法杖生成

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Wand Generation Procedure

The tier of a wand determines the available cost for improving the wand. The improvement of the wand is determined by certain probability distributions. The order in which the costs are paid to improve the wand statistics is partially random.

  1. Mana Max, Mana Charge Speed, Speed Multiplier
  2. {Recharge Time, Cast Delay, Spread}
  3. Capacity
  4. {Shuffle, Spells/Casts}
  5. Final adjustment (Capacity Increment, No Shuffle)

If there is not enough cost for wand improvement, all the costs that can be paid will be used for the improvement. If the cost of wand improvement is negative, effectively downgrading the wand, the cost will be received.

Please refer to Wand and Spell Tiers to see which wands are generated by a particular biome.

Cost available
Wand tier Cost available
1 30 or 35 (50% Chance)
2 40
3 60
4 80
5 100
6 120
10 (11)[1] 180 (Limatoukka drop) or 200 (Nightmare Hell)
  • This cost is subject to random modification of up to +/-3.
  • There is a 5% chance of generating a rare wand that increases the cost by 65 and it has an Always Cast Spell. [2]

Mana Max and Mana Charge Speed

These statistics are independent of the wand improvement cost.

  • Mana Max is calculated as 50 + 150 * tier + Random(-5,5) * 10.
  • Mana Charge Speed is calculated as 50 * tier + Random(-5,5 * tier).

There is a 15% chance of generating a wand with fast mana charge. For these wands:

  • Mana Max is divided by 3.
  • Mana Charge Speed is multiplied by 5.

There is a 17% chance of generating a wand with slow mana charge. For these wands:

  • Mana Max is multiplied by 3.
  • Mana Charge Speed is divided by 5.

For better wands, there are no fast mana charge wands and a 20% chance of generating slow mana charge wands.

Speed Multiplier

The speed multiplier is independent of the wand improvement cost. Multiple probability distributions are used to determine this statistic, and once the distribution is randomly selected, it determines the speed multiplier.

Speed Multiplier Probability
Probability Min Max Mean Sharpness
48% 0.8 1.2 1 6
48% 0.8 1.2 1 0
2% 1 2 1.1 3
2% 0.5 1 0.9 3
0.0476% 1 10 5 2
Better wand 0.8 1.2 1 6
Speed Multipiler Probability

Recharge Time

  • Recharge time is expressed in frame counts at 60 fps.
  • If 0 costs are paid, the recharge time is 60 frames (1 second).
  • Paying 1 cost reduces the recharge time by 5 frames (0.083 seconds).
  • When paying 11.8 costs, the recharge time reaches its minimum value of 1 frame (0.017 seconds).
Recharge Time Probability
Probability Min Max Mean Sharpness
53% 5 60 30 2
27% 1 100 40 2
19% 1 240 40 0
1% 1 100 40 0
Better wand 5 40 20 2

Recharge Time Probability

Purple Line: 60 (0 costs), Black Line: 35 (5 costs)

Cast Delay

  • Cast delay is expressed in frame counts at 60 fps.
  • If 0 costs are paid, the cast delay is 16 frames (0.27 seconds).
  • Paying 1 cost reduces the cast delay by 1 frame (0.017 seconds).
  • When paying 31 costs, the cast delay reaches its minimum value of -15 frames (-0.25 seconds).


Recharge Time Probability
Probability Min Max Mean Sharpness
61% 1 30 5 2
27% 0 35 12 0
6% 1 50 15 3
6% -15 15 0 3
Better wand 1 35 5 2

Cast Delay Probability

Purple Line: 16 (0 costs), Black Line: 11 (5 costs)

Spread

  • If 0 costs are paid, the spread is 16.
  • Paying 1 cost reduces the spread by 1.
  • When paying 51 costs, the spread reaches its minimum value of -35.
Spread Probability
Probability Min Max Mean Sharpness
91% -5 10 0 3
9% -35 35 0 0
Better wand -1 2 0 3

Spread Probability

Purple Line: 16 (0 costs), Black Line: 11 (5 costs)

Capacity

  • If 0 costs are paid, the capacity is 6.
  • Paying 5 costs increases the capacity by 1.
  • In the non-shuffle priority state (see below), the initial limit of the capacity is worse.
    • (cost ≤ 45) the limit is (cost - 15)/5.
    • (cost > 45) the limit is (cost - 45)/10 + 6.
    • Considering these limits, the capacity is fixed at 2 in the non-shuffle priority state.
  • After all statistics have been determined, pay all remaining costs to increase the capacity.
    • If the wand is non-shuffle, the cost to increase the capacity is 10 on this occasion.
    • There is a 0.5% chance that this opportunity will not occur.
  • The minimum capacity is 2.
  • The maximum capacity is 26, but there is a 0.01% chance of ignoring this limit.


Capacity Probability
Probability Min Max Mean Sharpness
39% 3 10 6 2
39% 1 20 6 0
5.9% 3 12 6 6
5.9% 5 11 8 2
4.7% 2 20 8 4
3.9% 2 7 4 4
2.0% 1 5 3 4
Better wand 5 13 8 2

Capacity Probability

Purple Line: 6 (0 costs), Black Line: 7 (5 costs)

Shuffle

There is a (15 + tier*6)% chance that this statistic will be determined before spells/cast (non-shuffle priority state). Otherwise, there is a 50% chance that spells/cast will be determined first.

The following conditions are required for the wand to be non-shuffle:

  • The capacity of the wand is 9 or less, and
  • Either the wand is in non-shuffle priority state OR there is a 50% chance, and
  • Cost 15 + capacity*5 can be paid.

If the wand is generated with non-shuffle, the shuffle statistic is determined at no cost. If the cost has already been paid, it does not return.

  • In some biomes (see Wand and Spell Tiers)
  • No More Shuffle

Spells/Casts

  • The costs are determined from the following table based on the wand's capacity and spells/cast.
  • If the recharge time is 1 second or longer, there are two independent opportunities to increase spells/cast:
    • 70% chance to increase by 1 (10% chance of multiple increases)
    • 50% chance to increase up to the capacity (6 times asymptotically)
  • The maximum spells/cast is equal to the wand's capacity.
Spells/Cast Cost
Spells/Cast Cost
1 0
2 5+capacity*2
3 15+capacity*3.5
4 35+capacity*5
5 45+capacity*capacity
Spells/Cast Probability
Probability Min Max Mean Sharpness
44% 1 3 1 3
44% 1 5 2 0
8.9% 2 4 2 8
2.2% 1 5 2 2
Better wand 1 3 1 3

Distribution Formula

Given that the minimum and maximum values ​​are normalized from 0 to 1, the probability of generating a random number x follows the formula:

pow(sin(pi*(0.5-mean+x),sharpness)) (In |x-mean|<0.5, 0<x<1)

Notes

  1. When a tier 10 wand is spawned, the game actually calls for a tier 11 wand to be generated.
  2. Always Cast wand genarated on 4% chance indepenedently.