Siege Times: Monte Carlo simulations

Siege Times: Monte Carlo simulations

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alpaca

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Always wanted to know how long sieges take in 1.13? Nobody ever checks the guides subforum, so here you go

I was made aware that the guides forum is subscription-only, so here is a copy of the post:

So, I wanted to find out how long sieges generally take in the current game version. I believe the table on the wiki is still from the olden days, when you'd always get 1 siege progress, but since then things have changed quite a bit. Since sieges now depend on the siege history, algebraic expressions become pretty much impossible to use since factoring in all the different outcomes is, well, not easily done. But if you are better at combinatorics than I am, please let me know how to do it.

The Basics

You can find info on how sieges work on the wiki. Apart from the mean siege times table, the info seems up-to-date.

Monte Carlo

The general idea of a Monte Carlo simulation is to take a problem that involves any kind of random process and run the problem a sufficiently large number of times, varying the starting parameters randomly or over a given representative sample if needed. Examples for this can be found in nearly any scientific field, for example you could use it to simulate the motion of molecules, the weather, or the spread of the flu. Generally, the questions the MC simulation is supposed to help answer are parameter changes: what happens if people wash hands more often?

In the case of sieges in EU4, I used MC simulations to investigate the probability distribution of how many siege phases you need for certain siege scenarios. Some of the questions one can answer with this are: how much does artillery help? How much do siege leaders help? How long does it take, on average, to siege down a fort of a given level? How long for the 19/20 quantile, or 95% probability of having sieged the fort?

I simulated the siege process to the best of my knowledge using Wolfram Mathematica and implementing a siege behaviour like that observed in the game. I started each scenario 10 000 times (i.e. ran 10k virtual sieges) and compiled a histogram from the results. 10k simulations seems good enough if you're not too interested in far outliers and can be calculated in a few seconds on my rig; the average value generally fluctuated less than 0.1 siege phases. I can also evaluate average siege progress on completion, shifted distribution after one already is at a certain siege progress, etc. but I'm too lazy to prepare all the data for presentation, and most players probably don't care about it much.

Results

All results are given in siege phases. How long these take depends on several values not covered here and not pertinent to the discussion. Since the distributions all look fairly similar (especially to the untrained eye), I put them in spoilers

Here is an overview table of the different scenarios mentioned in detail
Code:
Scenario    Artillery    Leader    Lvl    Blockade    Obsolete    Mean    Median    95% quantile
1    0    0    -2    0    0    11.5    11.    17
2    0    0    -1    0    0    9.8    10.    15
3    0    0    -3    0    0    13.4    13.    21
4    0    0    -2    -2    0    15.7    15.    25
5    1    0    -2    0    0    9.5    9.    14
6    5    0    -2    0    0    5.2    5.    8
7    5    4    -2    0    0    3.0    3.    6
8    1    0    -4    0    0    12.4    12.    19
9    5    0    -4    0    0    6.4    6.    10
10    0    0    -6    0    0    23.7    21.    44
11    1    0    -6    0    0    16.4    15.    27
12    0    0    -5    0    0    18.9    18.    31
13    5    0    -6    0    0    7.85    8.    12
14    0    0    -8    0    0    43.2    38.    86
15    1    0    -8    0    0    23.2    21.    41
16    5    0    -8    0    0    9.5    9.    14
17    5    0    -10    0    0    11.6    11.    18

Scenario 1: Fort level 2, no bonuses

This is the standard scenario for the early game non-capital forts.

Average: 11.5, Median: 11, 19th/20 quantile: 17

View attachment 138016
For the experts: As you can see, the distribution looks sorta Poisson-like, which is very much to be expected given that sieges are random and independent.

Scenario 2: Fort level 1, no bonuses

Capital-only fort. This is equivalent to a level 2 fort besieged by a 1-pip leader

Average: 9.9, Median: 10, 19th/20 quantile: 15


I actually expected more of a difference here, but capital forts aren't that much weaker than normal forts, requiring only 1.6 additional siege phases. In-game the intuitive difference is probably enlarged by capital forts requiring only 5 artillery for a full siege bonus (see below).

Scenario 3: Fort level 3, no bonuses

Capital plus normal fort, or bastion against a leader pip, etc

Average: 13.4, Median: 13, 19th/20 quantile: 21


Scenario 4: Fort level 2, -2 for coastal fort

If the fort is coastal, you need to blockade it or suffer an additional -2 modifier to the die roll. This also works for a bastion if you have no artillery.

Average: 15.7, Median: 15, 19th/20 quantile: 25


This takes quite a bit longer than the normal level 2 fort, so putting some ships there is a really big advantage. This observation corresponds nicely to my in-game experience.

Scenario 5: Fort level 2, +1 artillery bonus

This is a common scenario after artillery becomes available, but is not yet useful in battle, and when widespread application is too expensive.

Average: 9.5, Median: 9, 19th/20 quantile: 14


You may be wondering why this is not the same as a level 1 fort. The reason is that artillery, in addition to providing a bonus, increases your chance for a breach. Without artillery, you get a breach only on a die roll of 14. With a single artillery regiment, you get it on a roll of 13 or 14, so the probability for a breach doubles. Since breaches are high-impact events that provide a full +3 siege progress, and effectivel increase max progress, this is on average 0.4 siege phases shorter than the level 1 fort. Average number of breaches at siege won increases from 0.44 to 0.89 as expected.

+1 artillery is, however, equivalent to getting a +1 obsolete fort bonus, so this scenario also works out if you siege without art but when you already discovered bastions.

Scenario 6: Fort level 2, +5 artillery

You got the money, you got the siege.

Average: 5.2, Median: 5, 19th/20 quantile: 8


Turbo siege mode. More than twice as fast as without artillery

Scenario 7: Fort level 2, +5 artillery, +4 leader bonus

Just out of curiosity how far you can push it. This happened to me in a game only once or twice so far

Average: 3.0, Median: 3, 19th/20 quantile: 6


Scenario 8: Fort level 4, +1 artillery

For bastions or coastal forts

Average: 12.4, Median: 12, 19th/20 quantile: 19

Artillery is even more useful here, saving you >3 siege phases

Scenario 9: Fort level 4, +5 artillery

Probably the most common bastion scenario

Average: 6.4, Median: 6, 19th/20 quantile: 10



Scenario 10: Fort level 6

Star forts or bastions with an unchallenged coastal modifier

Average: 23.7, Median: 21, 19th/20 quantile: 44


To put it simply: you could be here a while. Even the average is more than 2 years on a 30 day siege timer

Scenario 11: Fort level 6, +1 artillery

Star forts with a sprinkle of artillery

Average: 16.4, Median: 15, 19th/20 quantile: 27


Still a while, but more manageable.

Scenario 12: Fort level 5

Technically a bastion with capital fort, or a star fort against a leader pip

Average: 18.9, Median: 18, 19th/20 quantile: 31


Almost two siege phases longer than with an artillery unit on a level 6 fort. The breach chance increase really makes itself felt here


Scenario 13: Fort level 6, +5 artillery

Star forts or bastions with an unchallenged coastal modifier

Average: 7.8, Median: 8, 19th/20 quantile: 12


Now we're talking. Get artillery, lots of it.

Scenario 14: Fort level 8

Well, this is only for academic purposes, really. Or are you willing to wait 4 years for each siege on average?

Average: 43.2, Median: 38, 19th/20 quantile: 86


Scenario 15: Fort level 8, +1 artillery

Let's see if adding artillery helps

Average: 23.2, Median: 21, 19th/20 quantile: 41


This is still quite painful...

Scenario 16: Fort level 8, +5 artillery

Maybe morey arty?

Average: 9.5, Median: 9, 19th/20 quantile: 14


Well, I guess this is sort of ok, but still, those high-level forts are a royal pain in the backside

Scenario 17: Fort level 10, +5 artillery

You sure you don't wanna put a few ships out there?

Average: 11.6, Median: 11, 19th/20 quantile: 18


Batch Results

I also ran a larger dataset, for which I didn't compile the results manually. To understand this table, you first need to realize that the artillery bonus and fort level are effective values. A larger fort level, blockade and leader bonus all work the same way - except that in the game, you need more troops for the higher fort level, you will get the same result for a level 4 fort and a level 6 fort besieged by a 2 pip general. So

effective fort level = fort level - leader siege pips + blockade

That is, a fort level of -6 in the table below can be a level 6 fort, a level 4 fort with no blockade, a level 7 fort with a 1 pip leader, etc.

The same reasoning applies to artillery and the obsolete fort bonus,

effective artillery bonus = artillery bonus + obsolete bonus

Therefore, the effective fort level varies from +3 (siege 4 leader on a capital fort) to -11 (level 8 coastal capital fort without blockade), while the effective artillery bonus varies from 0 to 8 (5 art + 3 levels obsolete)

Then there is MaxProgress: as you discover higher-level forts, the game lets you accumulate higher levels of siege progress. It starts at 12, and increases by 1 for every new fort building you discover. So if you are at tech 14, MaxProgress would be 13.

Note that a value of 10000 siege phases means the siege will not terminate
Code:
MaxProgress   Lvl     Art       Mean       Median        95% quantile
12        3        0        5.86        6        9
12        3        1        5.04        5        8
12        3        2        4.31        4        7
12        3        3        3.63        3        6
12        3        4        3.12        3        6
12        3        5        2.68        3        5
12        3        6        2.35        2        5
12        3        7        2.11        2        4
12        3        8        1.88        2        4

12        2        0        6.62        6        10
12        2        1        5.63        5        9
12        2        2        4.84        5        8
12        2        3        4.19        4        7
12        2        4        3.56        3        6
12        2        5        3.03        3        6
12        2        6        2.62        2        5
12        2        7        2.32        2        4
12        2        8        2.06        2        4

12        1        0        7.53        7        11
12        1        1        6.39        6        10
12        1        2        5.52        5        9
12        1        3        4.73        5        8
12        1        4        4.13        4        7
12        1        5        3.48        3        6
12        1        6        3.02        3        5
12        1        7        2.60        2        5
12        1        8        2.26        2        4

12        0        0        8.59        8        13
12        0        1        7.32        7        11
12        0        2        6.28        6        10
12        0        3        5.40        5        8
12        0        4        4.68        5        7
12        0        5        4.10        4        7
12        0        6        3.46        3        6
12        0        7        2.99        3        5
12        0        8        2.60        2        5

12        -1        0        9.92        10        15
12        -1        1        8.33        8        12
12        -1        2        7.10        7        11
12        -1        3        6.16        6        9
12        -1        4        5.27        5        8
12        -1        5        4.57        4        7
12        -1        6        4.02        4        7
12        -1        7        3.42        3        6
12        -1        8        2.96        3        5

12        -2        0        11.6        11        18
12        -2        1        9.56        9        14
12        -2        2        8.12        8        12
12        -2        3        6.88        7        10
12        -2        4        5.95        6        9
12        -2        5        5.17        5        8
12        -2        6        4.49        4        7
12        -2        7        3.92        4        6
12        -2        8        3.36        3        6

12        -3        0        13.5        13        21
12        -3        1        10.9        11        17
12        -3        2        9.12        9        14
12        -3        3        7.69        7        12
12        -3        4        6.67        6        10
12        -3        5        5.79        6        9
12        -3        6        5.01        5        8
12        -3        7        4.41        4        7
12        -3        8        3.86        4        6

12        -4        0        15.8        15        25
12        -4        1        12.4        12        19
12        -4        2        10.2        10        16
12        -4        3        8.63        8        13
12        -4        4        7.39        7        11
12        -4        5        6.40        6        10
12        -4        6        5.60        5        9
12        -4        7        4.87        5        7
12        -4        8        4.25        4        7

12        -5        0        18.8        18        31
12        -5        1        14.2        13        23
12        -5        2        11.5        11        18
12        -5        3        9.61        9        15
12        -5        4        8.19        8        12
12        -5        5        7.07        7        11
12        -5        6        6.16        6        9
12        -5        7        5.41        5        8
12        -5        8        4.73        5        7

12        -6        0        24.0        21        44
12        -6        1        16.4        15        27
12        -6        2        12.9        12        20
12        -6        3        10.7        10        17
12        -6        4        9.04        9        14
12        -6        5        7.83        8        12
12        -6        6        6.80        7        10
12        -6        7        5.97        6        9
12        -6        8        5.24        5        8

12        -7        0        32.0        28        65
12        -7        1        19.2        18        33
12        -7        2        14.5        14        23
12        -7        3        11.9        11        19
12        -7        4        10.1        10        16
12        -7        5        8.62        8        13
12        -7        6        7.50        7        11
12        -7        7        6.48        6        10
12        -7        8        5.73        6        9

12        -8        0        43.7        39        87
12        -8        1        22.9        21        40
12        -8        2        16.9        16        28
12        -8        3        13.3        13        21
12        -8        4        11.1        11        17
12        -8        5        9.46        9        14
12        -8        6        8.24        8        12
12        -8        7        7.17        7        11
12        -8        8        6.29        6        9

12        -9        0        56.9        52        107
12        -9        1        27.8        26        51
12        -9        2        19.3        18        32
12        -9        3        15.2        14        25
12        -9        4        12.4        12        20
12        -9        5        10.5        10        16
12        -9        6        9.04        9        14
12        -9        7        7.85        8        12
12        -9        8        6.90        7        10

12        -10        0        10000        10000        10000
12        -10        1        37.2        34        70
12        -10        2        22.8        21        40
12        -10        3        17.2        16        28
12        -10        4        13.9        13        22
12        -10        5        11.6        11        18
12        -10        6        9.94        10        15
12        -10        7        8.53        8        13
12        -10        8        7.47        7        11

12        -11        0        10000        10000        10000
12        -11        1        10000        10000        10000
12        -11        2        31.2        28        60
12        -11        3        20.7        19        36
12        -11        4        15.7        15        26
12        -11        5        13.1        12        21
12        -11        6        11.0        10        17
12        -11        7        9.44        9        14
12        -11        8        8.14        8        12

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

13        3        0        5.86        6        9
13        3        1        5.03        5        8
13        3        2        4.32        4        7
13        3        3        3.63        3        6
13        3        4        3.11        3        6
13        3        5        2.68        2        5
13        3        6        2.38        2        5
13        3        7        2.11        2        4
13        3        8        1.87        2        4

13        2        0        6.61        6        10
13        2        1        5.60        5        9
13        2        2        4.83        5        8
13        2        3        4.22        4        7
13        2        4        3.53        3        6
13        2        5        3.04        3        6
13        2        6        2.63        2        5
13        2        7        2.32        2        4
13        2        8        2.04        2        4

13        1        0        7.50        7        11
13        1        1        6.43        6        10
13        1        2        5.49        5        9
13        1        3        4.75        5        8
13        1        4        4.13        4        7
13        1        5        3.51        3        6
13        1        6        3.01        3        5
13        1        7        2.60        2        5
13        1        8        2.31        2        4

13        0        0        8.58        8        13
13        0        1        7.27        7        11
13        0        2        6.24        6        9
13        0        3        5.38        5        8
13        0        4        4.65        4        7
13        0        5        4.09        4        7
13        0        6        3.47        3        6
13        0        7        2.97        3        5
13        0        8        2.61        2        5

13        -1        0        9.84        10        14
13        -1        1        8.30        8        12
13        -1        2        7.07        7        11
13        -1        3        6.09        6        9
13        -1        4        5.29        5        8
13        -1        5        4.57        4        7
13        -1        6        4.01        4        6
13        -1        7        3.40        3        6
13        -1        8        2.92        3        5

13        -2        0        11.4        11        17
13        -2        1        9.49        9        14
13        -2        2        8.01        8        12
13        -2        3        6.92        7        10
13        -2        4        5.98        6        9
13        -2        5        5.17        5        8
13        -2        6        4.50        4        7
13        -2        7        3.91        4        6
13        -2        8        3.36        3        6

13        -3        0        13.2        13        20
13        -3        1        10.7        10        16
13        -3        2        9.00        9        13
13        -3        3        7.73        8        12
13        -3        4        6.66        7        10
13        -3        5        5.79        6        9
13        -3        6        5.02        5        8
13        -3        7        4.40        4        7
13        -3        8        3.85        4        6

13        -4        0        15.2        15        23
13        -4        1        12.2        12        18
13        -4        2        10.1        10        15
13        -4        3        8.58        8        13
13        -4        4        7.39        7        11
13        -4        5        6.39        6        10
13        -4        6        5.59        5        8
13        -4        7        4.84        5        8
13        -4        8        4.28        4        7

13        -5        0        17.7        17        27
13        -5        1        13.7        13        21
13        -5        2        11.3        11        17
13        -5        3        9.51        9        14
13        -5        4        8.16        8        12
13        -5        5        7.05        7        11
13        -5        6        6.15        6        9
13        -5        7        5.43        5        8
13        -5        8        4.72        5        7

13        -6        0        21.2        20        35
13        -6        1        15.8        15        25
13        -6        2        12.6        12        19
13        -6        3        10.5        10        16
13        -6        4        9.03        9        14
13        -6        5        7.77        8        12
13        -6        6        6.75        7        10
13        -6        7        5.96        6        9
13        -6        8        5.27        5        8

13        -7        0        26.1        24        46
13        -7        1        18.2        17        30
13        -7        2        14.2        14        23
13        -7        3        11.7        11        18
13        -7        4        9.93        10        15
13        -7        5        8.55        8        13
13        -7        6        7.46        7        11
13        -7        7        6.49        6        10
13        -7        8        5.72        6        9

13        -8        0        34.2        30        67
13        -8        1        21.1        20        35
13        -8        2        16.1        15        26
13        -8        3        13.1        13        20
13        -8        4        11.0        11        17
13        -8        5        9.40        9        14
13        -8        6        8.16        8        12
13        -8        7        7.15        7        11
13        -8        8        6.26        6        9

13        -9        0        44.9        40        87
13        -9        1        25.1        23        44
13        -9        2        18.3        17        30
13        -9        3        14.6        14        23
13        -9        4        12.2        12        19
13        -9        5        10.4        10        16
13        -9        6        8.95        9        13
13        -9        7        7.79        8        12
13        -9        8        6.88        7        10

13        -10        0        57.3        52        107
13        -10        1        29.1        27        51
13        -10        2        20.6        19        34
13        -10        3        16.3        15        26
13        -10        4        13.5        13        21
13        -10        5        11.4        11        17
13        -10        6        9.78        9        15
13        -10        7        8.45        8        12
13        -10        8        7.46        7        11

13        -11        0        10000        10000        10000
13        -11        1        38.4        35        70
13        -11        2        24.3        23        41
13        -11        3        18.4        17        29
13        -11        4        15.0        14        24
13        -11        5        12.6        12        19
13        -11        6        10.7        10        16
13        -11        7        9.30        9        14
13        -11        8        8.05        8        12

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

14        3        0        5.85        6        9
14        3        1        5.02        5        8
14        3        2        4.31        4        7
14        3        3        3.61        3        6
14        3        4        3.09        3        6
14        3        5        2.70        3        5
14        3        6        2.36        2        5
14        3        7        2.10        2        4
14        3        8        1.89        2        4

14        2        0        6.60        6        10
14        2        1        5.65        6        9
14        2        2        4.87        5        8
14        2        3        4.20        4        7
14        2        4        3.55        3        6
14        2        5        3.02        3        6
14        2        6        2.62        2        5
14        2        7        2.30        2        4
14        2        8        2.05        2        4

14        1        0        7.43        7        11
14        1        1        6.39        6        10
14        1        2        5.51        5        9
14        1        3        4.78        5        8
14        1        4        4.14        4        7
14        1        5        3.48        3        6
14        1        6        3.00        3        5
14        1        7        2.61        2        5
14        1        8        2.30        2        4

14        0        0        8.54        8        12
14        0        1        7.33        7        11
14        0        2        6.27        6        10
14        0        3        5.39        5        8
14        0        4        4.66        5        7
14        0        5        4.11        4        7
14        0        6        3.45        3        6
14        0        7        2.97        3        5
14        0        8        2.60        2        5

14        -1        0        9.77        10        14
14        -1        1        8.29        8        12
14        -1        2        7.09        7        11
14        -1        3        6.16        6        9
14        -1        4        5.28        5        8
14        -1        5        4.58        4        7
14        -1        6        4.03        4        7
14        -1        7        3.38        3        6
14        -1        8        2.93        3        5

14        -2        0        11.3        11        16
14        -2        1        9.44        9        14
14        -2        2        8.01        8        12
14        -2        3        6.88        7        10
14        -2        4        5.97        6        9
14        -2        5        5.15        5        8
14        -2        6        4.51        4        7
14        -2        7        3.94        4        6
14        -2        8        3.37        3        6

14        -3        0        13.0        13        19
14        -3        1        10.6        10        16
14        -3        2        9.03        9        13
14        -3        3        7.69        7        11
14        -3        4        6.65        6        10
14        -3        5        5.77        6        9
14        -3        6        5.01        5        8
14        -3        7        4.40        4        7
14        -3        8        3.87        4        6

14        -4        0        14.9        14        22
14        -4        1        12.1        12        18
14        -4        2        10.0        10        15
14        -4        3        8.59        8        13
14        -4        4        7.35        7        11
14        -4        5        6.42        6        10
14        -4        6        5.59        5        8
14        -4        7        4.83        5        8
14        -4        8        4.27        4        7

14        -5        0        17.3        17        26
14        -5        1        13.6        13        21
14        -5        2        11.2        11        17
14        -5        3        9.58        9        14
14        -5        4        8.18        8        12
14        -5        5        7.07        7        11
14        -5        6        6.18        6        9
14        -5        7        5.43        5        8
14        -5        8        4.71        5        7

14        -6        0        20.2        19        32
14        -6        1        15.4        15        24
14        -6        2        12.5        12        19
14        -6        3        10.5        10        16
14        -6        4        9.01        9        14
14        -6        5        7.77        8        12
14        -6        6        6.75        7        10
14        -6        7        5.95        6        9
14        -6        8        5.24        5        8

14        -7        0        24.0        23        39
14        -7        1        17.6        17        28
14        -7        2        14.0        13        22
14        -7        3        11.7        11        18
14        -7        4        9.87        10        15
14        -7        5        8.56        8        13
14        -7        6        7.41        7        11
14        -7        7        6.49        6        10
14        -7        8        5.72        6        9

14        -8        0        29.7        27        52
14        -8        1        20.1        19        33
14        -8        2        15.7        15        25
14        -8        3        13.0        12        20
14        -8        4        10.9        11        17
14        -8        5        9.33        9        14
14        -8        6        8.12        8        12
14        -8        7        7.11        7        10
14        -8        8        6.22        6        9

14        -9        0        37.9        34        71
14        -9        1        23.7        22        40
14        -9        2        17.8        17        29
14        -9        3        14.4        14        22
14        -9        4        12.0        11        18
14        -9        5        10.3        10        16
14        -9        6        8.93        9        13
14        -9        7        7.77        8        11
14        -9        8        6.89        7        10

14        -10        0        46.2        42        88
14        -10        1        26.5        25        45
14        -10        2        19.8        19        32
14        -10        3        15.9        15        25
14        -10        4        13.2        13        20
14        -10        5        11.2        11        17
14        -10        6        9.67        9        14
14        -10        7        8.41        8        12
14        -10        8        7.46        7        11

14        -11        0        58.6        54        108
14        -11        1        31.3        29        53
14        -11        2        22.3        21        36
14        -11        3        17.8        17        28
14        -11        4        14.6        14        22
14        -11        5        12.3        12        19
14        -11        6        10.6        10        16
14        -11        7        9.22        9        13
14        -11        8        8.04        8        12

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

15        3        0        5.86        6        9
15        3        1        5.00        5        8
15        3        2        4.35        4        7
15        3        3        3.64        3        6
15        3        4        3.13        3        6
15        3        5        2.70        3        5
15        3        6        2.34        2        5
15        3        7        2.09        2        4
15        3        8        1.87        2        4

15        2        0        6.62        6        10
15        2        1        5.62        5        9
15        2        2        4.82        5        8
15        2        3        4.16        4        7
15        2        4        3.52        3        6
15        2        5        3.01        3        6
15        2        6        2.62        2        5
15        2        7        2.32        2        4
15        2        8        2.05        2        4

15        1        0        7.42        7        11
15        1        1        6.44        6        10
15        1        2        5.48        5        9
15        1        3        4.76        5        8
15        1        4        4.13        4        7
15        1        5        3.49        3        6
15        1        6        3.00        3        5
15        1        7        2.63        2        5
15        1        8        2.29        2        4

15        0        0        8.53        8        12
15        0        1        7.26        7        11
15        0        2        6.23        6        10
15        0        3        5.38        5        8
15        0        4        4.67        5        7
15        0        5        4.09        4        7
15        0        6        3.42        3        6
15        0        7        2.98        3        5
15        0        8        2.60        2        5

15        -1        0        9.76        10        14
15        -1        1        8.26        8        12
15        -1        2        7.06        7        11
15        -1        3        6.12        6        9
15        -1        4        5.27        5        8
15        -1        5        4.58        4        7
15        -1        6        4.01        4        7
15        -1        7        3.41        3        6
15        -1        8        2.92        3        5

15        -2        0        11.3        11        16
15        -2        1        9.35        9        14
15        -2        2        8.05        8        12
15        -2        3        6.87        7        10
15        -2        4        5.98        6        9
15        -2        5        5.13        5        8
15        -2        6        4.51        4        7
15        -2        7        3.95        4        6
15        -2        8        3.35        3        6

15        -3        0        12.9        13        19
15        -3        1        10.6        10        16
15        -3        2        8.99        9        13
15        -3        3        7.72        8        11
15        -3        4        6.64        6        10
15        -3        5        5.80        6        9
15        -3        6        5.00        5        8
15        -3        7        4.40        4        7
15        -3        8        3.84        4        6

15        -4        0        14.8        14        22
15        -4        1        12.0        12        18
15        -4        2        10.0        10        15
15        -4        3        8.55        8        13
15        -4        4        7.37        7        11
15        -4        5        6.40        6        10
15        -4        6        5.60        5        8
15        -4        7        4.89        5        8
15        -4        8        4.26        4        7

15        -5        0        17.0        17        25
15        -5        1        13.6        13        20
15        -5        2        11.2        11        17
15        -5        3        9.49        9        14
15        -5        4        8.14        8        12
15        -5        5        7.05        7        10
15        -5        6        6.18        6        9
15        -5        7        5.41        5        8
15        -5        8        4.72        5        7

15        -6        0        19.6        19        30
15        -6        1        15.3        15        23
15        -6        2        12.6        12        19
15        -6        3        10.5        10        16
15        -6        4        8.94        9        13
15        -6        5        7.75        8        11
15        -6        6        6.80        7        10
15        -6        7        5.92        6        9
15        -6        8        5.25        5        8

15        -7        0        23.2        22        37
15        -7        1        17.3        17        27
15        -7        2        13.9        13        21
15        -7        3        11.6        11        18
15        -7        4        9.82        10        15
15        -7        5        8.52        8        13
15        -7        6        7.43        7        11
15        -7        7        6.48        6        10
15        -7        8        5.72        6        9

15        -8        0        28.0        26        46
15        -8        1        19.7        19        32
15        -8        2        15.6        15        24
15        -8        3        12.9        12        20
15        -8        4        10.9        11        17
15        -8        5        9.39        9        14
15        -8        6        8.06        8        12
15        -8        7        7.11        7        11
15        -8        8        6.26        6        9

15        -9        0        35.1        32        65
15        -9        1        22.9        21        38
15        -9        2        17.5        17        28
15        -9        3        14.3        14        22
15        -9        4        12.0        11        18
15        -9        5        10.3        10        15
15        -9        6        8.90        9        13
15        -9        7        7.80        8        11
15        -9        8        6.86        7        10

15        -10        0        40.1        37        73
15        -10        1        25.5        24        43
15        -10        2        19.2        18        30
15        -10        3        15.6        15        24
15        -10        4        13.1        13        20
15        -10        5        11.2        11        17
15        -10        6        9.64        9        14
15        -10        7        8.45        8        12
15        -10        8        7.42        7        11

15        -11        0        48.6        44        88
15        -11        1        28.8        27        48
15        -11        2        21.3        20        34
15        -11        3        17.2        16        26
15        -11        4        14.2        14        21
15        -11        5        12.2        12        18
15        -11        6        10.5        10        15
15        -11        7        9.19        9        13
15        -11        8        8.07        8        12

Notebook

If you have Mathematica and would like to play around with this, here is a copy of my notebook: https://dl.dropboxusercontent.com/u/95609184/sieges.nb
 
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alpaca

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The die goes from 0 to 14 in game, not from 1 to 14 as the wiki claims. I redid the simulations, so the numbers changed a little.
 

Seraphithan

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Are you certain? I'm fairly sure that the worst siege roll is one.

Great work overall. Seems to me that until Starforts hit only sieging with one artillery leads to acceptable siege times, but beyond that it really is +5 or bust.

Have you tested how the increase in max siege progress impacts the various forts?
 
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alpaca

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Are you certain? I'm fairly sure that the worst siege roll is one.

Great work overall. Seems to me that until Starforts hit only sieging with one artillery leads to acceptable siege times, but beyond that it really is +5 or bust.

Have you tested how the increase in max siege progress impacts the various forts?
No, I'm not really sure. I guess it's possible I checked the siege before the first phase was concluded. I'll have a look later. The values don't change that much, anyways. I haven't specifically checked how much the breach additional progress impacts sieges on the different levels, but you can check the results with artillery vs a lower fort level by interpolating the result for, say, level 7 between those of 6 and 8 (linear interpolation is ok). I might run the test a bit more in-depth if I have time.
 

alpaca

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Seems you're right, my bad
 

Arumba

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I wonder if this information might be a better reference guide if it was a table, showing Fort defense vs offensive modifiers (whether they be siege pips or artillery, though art have that extra breach chance...)

It's hard to see specifically how much better that 1 pip siege general is vs the 2 pip for example.

Also, from looking at this it seems to me that what really matters the most is siege speed or fort defense modifiers. If a siege will average 10 ticks, 20% fort defense is worth a ton.
 
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FatHippo

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Hmm, this is really interesting. To be honest, my intuition would have told me that the first artillery against the level 2 forts would have a greater effect, but it's only about 2 siege phases. Thanks for crunching the numbers for the rest of us, this should get added to the wiki.

Now just imagine sieging a level 8 fort with no artillery and +50% defensiveness. *shudders* THE HORROR!
 

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Great work alpaca, thanks a lot.
I wonder if this information might be a better reference guide if it was a table, showing Fort defense vs offensive modifiers (whether they be siege pips or artillery, though art have that extra breach chance...)

It's hard to see specifically how much better that 1 pip siege general is vs the 2 pip for example.

Also, from looking at this it seems to me that what really matters the most is siege speed or fort defense modifiers. If a siege will average 10 ticks, 20% fort defense is worth a ton.
I happen to agree with this. Would it be possible to produce a table giving average and median siege phases with regards to fort levels (blockaded or not) and siege bonuses? Could be useful to know the impact of moving a general from one place to the other, or keep sieging, etc...
 

moyang

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Wiki is not updated with 1.13: siege status can go up to 12/13/14/15 with fort building level 1/2/3/4
 

alpaca

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I wonder if this information might be a better reference guide if it was a table, showing Fort defense vs offensive modifiers (whether they be siege pips or artillery, though art have that extra breach chance...)

It's hard to see specifically how much better that 1 pip siege general is vs the 2 pip for example.

Also, from looking at this it seems to me that what really matters the most is siege speed or fort defense modifiers. If a siege will average 10 ticks, 20% fort defense is worth a ton.
Thanks for the suggestion, I agree it would be more useful as a table, which is why I was working on batching the different scenarios while you were answering :D I updated the OP with some tables.

Wiki is not updated with 1.13: siege status can go up to 12/13/14/15 with fort building level 1/2/3/4
Really? I wasn't aware of that, let me check it out.
 

alpaca

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Wiki is not updated with 1.13: siege status can go up to 12/13/14/15 with fort building level 1/2/3/4
At least for bastions, progress doesn't go beyond level 12. Can you provide some screenshots as proof?
 

couchfighter78

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Nice job, very impressive.

Could you also factor in +20% seige ability as per the Offensive Idea group? I am very curious as to relative bang-for-your-buck vs. one or two leader seige pips.
 

moyang

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From patch notes:
  • Siege memory (the amount of siege progress you can store up from time) is now increased with unlocking new fortifications, so that late game forts are not so impossible to besiege.
From defines.lua:
Code:
SIEGE_MEMORY = 11,
SIEGE_MEMORY_SCALED = 0.5,                        -- per fort level

I don't have screenshot though. I did saw 13 siege memory but not fully sure what fort level it was now.
 

alpaca

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Nice job, very impressive.

Could you also factor in +20% seige ability as per the Offensive Idea group? I am very curious as to relative bang-for-your-buck vs. one or two leader seige pips.
The numbers are given in siege phases. If your siege phase length goes down by 20%, you will get the province 20% faster, but the number of siege phases doesn't change. Comparing siege pips to siege ability is a bit like comparing apples to oranges, because siege phase length also depends on terrain, defensive ability and so forth, so I can't really give hard numbers here. As a rule of thumb, I'd say each siege pip is worth about the same as a +10% siege ability modifier. I'd still prefer the latter as it helps leaderless sieges, which is the more common case in my experience.

From patch notes:
  • Siege memory (the amount of siege progress you can store up from time) is now increased with unlocking new fortifications, so that late game forts are not so impossible to besiege.
From defines.lua:
Code:
SIEGE_MEMORY = 11,
SIEGE_MEMORY_SCALED = 0.5,                        -- per fort level

I don't have screenshot though. I did saw 13 siege memory but not fully sure what fort level it was now.
Ah, I didn't see that. It's probably rounded down and uses building level, so it would only matter for star forts and higher. Thanks for the info, I'll check it out
 
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alpaca

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From patch notes:
  • Siege memory (the amount of siege progress you can store up from time) is now increased with unlocking new fortifications, so that late game forts are not so impossible to besiege.
From defines.lua:
Code:
SIEGE_MEMORY = 11,
SIEGE_MEMORY_SCALED = 0.5,                        -- per fort level

I don't have screenshot though. I did saw 13 siege memory but not fully sure what fort level it was now.
No dice, siege progress doesn't go above 12 even for the high fort levels. This is either a bug, or they reconsidered at some point. Besieging a fortress without artillery is hilarous, you need a 14 to even start the siege properly. I'm happy about it since it means I don't have to switch from effective fort level to something else for the calculations.
 

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Seraphithan

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No dice, siege progress doesn't go above 12 even for the high fort levels. This is either a bug, or they reconsidered at some point. Besieging a fortress without artillery is hilarous, you need a 14 to even start the siege properly. I'm happy about it since it means I don't have to switch from effective fort level to something else for the calculations.

Did you increase your tech for this test? Because progress does go to 15, that was what I was referring to in my question earlier.
 

alpaca

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Did you increase your tech for this test? Because progress does go to 15, that was what I was referring to in my question earlier.
Oh, ok, I see now. I thought it depended on the fort level rather than the attackers tech level. I wish Paradox would make a clean ruleset that works for the whole timeline and stick to it instead of adding ever more obscure exceptions. So Bastion level allows you to go to 13, Star Fort to 14 and Fortress to 15, right? Does it only apply to higher-level forts or can you also go to 13 on a castle if you have the sufficient tech?

Edit: To answer my own question, you can go over 12 on a castle. One has to be amazed why the devs decide to use a balancing option to improve late game sieges that speeds up sieges on obsolete forts even more when options are available that really only affect late-game forts.
 

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Posting here so that I remember this thread later.

I kinda want to take this data and play around with it.

Is it possible to import a Mathematica file (or whatever format your data are saved as?) to Excel or SPSS?
 

alpaca

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Added the max siege progress as another dimension to the data. You can now compare how much more quickly your sieges will go after you research a certain tech.

Posting here so that I remember this thread later.

I kinda want to take this data and play around with it.

Is it possible to import a Mathematica file (or whatever format your data are saved as?) to Excel or SPSS?
I can export the data (end result of every run) as a TSV, it's about 40 MB in that format. Not sure if you want to touch that with Excel. I didn't bother about saving and reloading the data because even the full dataset takes only a few minutes to run. Writing it to disk almost takes longer than simulating it.

Each line corresponds to a single run, the format for the lines is
phase progress breaches
All numbers are taken at the end of the siege, of course. Each scenario has 10k runs, so 10k lines you'll want to run your statistics on. The scenarios I ran can be found in scenarios.tsv

https://dl.dropboxusercontent.com/u/95609184/eu4sieges.zip