Studying the Math/ Grind/ RNG in Destiny

[Sennex 1,903]

So my number one problem with Destiny is what we all know as "The Grind". 

 

Whether it is Weapon Parts, Motes, Faction, Etheric Light, etc.... we have all played for over a year to acquire shiny objects that did nothing more than reinforce that we needed to Keep playing. It has bothered me for the last few months to a point however since TTK it has bothered me more because it is far more blatant.

 

I don't know if you guys care, but I was going to gather up the various posts across the internet and share them here. 

 

My goal is not to make others stop playing, or get folks upset, but to actually track the changes as Bungie does their best to create newer and shinier carrots.

 

 

[Sennex 1,903]

Post #1

https://www.reddit.com/r/DestinyTheGame/comments/3sitny/bungie_it_took_me_32_bounties_91750_xp_and_44/

 

Bungie: It took me 32 Bounties (91,750 XP) and 44 Motes of Light + 1 Focused Light Buff totaling - 157,750 XP to max out a pair of Bog Wild Boots. Please tell me there was a "bug," if not, this needs looked at.

 

Over the past couple days I've been wondering how much it takes to level up gear. After doing multiple tests and using DestinyStatus.com, the first circle on Legendary Boots only takes 5,058 XP to fill it in. Which went in line with most of my testing I did when I used Motes of Light AND turning in bounties. So, here we go to the reason why I am making this post.

• This was after 16 Bounties (41,500 XP) : http://i.imgur.com/MJL8Xpm.png[1] 
• This was after another 16 Bounties for a TOTAL 32 Bounties at 91,750 XP : http://i.imgur.com/hpjAPq1.png[2] 

Feeling pretty frustrated, I then started testing how much a Mote of Light gives, they give 1,000 XP.

I then popped a Focused Light Boost (Red Bull Code 50% increase), so that would mean now a Mote of Light = 1,500 XP. I tested it on a Kingslayer Shell and it did in fact jump to 1,500 XP when I refreshed the page.

With a Focused Light popped, I then had to use 44 Motes of Light exactly to fully upgrade my boots. For a total of66,000 XP just on Motes of Light.

Making it a grand total of 157,750 XP used to level up ONE single piece of gear. SURELY there has to be something wrong here. It shouldn't take 3 days worth of bounties to level up 1 piece of gear, that's completely insane.

Are the bounties "bugged" where some are not giving their CORRECT pay out of XP or not giving it at all? Either way, where did all the XP go?

EDIT #1 : I just did another test. I completed a 2,500 XP Bounty. I made sure I only had on ONE piece of gear (Boots). I turned in the Bounty and the FULL 2,500 XP was applied to my Light Level Up Bar (for the 5 motes) and only 500 was applied to the Boots. There is something clearly wrong here OR they have nerfed how much XP is applied. Either way, this was never brought up by Bungie.

EDIT #2 : In one more test, Motes of Light XP (1,000 or 1,500) are FULLY applied to said piece of armor/weapon.

EDIT #3 :

• Video proof of applying only the 2,500 XP to my Boots only : https://www.youtube.com/watch?v=p1JrFxrwhQw[3]
• XP Bar Prior to 2,500 XP : http://i.imgur.com/NfD1ToY.png[4] 
• XP Bar AFTER Turn In : http://i.imgur.com/6XmSAhm.png[5] 
• Boots Prior to 2,500 XP : http://i.imgur.com/W2FyvVU.png[6] 
• Boots AFTER Turn In : http://i.imgur.com/bXHE2R9.png[7] 

[Sennex 1,903]

Followup to Post #1

 

I just spent a lot of time testing this last night, was going to write up a post but may as well add it here. I have more details (don't have my notes with me) but my testing lines up with OP's results.

I tried blues, purples, exotics, all got the same amount of XP.

Also tried equipping some fully leveled items, didn't change how much XP was applied to non-leveled items.

I did my testing by loading destinystatus.com, applying some XP, then reloading destinystatus.com

Class item boost means equipping a class item that has "increased rate for hand cannon/etc"

 

Item                                                      Weapon             Armor (including Ghost shell)                Subclass/Light Level Bar

 

2500 XP Bounty                                    525 XP                500 XP                                                    2500 XP

3000 XP Bounty                                    600 XP                ?                                                            3000 XP                                            

Mote                                                     1000 XP               1000 XP                                                None

Mote with Telemetry                             1312 XP               N/A                                                          None

Mote with Class Item Boost                  1312 XP               N/A                                                         None

Mote with Telem + Class Item              1312 XP               N/A                                                         None

As you can see, bounties are either bugged or have been nerfed for some reason.

------------------------------------------

 

 

"... bounties are either bugged or have been nerfed for some reason."

 

Nerfed. It would explain why Bungie gave us 16 bounty slots... Because we'll need them.

 

Looking around Destiny, it also aligns with other displays of Bungie logic (paraphrasing to follow):

Bungie statement: "Hey kids! In light of all the salt about weapons parts droughts we're going to allow you to buy weapons parts for glimmer very soon."

Bungie action: Nerf glimmer earning potential when you make too much too fast, in spite of the fact they've given us glimmer supps and ghosts that increase earnings.

It's all subterfuge on their part. There is just too much of this type of logic displayed since TK dropped, and in too many ways, for it to be interpreted as anything other than them publicizing what they give to us while simultaneously taking something/changing/nerfing an associated item.

[Sennex 1,903]

Post #2

 

You will never be Max Light Level, and I'll show you why. (statistical breakdown)

 

So, I decided to do some math and figure out how exactly the new "Forever 29" thing was going to play out. The following data uses a few assumptions, some of which I put into Bungie's Favor, as I didn't know exact numbers.

In the data below, the following was assumed:

• The Max Light Level will increase in 4 months (or approx 18 weeks). This is based off the release schedule of year 1.
• All items in the Raid have a 50% drop rate (obviously, they don't. Some items are in more than 1 loot pool)
• An item has a 10% chance to drop at max light level. This means you have a 10% chance of a 50% chance to get a max light level item in any given slot.
• You're only means of Max Light Level gear is from the raid

So on to the data.

This is template for a single player in the equation. Basically, every they get one roll at each slot every week. If that Roll is a 1-5, then they hit a jackpot and got Max LL item. An "O" is flagged at the bottom to show that a Max LL item in this category has been obtained. If after 18 weeks, a player has obtained 1 max LL item for each category, they have hit Max LL and their "X" becomes and "O".

http://i.imgur.com/Fmnf8N2.png [1]

Now, These markers carry over to this template here:

http://imgur.com/2SC3Vcr.png [2]

What you'll notice is that in 20 cases, 0 players will have reached max light level.

Obviously, 20 isn't enough for a solid statistic, so I ran it multiple times. Out of 2000 players, only 12 players reached max light level. Or 0.6%.

Again, obviously some of this is bad data and doesn't match the actual drop rates in game, but I'd like to think I've been generous with the possibilities.

If anyone is curious about the excel functions.

The basic attempts are used as =RandBetween(1, 100).

Conditionals were =IF(OR(Attempt1<DropRatePercentage, Attempt2<DropRatePercentage, etc...

So what this means, is that yes, we are back to the Forever 29 scenario. You will never be max light level.

Lastly, there are obviously other ways to get Max Light Level items, and that is great, but considering all of them are also on weekly 1-time resets, your odds are still terrible.

[JsinOwl 644]

I was going to share this, might as well stick it here:

http://kotaku.com/for-two-months-all-i-played-was-destiny-i-m-taking-a-1741788398

Sorry, but copying the article text is too big a pain on my phone.

When I took my break from Destiny, it was primarily because they obsoleted all the gear I had worked so hard for. The infusion mechanic rights this wrong, assuming we will be able to keep infusing y2 items no matter how high the light level cap rises.

The amount of time it takes to get stuff, or level stuff doesn't bother me. I play simply because I enjoy the act of playing, and when I no longer do, I'll stop. Whether it takes 5 hours or 5 months to max out a pair of boots makes no difference to me. That said, I completely understand where you're coming from Bart. Ultimately, there's only so long one can play the same game before it becomes stale and there's no amount of patching that will change that.

CoD has been doing this forever with the prestige mechanic. Is there anything more pointless in all of gaming than completely resetting your progress for a bit of 'prestige'? It's there for no reason other than to keep people playing ad nauseum.

[Sennex 1,903]

Should probably put that in its own post.

[Sennex 1,903]

Post #3

 

https://www.reddit.com/r/DestinyTheGame/comments/3s6wdz/equilibrium_adjustment_in_destiny_a_crucible_data/

 

Equilibrium Adjustment in Destiny - A Crucible Data Analysis Story

 

*Warning – This is a rather long discussion of some data analysis, which reaches conclusions that most likely everyone already knows. But it’s a cool data-story. If you want the quick and dirty, you can see the related graphs in this album [1] *

 

Background

 

Last week, u/MasterBarek [2] visited my website and suggested looking at K/D stats for individual weapons over time. The idea was that seeing usage weapon rates like those here[3] is useful, but information on the effectiveness of weapons in PvP, and possibly identifying under-utilized guns, would also be nice to see.

 

After thinking about the problem and analyzing some data from the API and my website, I came across some patterns which I thought people might find interesting. What follows is a discussion of the data analysis I went through, and some probably not novel conclusions that came out of it. The basic patterns are similar for most weapon types, so I’ve focused the discussion on Pulse Rifles and Nirwen’s Mercy. I’m more of a PvE person personally, so I would appreciate any other thoughts / explanations as I don’t have the most in-depth understanding of PvP issues.

 

Comparing Weapon Effectiveness and Usage

 

So, one initial thought might be that more effective weapons should be used more, and we should see a positive relationship between usage rates and effectiveness. I’ll explain later why I think we don’t end up observing this, but for now I want to focus on measuring effectiveness.

 

For each match, the API lets you observe how many kills a player got with a specific weapon, and how many overall kills/assists/ and deaths. It does not let you see how many times a player died while having a specific weapon in hand. So, in terms of K/D, I look at the number of overall kills to deaths of players who used specific pulse rifles as my first measure of effectiveness.

 

Of course, Kills aren’t the only measure of performance. To get at overall performance, I also look at two other statistics. First, what is the ex-post win percentage of players who used a specific weapon? This is pretty simple – for each player-game observation (where the player got at least 1 kill with the specific weapon), what is the percentage of observations that won? For a more specific measure, I used an SVM to calculate the probability of winning a match based on your Specific weapon Kills / Remaining

kills/Deaths/Assists/Suicides/Resurrections Performed/and Orbs dropped. This is a quick and dirty approach, which only has a successful prediction rate of around 70%. Regardless, I like this a little better than the ex-post win percentage, because players who had a good game but lost will still end up having a pretty high “effectiveness” score.

 

Below are scatter plots for each measure of effectiveness vs. the number of player-game observations in a random sample of Rift and Control matches where player’s used a pulse rifle:

 

K/D Measure [4]

Ex-Post Measure [5]

SVM Prediction Measure [6]

 

It may not be surprising that there’s not a clear relationship. That is, the guns which are used most have effectiveness ratings pretty much in the center of the distribution. Does that mean people are using bad guns? I think the answer is no, and here’s my thinking:

 

1) As we move down to less-used guns, there are less observations, so the measurement of effectiveness is getting noisier (more variance).

 

2) We are observing an equilibrium outcome, and the “effectiveness” measure we see is mostly reflecting the fact that it is a highly used gun.

 

Point (2) is really the main explanation and deserves a little more discussion. Consider this extreme example: Imagine there was a gun that was so good, everyone used it. What would the expected win-rate be of players using it? Well, since everyone is using it, it would be 50%. This doesn’t mean the gun is bad, or that there are better alternatives out there, in fact it’s quite the opposite.

 

Equilibrium Adjustment – The Case of Nirwen’s Mercy

 

So my hypothesis (which is not novel, and has likely been known in this game’s community, as well as other games like LoL, for some time now) was that what we are seeing in the scatter plots is just the result of a game-theory type equilibrium playing out. Once a good gun is discovered, it initially does really well. Then more people discover it. This can happen from either playing against it, or through information dissemination – Social media / watching streams / etc. As more people start to use it, the average “effectiveness” stats will start falling. Additionally, we might expect that the first people to discover the good gun will be high-skill players, both because they simply play more and also they might be more likely to notice advantageous differences between weapons.

 

Nirwen’s Mercy provides a great way to test this hypothesis. As can be seen here[7] , Nirwen’s Mercy suddenly became very popular in mid-October. So, using a random selection of Rift/Control matches, I gathered the Skill rating for players using Nirwen’s Mercy over time, sourced from Destiny Tracker[8] . Measuring player skill is a very complicated and difficult task, and DTR does a rather nice job at it.

 

Then, I plotted the average player skill against usage and effectiveness:

 

Nirwen’s Mercy – Daily Average Skill vs. Average Usage [9]

 

Nirwen’s Mercy – Daily Average Skill vs. Average Effectiveness [10]

 

Now, these measures are noisy for sure, but the graphs seem to show that the hypothesis plays out somewhat nicely. The rapid increase in usage is accompanied by a decline in average player skill. Moreover, on the initial uptake of the weapon, the average player performance with the weapon falls quite substantially. This makes sense, as it was a new weapon and players need to learn how to use it effectively. After about 4-7 days, behavior seems to reach equilibrium. So adjustment time in Destiny appears to be rather quick.

 

Epilogue

 

I saw this and thought it was a cool example of how player behavior adjusted to an equilibrium in Destiny. Similar patterns played out for the shotgun Conspiracy Theory-D, and the graphs for that are below:

 

Conspiracy Theory-D – Daily Average Skill vs. Average Usage [11]

 

Conspiracy Theory-D – Daily Average Skill vs. Average Effectiveness [12]

 

So, hopefully that was interesting, and provides some food for thought. The main takeaway for me is that measuring weapon-effectiveness based on match outcomes alone is probably not going to be very informative, and I’ll need to do some more thinking as to whether or not a reliable measure can be created using just the API available data.

[Sennex 1,903]

Post #4

How big is the Dreadnaught?

 

Tl;dr: Length of the Dreadnaught is equal to the Moon's diameter: 3,475km.

 

Hey Guardians. I have seen few popular posts that discuss the mindblowing size of the Dreadnaught. Let's face it, that thing is HUGE. I wanted to nail down a more accurate sizing of the Dreadnaught and this [1] photo seems to be the best, though it is horrible due to the perspective. Here [2] are notable landmarks for the Rings of Saturn with Dreadnaught included. Edit 1: User /u/JazzmastaJ [3] posted a similar analysis here[4] with a much more detailedimage [5] . Between the two of us, we should be able to nail down an accurate range of size.

 

So let's add some numbers. The C Ring is 17,500km across compared to Earth's diamater, which is 12,740km. So already we know that earth will fit inside C Ring with room to spare. B Ring is 25,500km across, but due to the perspective of this photo that number really isnt of much use.

 

I took the liberty of comparing the distance from the edge of C Ring to the edge of the 'hole' that the dreadnaught created and it appears to be about 8,750km (due to perspective it could be as large as 12,115km but lets be conservative). The Dreadnaught is about 40% the size of the hole, and the hole itself appears about the same size as the distance from C Ring to said hole (making the hole 8,750km). This gives the Dreadnaught length as 3,500km! (Our moon is 3,475km in diameter)

 

That's no moon...

 

Let's talk about mass. Most of the dreadnaught is seemingly empty space. In the darkblade strike you walk into what seems to be a middle chasm and mostly empty space with giant hanging prisons or something. Let's guess that the Dreadnaught is about 25% mass, and 75% empty space. I would assume the material is probably somewhere between the density of Iron (7.8 g/cm³⁾ and Limestone (2.7 g/cm³⁾ for an average of 5.25 g/cm^3.

 

The width of the Dreadnaught appears to be 27% of the length, making it 950km across (diagonally since it is a diamond shape). We can now calculate the volume: 950x950x3500= 3,158,750,000km^3. Multiply by 25% for mass: 789,687,500km^3.

5.25g/cm³ = 5250 kg/m³ & our mass = 7.897e+17m³

Multiply! 5250 * 7.896875e+17 = 4.15e+21kg! (7.35e+22kg is the moon's mass) but these are hard number to conceptualize, there is only one option... Do more math!

 

Okay! Let's find out what the gravitational pull would be if you were standing on the edge of the hole the Dreadnaught made. We have the mass, we can assume a standard 100kg Guardian, we know the radius of the hole (8,750,000m), and we can look up the universal gravitational constant (6.67408e-11 m³ kg^-1 s^-2). Now plug into the gravitational force equation: F=G((m1*m2)/r²⁾ = 0.3617N. Which gives an acceleration of 0.0036m/s^2. This is 0.03% of Earth's gravity which would hardly compare to Saturn's gravitational influence on the Rings.

 

Edit 2: Some have pointed out that other images in-game would provide better scale and I believe they are right! If you can find a good image and put it up on imgur I can take a look and refine my results. I noted below that the current possible range of size should be somewhere between 3400km - 5500km based on perspective of the first image. Hopefully we can get that range narrowed down some.

 

Edit 3: /u/JazzmastaJ [6] came up with some great images: Image 1 [7] & Image 2 [8] .

Based on some rough calculations and measurements: Image 2 shows the Dreadnaught at 1,275km (quite smaller than our original numbers). Image 1 is more difficult. I cannot tell quite where C Ring ends and B ring begins, there are two options that give the Dreadnaught size at: a) 1,600km or 3,635km. 'a' is more in line with image 2, but 'b' is more in line with our original calculations... Conclusion: We need more data!

 

Edit 4: /u/monarch_j [9] pointed out this[10] post where /u/DLuke5853 [11] came up with a length of 3,444km which is very nearly the number I got from the first image! I am calling it now, that the design of the 'naught is intended to be the diameter of the Moon and is therefore 3,475km

[Sennex 1,903]

Post #5

 

October Crucible Stats

 

https://www.reddit.com/r/DestinyTheGame/comments/3r5em7/octoberish_crucible_stats/

 

It's your Crucible statistician Kerrsive here, and I wanted to give you guys a look at the Crucible figures I've been tracking over the past few weeks. I hadn't been tracking these things lately, but with the revamp of Guardian GG[1] , I thought I'd get back to charting out Crucible stats.

And without any further ado, here are your weapon class stats for the last two-plus weeks.

Crucible Weapon Kills -- Late October

1 of 3

Total Kills by Weapon Type

2 of 3

Total Kills by Primary and Special Weapons

3 of 3

 

Total Kills by Heavy Weapons and Abilities

 

 

 

[2]

 

Methodology: I use Destiny Tracker's Population Stats[3] each day to get a running total of the Crucible kills for each weapon type. I use a spreadsheet to calculate the daily kills for each weapon, I aggregate the daily totals, and I use the totals to give me a percentage. Then I make charts with lines and stuff.

Green section on the charts represents Iron Banana. Yellow section represents Trials of Osiris. The charts all show the same information, but I made three: (1) all weapon types, (2) primaries and specials, and (3) heavies and abilities. The data does not change between the charts; I simply made multiple to make them clearer and less jumbled.

 

Going forward, I'm going to track this more. Enjoy.

 

Edit -- The one thing I will say about these stats is: Bungie, your nerf of special ammo has done nothing to stop shotgun dependency. It has ruined the other two classes of special weapons because there is never ammo for them. Shotguns don't waste ammo because they are one-shot kills. Snipers and pulse rifles are much less forgiving with ammo (I have 72% sniper headshots in Crucible, so don't tell me to "get gud"). I never have sniper ammo while kids run around with shotguns for primaries. Your ammo nerf didn't change shotgun abuse. Undo it.

[Baabcat 1,646]

On the xp needed to level stuff up I saw a you tube video soon after TTK came out that suggested the gains from just using stuff on missions etc was a lot more than the gains you would make by cashing in bounties. Seemed like the intention was to level gear by playing, and bounties were more aimed at faction levelling

Never tried it myself but might be worth checking out.

[Sennex 1,903]

On the xp needed to level stuff up I saw a you tube video soon after TTK came out that suggested the gains from just using stuff on missions etc was a lot more than the gains you would make by cashing in bounties. Seemed like the intention was to level gear by playing, and bounties were more aimed at faction levelling

Never tried it myself but might be worth checking out.

 

That doesn't really hold true though, the reason being at max level, most mobs only give about 6-12 XP. Also, after finishing the quests, your XP gains drop off significantly, unless you do bounties.

 

I misread your post. Using it on missions, will indeed level it up, as will turning in bounties with it equipped, and using motes.

That is how it has always been.

[techno 3,511]

I remember that video his gear levelled quicker by using it.

[Sennex 1,903]

Since you guys are focussed on that post, here are some other points:

 

 

I know in Vanilla/TDB/HoW, Dregs in Patrol were worth 20 XP.

 

In 2.0/Taken King there are now worth 5 XP.

 

I believe it is only like this because it only takes 25,000 XP to level up and get Motes. Which makes sense. But the fact we have to rely on Motes basically to apply FULL XP on a piece of gear? Absurd. Bounties should be directly applied as well, not just a fraction.

 

I believe XP is gated throughout this game now, even in PvP. I wonder how much XP you get for an Acolyte in King's Fall as opposed to Patrol. Probably a big difference, I'm assuming.

[Plumbers Crack 4,062]

I won't pretend to understand all of it, but it's an interesting thread, Bart

[Sennex 1,903]

I enjoy studying the math and trends in games.