% (12/21)
                        Level 12: 38% (12/34)
                        Level 13: 39% (12/27)
                        Level 14: 35% (12/36)
                        Level 15: 29% (12/36)

                        Comment


                        • #13
                          Re: Gunslinger Lt Math

                          Thanks for the time u took to do the math for us all PerpleX. Another BM lt that is a waste of fp, too good to be true that hed actually have a decent benefit. I'd throw this new one into the trash heap @ the far right.
                          And while i agree with majority of that list made, I think some of those lts are more highly-prized based on ur build

                          Comment


                          • #14
                            Re: Gunslinger Lt Math

                            One possibility for using gunslinger is to have a loadout with gunslinger (preferably in RH with envy/vice boosting timer), and then switch to a non-gunslinger loadout every time you use a token, switching back to gunslinger when not using tokens. It would seem like you would get the benefits of gunslinger, but unfortunately, you don't. Here are a couple screen shots:

                            After getting a new token:


                            After switching to non-gunslinger loadout, using a token, and switching back to gunslinger loadout:


                            Notice that the stamina timer has decreased by 36 seconds,corresponding to real time, while the token timer has only decreased by 30 seconds. Somehow, switching loadouts has caused the token timer to slow down by 6 seconds.

                            What ends up happening is that gunslinger's faster token regeneration time doesn't accumulate. It only accumulates if you have gunslinger seated at all times, making him far less useful.

                            I discovered this because I have 2 toons, one where I switch loadouts as above, and one where I don't use gunslinger at all. Every time I compare the token timer between the two toons, one is always 6 seconds less than the other.

                            Devs, could you look into this? I'm not going to bother to submit a ticket because I already have 2 tickets that they have been ignoring for almost a month.
                            Last edited by Carl; 12-10-2015, 09:02 PM. Reason: More information

                            Comment


                            • #15
                              He just keeps getting worse for me.. Having had him seated for 40mins (mind u I did get the 4 tokens finally after 8 wars @6* with 6* Envy) I switched off just long enough to use adren rush and went from 27 down to 25 tokens.. So any tokens you have built seem to magically disappear if you switch him off?!? What is that?! At very least we should get to keep a token if we earned it having him seated as the description implies.
                              Last edited by chelsea; 12-10-2015, 11:33 PM.

                              Comment

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