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General
True Hit

This is a phenomenon that occurs in FE6~12 (although it has not yet been directly confirmed in FE10).

During battles, the Hit (or accuracy) value displayed is actually false.

Or, at the very least, misleading. This is due to the fact that the game uses 2 RNs (random numbers) to determine whether an attack successfully hits or not. This causes the probability of a successful hit to be skewed. The best way to explain this oddity is perhaps to compare the difference in using just 1 RN or using 2 RNs.

1 RN system

The natural method, and the one used in FE1~5, is to use 1 RN to determine a successful strike. We can treat the RNs as integer numbers ranging from 0 to 99, with each number having an equal chance of appearing. If the RN is lower than the Hit value, the attack will hit. Otherwise the attack will miss.

For example:

Say, the Hit value is 70. RNs from 0~69 will cause the attack hit. RNs from 70~99 will cause the attack to miss. There are a total of 100 RNs, so 70 out of 100 RNs (70%) result in a hit and 30 out of 100 RNs (30%) result in a miss.

In this case the Hit value is a perfect representation of the actual chance of hitting the enemy.

2 RN system

However, in the other games, 2 RNs are used. The RNs are averaged, and if the averaged value is lower than the Hit value, the attack will hit.

For example:

The mathematics can get horrendous, so I'll take the extreme case of a Hit value of 1.

To miss, the averaged value of the 2 RNs must be lower than 1. In other words, the total value of the 2 RNs must be lower than 1 + 1 = 2. There are only three case where that occurs, and that is when the RNs are 00 00, 00 01 and 01 00. Any other combination results in a total value that is equal to or higher than 2.

There are 100 RNs, so the total possible number of combinations is 100 x 100 = 10,000. Thus, the case of hitting is 3 out of a possible 10,000 cases, with the other 9,997 cases resulting in a miss. This means the probability of hitting is 3 / 10,000 (%) = 0.03%.

So, while the Hit value displayed in the game is 1%, the actual chance to hit is 0.03%.

Table of Displayed Hit - True Hit

All values are percentages.

Disp. Hit
True Hit
Disp. Hit
True Hit
Disp. Hit
True Hit
Disp. Hit
True Hit
Disp. Hit
True Hit
0 0.00 20 8.20 40 32.40 60 68.40 80 92.20
1 0.03 21 9.03 41 34.03 61 69.97 81 92.97
2 0.10 22 9.90 42 35.70 62 71.50 82 93.70
3 0.21 23 10.81 43 37.41 63 72.99 83 94.39
4 0.36 24 11.76 44 39.16 64 74.44 84 95.04
5 0.55 25 12.75 45 40.95 65 75.85 85 95.65
6 0.78 26 13.78 46 42.78 66 77.22 86 96.22
7 1.05 27 14.85 47 44.65 67 78.55 87 96.75
8 1.36 28 15.96 48 46.56 68 79.84 88 97.24
9 1.71 29 17.11 49 48.51 69 81.09 89 97.69
10 2.10 30 18.30 50 50.50 70 82.30 90 98.10
11 2.53 31 19.53 51 52.47 71 83.47 91 98.47
12 3.00 32 20.80 52 54.40 72 84.60 92 98.80
13 3.51 33 22.11 53 56.29 73 85.69 93 99.09
14 4.06 34 23.46 54 58.14 74 86.74 94 99.34
15 4.65 35 24.85 55 59.95 75 87.75 95 99.55
16 5.28 36 26.28 56 61.72 76 88.72 96 99.72
17 5.95 37 27.75 57 63.45 77 89.65 97 99.85
18 6.66 38 29.26 58 65.14 78 90.54 98 99.94
19 7.41 39 30.81 59 66.79 79 91.39 99 99.99
20 8.20 40 32.40 60 68.40 80 92.20 100 100.00

Why?

So, why does the game "lie" to us? If you browse the table above, the answer might be obvious.

The 2 RN system encourages low Hits missing and encourages high Hits hitting. What does this have to do with anything? Well, it mostly benefits the player, as playable characters usually have high Hit and enemy characters usually have low Hit. Thus playable characters will tend to hit more often than usual and enemy characters will tend to miss more often than usual.

For example:

With the 1 RN system, characters will miss with 99 Hit 1 out of 100 times. However with the 2 RN system, characters will miss 1 out of 10,000 times. That's a factor of 100 in difference!

Consequences

If you have played a game from FE1~5, you should notice the difference in Hit percentages while playing. Even though your characters have 90 or so Hit, they will miss fairly often and, conversely, even though enemies have 30 or so Hit, they will hit quite often. If Sety or Shanan (or other characters with high Avoid) appeared in FE6~11, they would be even better dodge-machines than they already were!

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