
01 Nov 2007, 01:11  #1 (permalink) 
Shas'Saal
Join Date: Aug 2006
Posts: 104

Marker light counter analysis: +1 BS or 1 CS?
Last week I was playing a game of warhammer 40k (tau vs. Eldar). And I used a Sniper Drone to shoot at some Dark Reapers in some woods (+5 cover save). There I used the marker light hit of a spotter to increase the BS of the sniper drone or decrease the cover save (CS) of the dark reaper. At that time I thought it wouldn't really matter whether I choose for the +1 BS or de 1 CS. I was wrong. After doing some math I realised it DOES matter!
(Note: when one uses a Marker counter to 'decrease the CS with 1', one subtracts a one from the die roll, effectively increasing the value for the CS: from for example a 5+ to a 6+: when one rolls a 5, with the counter this becomes a 4, thus one needs to roll a 6 for a succesfull armor save. Thus when talking about decrease in CS, I mean in an increase in the value needed to roll to have a succesfull armor save.) The general picture When one calculates the chance of a kill, it depends on the BS of the shooter, the Strength of the weapon used and the targets toughness, and of the armour save: Tokillfunction = (chance of hit)x(chance of wound)x(chance of armour save failure) Example 1: The sniper drones shoots at the Dark Reaper in the woods. The drones scores a hit on a 4,5 and 6, so the 'chance of hit' is (3/6). The chance of wound is given by the strength of the Rail Rifle and the toughness of the Dark Reaper: (5/6). Since the Dark Reaper is in the woods, is has a 5+ cover save, thus it will fail its cover save on a 1,2,3 and 4: chance of armour save failure is 4/6. (The armor save is ignored due to the AP of the rail rifle.) The Tokill function (TKF) becomes: TKF = (3/6)x(5/6)x(4/6) = 60 / 216 = 0,278 If there would be a succesfull Marker hit, the marker counter can be used in two ways (I will ignore the 1 Ld option for this analysis): +1 BS or 1 CS. These two options have different effects on the TKFvalue: BS +1: TKF = (4/6)x(5/6)x(4/6) = 80 / 216 = 0,370 CS 1: TKF = (3/6)x(5/6)x(5/6) = 75 / 216 = 0,347 As can be seen: if the BS is increased, in stead of the decrease in CS, the chance of a kill is higher! Conclusion The conclusion is that, if the 'chance of hit' is lower than the 'chance of cover save failure', then the +1 BS increase should be used. If the 'chance of cover save failure' is lower than the 'chance of hit', then the 1 CS should be used (if one wants the highest kill chance possible). If one has multiple marker hits than can be used, after the use of one counter, has to look again to what the lowest chance is, and decide again according to the above way on how to use the second counter. For the use of the third counter, one has to reevaluate whether what the lowest chance is, and increase that one. (This way it can happen that for example two counters are used for BS increase and one for the cover save decrease.) Analysis The analysis includes some tedious math, that is the reason I presented the conclusion above the analysis, instead of after the analysis: the analysis may be discouraging to read further. The TKF function can be adjusted by marker counters in two ways: BS increase and/ or CS decrease. You could say that the function depends on two variables: the BS and the CS. One can write the TKF in a more general form (for the Sniper Drone vs. Dark Reaper in the woods): TKF = (BS/6)x(5/6)x(1[7CS]/6) If for example the CS is 5+, then the chance of failure is 1[75]/6 = 1 – 2/6 = 4/6. It is a failure on the 1,2,3 and 4. If the BS equals 3, then 'chance of hit' is 3/6: it is a hit on 4,5 and 6. Higher BS scores than 5 can be considered as BS = 5. The TKF can be plot as a function of the BS and of the CS in a threedimensional graph. The vertical axis is the value of the Tokillfunction (thus the chance of a kill), and the two horizontal axis correspond to the BS and to the CS. (Note that the CS only runs from 3 to 6, since 3+ is the lowest cover save possible.) The example above (without the use of the marker counter) corresponds to the black cross in the graph above: a BS of 3 and a CS of 5. If one uses the Marker counter to increase the BS, then the point of TKFvalue (the black cross), will move along the brown arrow, upto the tip of the brown arrow. As can be seen: it goes up hill: the value of TKF increases. If one uses the marker counter to decrease the cover save, effectively this means from 5+ to a 6+ cover save, one will follow the purple arrow. This arrow goes up hill as well, but less steep then the brown arrow of the BS increase. Since without the marker counter, the two starting points or the arrows are the same (just the 0,278 value for TKF), you know that one you apply the marker counter such that you get the steepest arrow, one has the highest possible value for the TKF one can get with the use of a marker counter. How can you now, when in a game, what will give the steepest rise? For this to answer, one needs to go a bit more deeper into analysis of a straightline (also known as a linear function) function. The red and the green lines in the graph above correspond to two crosssections of the TFK. The red lines is for a constant value of the BS (BS = 3), and along the line, the value for CS varies. The green line corresponds to a constant value for the CS (CS = 5+) and along this line, the value for the BS changes. In the graph below, the two crosssections are shown together in one graph. As can be seen, the line with varying BS (let's name it TKF_BS) is steeper than the red line (TKF_CS). Both functions (TKF_BS and TKF_CS) can be written in the form TKF_BS = (a_BS) x BS and TKF_CS = (a_CS) x CS. Where the a_BS and a_CS are two different constants. This constant (in the graph the constant is a simple 'a' is the rise in value of TKF when one goes one step to the right: in increament of +1 BS or 1 CS. As is illustrated in the graph with the black line. The key to this all, are the constants a_BS and a_CS: the larger this constant, the larger the increase in TKF in one increases the BS with 1 or decreases the CS with 1. Thus the larger a_BS, the larger the increase of TKF when one uses the +1 BS marker counter. The larger the a_CS, the larger the increase in the value for TKF when one uses the 1 CS marker counter. But what are these a_BS and a_CS? If CS = 5, then TKF function equals TKF_BS, thus TKF = (1/6)x(5/6)x(1[7CS]/6) x BS = (BS/6) x(chance of wound)x(chance of armour save failure) =( a_BS)xBS Thus:a_BS = (1/6) x(chance of wound)x(chance of cover save failure) Thus the constant a_BS depends on 'chance of failure of cover save' (we take the 'chance of wound' to be constant). Thus the higher the chance of the cover save failure, the larger the value for a_BS, the larger the increase in chance of a kill when one uses a marker counter as +1 BS.The same is true for the TKF_CS function: the constant a_CS is given by a_CS = (chance of hit)x(chance of wound)x(1/6) Thus if the chance of a hit is very large, (high BSstat), then a_CS is very large, and thus the increase in the chance of a kill (the TKFvalue) is large when one uses the marker counter to decrease the armor save.Thus if a_CS is larger then a_BS (thus chance of a hit is larger than the chance of cover save failure), one should use the marker counter to decrease the cover save, because the chance of a kill function rises faster for decrease in cover save, than for increase in BS. If a_BS is larger then a_CS ( thus chance of a hit is smaller than the chance of cover save failure), then one should increase the BS because then the TKF increases faster if one goes one step in the direction of higher BS, then it does for the direction of a worse cover save. Different situations If one shoots at other units using different weapons then used above, only the numerical values changes, but the analysis is still valid. Multiple Marker counters If one can spend more then one marker counter, then each time you spend one, you will have to look which function has the largest constant (whether a_CS is larger or a_BS). If first the chance of cover save failure is larger then the chance of hit, one uses one marker counter to increase the BS. But the use of such a marker counter influences the value of the a_CS constant: it will increase since is depends in the 'to hit chance'. Therefore you will have to, before spending the second marker counter, look againg which chance is larger. Example 2: The BS = 4, CS = 3+ (in a bunker). (We take 'chance of wound' to be 5/6). Then the chance of a hit (4/6) is larger then the chance of cover save failure (2/6). Thus we need to use the marker light counter to decrease the CS by 1: (without use of counter) TKF = (4/6)x(5/6)x(2/6) = 0,185 (1 CS) TKF = (4/6)x(5/6)x(3/6) = 0,278 (as a test: +1 BS) TKF = (5/6)x(5/6)x(2/6) = 0,231 Suppose we have a second marker. After spending the first marker, we notice that the chance of cover save failure remains the lowest. Thus we want to use the 1 CS option again: (2 CS) TKF = (4/6)x(5/6)x(4/6) = 0,370 (as a test: 1 CS, +1 BS) TFK = (5/6)x(5/6)x(3/6) = 0,347 (as a test: +2 BS) TFK = (6/6)x(5/6)x(2/6) = 0,278 Suppose we have three marker counters. After spending two on the cover save, we notice that the chance of cover save failure is equal to the chance of 'to hit'. In this case, it does not matter we use it for +1 BS or 1 CS: (2 CS, +1 BS) TFK = (5/6)x(5/6)x(4/6) = 0,463 When using multiple counters, for the analysis you needs each time to look at the chances before deciding the option used for the marker light.(3 CS) TFK = (4/6)x(5/6)x(5/6) = 0,463 (Last note: to be entirely honest, the TKF_CS needs to be written as: TKF_CS = (a_CS)xCS + b_CS with b_CS as some constant. However, for this analysis, since both functions are equal at the black cross (the two starting points of the arrows corresponding to the use of a marker counter), I ignore this constant b_CS: only the steepness of the function is important. ) 

01 Nov 2007, 01:24  #2 (permalink)  
Shas'La

Re: Marker light counter analysis: +1 BS or 1 CS?
Wow... If you were taking a math major in college, I'm sure you could use this for a paper. "How math factors into gaming." ;D But a very good thing to consider. (I usually use Markerlights to max out the BS any way.)
__________________
"Our suits make us look badass, and you know it!" XV15, Dawn of War: Winter Assault mod Quote:
(0.o) please copy and paste this into your sig and '(__)' help him achieve world domination. 

01 Nov 2007, 01:49  #3 (permalink)  
Shas'O

Re: Marker light counter analysis: +1 BS or 1 CS?
I have the ideal title for this thread:
When MathHammer goes too far. :P Great write up, pretty informative. I shall use this for Pathfinders in their next outing. Oh, and someone should give you a cookie for doing this.
__________________
Quote:
We have done the impossible... and that makes us mighty. Firefly is pretty much made of Awesome, Funny, and Aww. Sometimes simultaneously. We'd better stop before we quote the entire script. –tvtropes.org 

01 Nov 2007, 02:01  #4 (permalink)  
Shas'O

Re: Marker light counter analysis: +1 BS or 1 CS?
Quote:
Anyway great job and of course +1 cookie! And by the way speaking of which everyone keeps saying who should and who should not get cookies. Does everyone thing I'm retarded or something? That I won't notice and give cookies where they are due? Seriously calm down, I don't need half a dozen emails on the subject, just crowds my inbox. : 

01 Nov 2007, 02:01  #5 (permalink)  
Shas'Saal
Join Date: Oct 2007
Location: Sun Prairie Wisconsin
Posts: 140

Re: Marker light counter analysis: +1 BS or 1 CS?
Very nice... very in depth and yes you do need a cookie like Ravanger Zero said
__________________
Quote:
Quote:


01 Nov 2007, 03:39  #6 (permalink)  
Shas'O

Re: Marker light counter analysis: +1 BS or 1 CS?
Quote:
We just don't know that you already have half a dozen other cookie requests.
__________________
Quote:
We have done the impossible... and that makes us mighty. Firefly is pretty much made of Awesome, Funny, and Aww. Sometimes simultaneously. We'd better stop before we quote the entire script. –tvtropes.org 

Bookmarks 
Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)  
Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
marker light  tecke  Tau  3  02 Sep 2010 02:49 
marker light question  baskotoiea  Tau  2  20 Jan 2009 12:05 
I like the Marker Light.  Daemonette Embrace  General 40K  7  13 Jul 2008 11:47 
Marker light counter  Olle P  Showcase  15  07 Oct 2007 18:18 
Marker light Independence  MYcrimsonTEARS  Tau  2  16 Apr 2006 02:12 