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Miffyli

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Monday, March 20th 2017, 12:17pm

[Statistics] Distances between shooters and targets, Battlefield 1 edition

Some time ago I did Battlefield 4 kill distances post which aimed to answer question at what distances Battlefield 4 (BF4) soldiers manage to kill other soldiers (and by rough extension, what are the engagement distances). Following this we decided to do the same for Battlefield 1 (BF1).

Compared to BF4, the methods used to gather the data are more sophisticated. The post-processing/analysing also includes additional steps to remove e.g. bias caused by some maps being more common than others.

Details of the data:
  • Using total of 2000 recorded kills per map (BF1 vanilla maps + Giant's Shadow) from multiple rounds. 2000 samples were randomly sampled from larger set of records per map.
  • Only kills by primary and secondary weapons were counted (no vehicles, gadgets or melee)
  • Total of ~15000 records used for plots and analysis below

We could also "patch around" bias from uneven distribution of the weapons, but the goal of numbers shown here is to reflect average game of BF1, including the players' taste for certain weapons or weapon classes.
I.e. these numbers reflect what a BF1 player should experience on average while playing any of the maps.

General kill-distance density
Following plot displays density function of the kill-distances, i.e. how large fraction of players were killed at given distance.
Mean, median, 75th and 90th percentile are also included in the image. "Xth percentile" means point where X% of the density is below that point.
E.g. In this plot 75th percentile is distance below which 75% of the kills happen.


(In case image is not visible: Mean: 30.6m, Median: 15.6m, 75th percentile: 37.0m, 90th percentile: 72.9m)

More than half of the kills happen at under 20m, with high number of kills focusing at around 5-10m and a long tail going well above 100m (max was 428m). 90% of the kills happen at under 73m.
The popularity of SMG (close-range) weapons could partly explain this.
Comparing to BF4, BF1 shares very similar kill-distance density graph and summary values. See more on this few headlines down.

Kill-distances per map
Some of the maps have vividly different themes: One has lots of open area while another takes place in a city. To study these ranges we can calculate statistics per map.
Note: Here we use all available samples per map (more than 2000 in most cases)

Source code

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             Map   Mean   Med  75th  90th
       MP_Forest:  17.9  11.6  21.4  42.7
       MP_Amiens:  20.7  13.9  29.6  48.9
 MP_MountainFort:  27.5  13.1  30.8  63.9
      MP_Chateau:  23.5  14.5  31.2  54.1
        MP_Giant:  30.6  17.0  40.1  70.9 
         MP_Scar:  34.7  17.1  41.7  95.4
 MP_ItalianCoast:  33.2  14.9  44.9  87.7
       MP_Desert:  37.0  19.2  46.0  86.4
         MP_Suez:  39.1  22.0  56.4 101.3
  MP_FaoFortress:  53.2  25.3  64.5 153.8

There's clear difference between some of the maps: Fao Fortress (mountains) has roughly 20m higher 75th percentile than other maps (minus Suez). Interestingly Suez (desert urban-ish) has the second largest kill distances, beating Desert map (desert with lots of open area) by 10m in 75th percentile and 15m in 90th percentile.

At the other end of the spectrum, Amiens (city) and Forest (thick forest) have more than 90% of the kills happening at under 50m, which is below optimal range of longer range snipers such as M1903 and Gewehr 98.

BF1 kill distances vs. BF4
Note: BF4 analysis was done slightly differently, e.g. it included gadgets and melees, and did not 'fix' map unbalance. As such these results should be taken with a pinch of salt.
Since we have very similar analysis done on BF4, we can compare these results. Along with comparing summary-statistics like mean and median, we can plot the densities in same plot.



Studying the graph, BF1 has lower fraction of kills at distances 20-40m but slightly more at above 40-80m.

Using the numbers from BF4 post, mean distance for BF4 is 35m and median is 17m. BF1 has mean of 30.6m and median of 15.6m, both of which are lower than for BF4. While this could indicate that kills in BF1 happen at closer range than in BF4.

It should be noted again that BF4 had different methods for gathering and analysing data. However there does not seem to be any exceptional difference between BF1 and BF4 kill distances.

Horizontal vs. vertical aiming ("Vertical gameplay")
We can also analyse what is the vertical angle between shooter and the target. This "vertical gameplay" where soldiers could have very different heights (e.g. player on a skyscraper and another on ground) spurred some discussion during BF4.

Following plot illustrates density of angles between shooter and the target, from the point of view of shooter. Negative angle means shooter had to aim downwards.


50% of kills happen between vertical angles -1.7 and 1.5 degrees, while 90% happen between angles -12.8 and 14.1. This was calculated by removing (1-0.5)/2 and (1-0.9)/2 of the density from both sides.

Slightly more than half of the kills happen inside 2 degree vertical deviation from horizontal line. At 37m (75th percentile of kill-distances) this translates into total of 2.6m deviation which is roughly 1m more than soldier's height.

The median of vertical angles is 0 and mean 0.45. Interestingly mean is slightly positive and the 50%/90% boundaries have larger absolute value for positive boundary. If we assume players always aim at same part of the body (e.g. torso),
this would mean kills happen slightly more often uphill (shooter aimed upwards) than downhill.

Conclusions and possible future work
Quick summary of conclusions:
  • Most BF1 infantry-on-infantry kills happen at under 20 meters from shooter to target. 90% of kills happen at under 73m.
  • No exceptional difference from BF4, there seems to be less kills at 20-40m range and more on <20m and 40-80m range.
  • Clear differences in kill-distances between some maps. Median ranges from 12m to 25m, while 90th percentile ranges from 42m to 153m.
  • Majority of kills happen at "horizontal" level. I.e. Shooter and target were on similar height. More than half of the kills happen inside -2 to 2 degree vertical angle.
Future work ideas:
  • One could plot out "kill locations" what was demoed in BF4 kill distances post. Maybe a more refined visualization could show something interesting.
  • Kill distances per weapon (class). Problem here is the possible lack of datapoints for some weapons, but this could show if weapons' have overlapping "kill ranges".
  • Engagement distances / effective engagement distances. For example, we could track damage done instead of kills. This could be used to analyze weapons' effective range.
  • Refining this kill-distance study by removing biasses caused by weapons and whatnot.

Credits:
elementofprgess - For doing a lot of the work behind all this. <3!
shellBullet at unknowncheats.me - For providing info that made our job easier.
Links to users' thread list who have made analytical/statistical/mathematical/cool posts on Symthic:
  • 3VerstsNorth - Analysis of game mechanics in BF4 (tickrates, effects of tickrate, etc)
  • leptis - Analysis of shotguns, recoil, recoil control and air drag.
  • Veritable - Scoring of BF4/BF1 firearms in terms of usability, firing and other mechanics.
  • Miffyli - Random statistical analysis of BF4 battlereports/players and kill-distances. (list is cluttered with other threads).
Sorry if your name wasn't on the list, I honestly can't recall all names : ( . Nudge me if you want to be included

VincentNZ

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Monday, March 20th 2017, 2:02pm

I just love things like this. Does that account for kill assists as well? With the new changes to the BAs, I wonder if the result would be different if you counted for average hit distances. Very nice work and summary again, very comprehensible, too.

Miffyli

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Monday, March 20th 2017, 4:25pm

I just love things like this. Does that account for kill assists as well? With the new changes to the BAs, I wonder if the result would be different if you counted for average hit distances. Very nice work and summary again, very comprehensible, too.

Sadly it is only pure kills (as in "Enemy killed"), so indeed this can't be taken as direct "engagement distance density". It would indeed be nice to get hits and/or "damage-done"s so we could start analysing how weapons function at distance on average, and how they relate to stats.
Links to users' thread list who have made analytical/statistical/mathematical/cool posts on Symthic:
  • 3VerstsNorth - Analysis of game mechanics in BF4 (tickrates, effects of tickrate, etc)
  • leptis - Analysis of shotguns, recoil, recoil control and air drag.
  • Veritable - Scoring of BF4/BF1 firearms in terms of usability, firing and other mechanics.
  • Miffyli - Random statistical analysis of BF4 battlereports/players and kill-distances. (list is cluttered with other threads).
Sorry if your name wasn't on the list, I honestly can't recall all names : ( . Nudge me if you want to be included

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Monday, March 20th 2017, 4:35pm

Some time ago I did Battlefield 4 kill distances post which aimed to answer question at what distances Battlefield 4 (BF4) soldiers manage to kill other soldiers (and by rough extension, what are the engagement distances). Following this we decided to do the same for Battlefield 1 (BF1).


Excellent work - I was thinking it would be very nice to combine this with my analysis:

What I propose is a weighted ranking of weapons using the score I have developed at each engagement distance (e.g. score multiplied by the percentage of kills that take place at that distance). Would it be possible to report percent kills at the following ranges: r<=17m, 17<r<=27, 27<r<=36, 36<r<=47, 47<r<=57, 57<r? I have a composite score for each SLR near the center of each of those discrete ranges, and the boundaries of each of those ranges are where the damage models change the average BTK (17 and 27 m for A8E, 27 and 36 for 1907, 36 for CR, and 47 for A8 and RSC)

For future work, I could even break down scoring by maps. For example, on the desert maps, the 1906 is going to score very highly if the mean kill distance is 50 m, whereas on a map like Argonne, I think the 1907 Factory will come out on top with it's average kill distance of 17 m. While these are kind of obvious results, the math might yield some interesting surprises (e.g. the Cei Rigotti and RSC are better than everyone thinks!).

Miffyli

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Monday, March 20th 2017, 4:49pm

@InterimAegis
Sure!

Source code

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0   < d <= 17  : 52.687%
17  < d <= 27  : 13.702%
27  < d <= 36  : 7.274%
36  < d <= 47  : 6.159%
47  < d <= 57  : 4.803%
57  < d <= inf : 15.234%


Note though that these results are biased by popularity of SMGs and whatnot. To get something like "at what range players are accurate" we would have to do ton more tweaking ^^.
But the core idea of your thing is interesting. I once thought about this too but never got time to do it. It would work much better with engagement distances / "accuracy distances" (accuracy plotted against distance).
Links to users' thread list who have made analytical/statistical/mathematical/cool posts on Symthic:
  • 3VerstsNorth - Analysis of game mechanics in BF4 (tickrates, effects of tickrate, etc)
  • leptis - Analysis of shotguns, recoil, recoil control and air drag.
  • Veritable - Scoring of BF4/BF1 firearms in terms of usability, firing and other mechanics.
  • Miffyli - Random statistical analysis of BF4 battlereports/players and kill-distances. (list is cluttered with other threads).
Sorry if your name wasn't on the list, I honestly can't recall all names : ( . Nudge me if you want to be included

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Monday, March 20th 2017, 5:21pm

@InterimAegis
Sure!

Source code

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0   < d <= 17  : 52.687%
17  < d <= 27  : 13.702%
27  < d <= 36  : 7.274%
36  < d <= 47  : 6.159%
47  < d <= 57  : 4.803%
57  < d <= inf : 15.234%


Note though that these results are biased by popularity of SMGs and whatnot. To get something like "at what range players are accurate" we would have to do ton more tweaking ^^.
But the core idea of your thing is interesting. I once thought about this too but never got time to do it. It would work much better with engagement distances / "accuracy distances" (accuracy plotted against distance).


FANTASTIC! I will update my results and shoot you a link. Amazing how much killing gets done inside of 17m.

I want to note that all of my scores are based on hit rater statistics, so I am to some degree taking into account accuracy.

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Monday, March 20th 2017, 8:03pm

So...

... Which weapons perform best out to 37m ?

Just in case I wanna cheese.
still playin' Motorstorm

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Monday, March 20th 2017, 8:18pm

So...

... Which weapons perform best out to 37m ?

Just in case I wanna cheese.

guess.


...rsc, cei rigotti and rem 8 .35
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stuff mostly unrelated to BF4 that interests nobody



bf4
on 13/05/2016
23rd M320FB user on pc(13/05/16)
rush mode score RANK:2794 TOP:2% OUT OF:215398
obliteration mode scoreRANK:994 TOP:1% OUT OF:159466
handgun medals RANK:2236 TOP:2% OUT OF:143874
longest headshot RANK:9512 TOP:4% OUT OF:257589
recon score RANK:10871 TOP:4% OUT OF:274899
general score per minute RANK:10016 TOP:4% OUT OF:294774

bf3
31/3/2012 4:58:

Headshot distance RANK:493* TOP:0%
Revives per assault minute RANK: 6019 TOP: 3%
Headshots / kill percentage RANK:25947 TOP:13%
MVP ribbons RANK:18824 TOP:11%

*= 6 if we not count the EOD BOT headshots

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Monday, March 20th 2017, 8:35pm

guess.


...rsc, cei rigotti and rem 8 .35


But the core idea of your thing is interesting. I once thought about this too but never got time to do it. It would work much better with engagement distances / "accuracy distances" (accuracy plotted against distance).


No guessing, only SCIENCE! (But actually you were correct!) Three plots, one with raw effective TTK and KPR, one with weapon scores at range increments, and a third with an aggregate score weighted by the above engagement distances. Scores are calculated based on an equal weighting of effective TTK and KPR (kills per reload) from hit rater with bullet velocity included.

Take aways:

1) The top weapon by my scores is still the Autoloading 8 Factory because of it's incredible TTK during 80% of engagements.
2) The RSC is #2, because it has a similar TTK to the Auto 8 most of the time, but more killing potential in a 2v1 engagement. This is the balanced choice.
3) The M1916 is #3, because you fire an endless amount of bullets.
4) The Cei Rigotti is #4 - another well balanced choice under 37 m.
5) If ALL you need to do is kill stuff under 27 m, use the 1907 Factory. However, you have only a hope and a prayer of getting a kill after that.
6) If ALL you need to to is kill stuff over 40 m, use the Luger 1906. You still have a hope and a prayer up close, unlike the more specialized 1907.
7) The Autoloading 8 Extended is kind of bad unless you are within 17m (effective TTK is the same as the M1916 at 20 m!).
8 ) The Mondragon is kind of good and bad at nothing in particular. Pretty safe choice, not going to do work for you, though.
9) I have the data for the Mondragon Storm. It is never better than the Mondragon Optical.
InterimAegis has attached the following files:
  • Raw.png (72.6 kB - 39 times downloaded - latest: May 22nd 2017, 2:43am)
  • Scores.png (39.73 kB - 42 times downloaded - latest: May 22nd 2017, 2:44am)
  • Agg.png (21.41 kB - 27 times downloaded - latest: Apr 25th 2017, 8:55pm)

This post has been edited 9 times, last edit by "InterimAegis" (Mar 20th 2017, 9:39pm) with the following reason: Updating statistics, improved graphics.


Miffyli

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Monday, March 20th 2017, 8:59pm

5) If ALL you need to do is kill stuff under 27 m, use the 1907 Factory. However, you have only a hope and a prayer of getting a kill after that.

Woo~. M1907 Trench is even better as you don't have to aim to be (relatively) accurate ^^.
Rep++.
Links to users' thread list who have made analytical/statistical/mathematical/cool posts on Symthic:
  • 3VerstsNorth - Analysis of game mechanics in BF4 (tickrates, effects of tickrate, etc)
  • leptis - Analysis of shotguns, recoil, recoil control and air drag.
  • Veritable - Scoring of BF4/BF1 firearms in terms of usability, firing and other mechanics.
  • Miffyli - Random statistical analysis of BF4 battlereports/players and kill-distances. (list is cluttered with other threads).
Sorry if your name wasn't on the list, I honestly can't recall all names : ( . Nudge me if you want to be included