What’s going on guys! My name is Theoatrix, and today I have a very interesting article for you guys, and that is how Defence works in Old School Runescape – like your Defence bonus or your Defence level. So, in the main part of this article, I am going to be explaining the math behind how Defence works, and then to finish the article off, I am going to be talking about some interesting outcomes from playing with the formulas, which might really, really help for PKers or even PvMers.
Defence and Pures
So, to start things off, your Defence level and Defence bonus – so, Defence in general – has absolutely nothing to do with the Max Hit that can be hit on you. So, if you have 1 Defence, and someone can Max Hit a 50, then if you got 99 Defence, the same person will still be able to hit a 50.
Defence only affects the accuracy of your enemy’s attacks, which basically means that it decreases the number of successful hits that your enemy will hit. But, it does not necessarily change the number or the damage that is hit.
Another quick fact about Defence is that it is a determinant of your Combat level, and what I mean by that is that your Defence level itself is one of the key levels which chooses your Combat level. So, for example, Mage, Ranged, Attack and Strength are all tied together. So, a high Range level means that you can get a lot of Strength and Attack levels without levelling your combat. But, with Defence on the other hand, it is all on its own. So, if you get a Defence level up, it really, really affects your Combat level.
So, now these 3 pieces of information that I just said are really key to understanding why 1 Defence Pures are so powerful. To summarise, Defence does not increase the Max Hit, which means that Pures have a huge advantage, since their Max Hit would be so high compared to those with Defence levels.
I’ve got one more factor to talk about before I get into the math side of things. Melee Defence and Range Defence are entirely dependent on your Defence level. But, Magic Defence is another story. Your Magic Defence is determined 70% by your Magic level and 30% by your Defence level. So, this piece of information makes Magic Pures a little bit less effective, mainly in terms of Pures, because a lot of Pures have a really, really high Magic level and 1 Defence. So, their high Magic level would mean that they would splash more often. But, the Range and Melee Defence would be really, really low since they have only 1 Defence.
The Math Behind Defence
So, now for the math… To work out the accuracy depending on your Defence level, you need to work out the attack roll – like rolling a dice – of our opponent, and you need to work out your Defence roll of your own Defence. So, the formula to work out the roll for both of these is equal to ‘E’ – your effective level – multiplied by your bonus, ‘B’ plus 64 [Roll = E x (B + 64)].
Working out E
To work out E, your effective level, this is what you need to do. Firstly, you get your Defence level, so this is just the level from the Skills Interface. If you have used a potion, you should get the boosted value, not your base value. Next, if you are using any Prayers, multiply it by the Prayer adjustment. So, for example, if I have Thick Skin activated, which increase my Defence by 5%, I multiply my Defence level by 1.05. If I have Piety on, my Defence is increased by 25%. So, I multiply it by 1.25. Now, you will probably get a number which is a decimal. What you want to do with the decimal is round it up to the nearest whole number. Now, this is the part that I found really, really interesting. Your Attack Stance – so, your accurate, controlled, aggressive, defence – they all actually play a large part in Combat. So, with the number that you rounded up – if you are using Defence Attack Style like Long Ranged or Defensive – you add 3 to that number that you had. If you are using Accurate, you add 0. If you are using Controlled, you add 1. Keep note that these are the values that you add for Defence if you are working out the Attack Roll. I will talk about that in a little bit. So, now you have a number and then what you want to do is add 8 to that number. I do not know why you have to add 8. But, you do.
The next part is where Void affects. So, this of course does not really matter for calculating your Defence Roll, since there is no Void affects which affect your Defence. But, this is important when you are working out your Attack Roll. For Void Melee, you would multiply it by 1.1, for Ranged, it is also 1.1, and then for Magic, it is 1.3. Now, you have your final effective level number. Round this number down if you ended up with a decimal, and this value that you have got is equal to ‘E’.
So, that was mainly based on your Defence Roll. But, if you want to work out the Attack Roll, you use the same thing. So, instead, you would use your Attack level and then of course, you would use the Melee Attack Prayers – not the Strength Prayers – only the Attack Prayers, and then you add the Stance bonus corresponding to the ones that I have on screen below. So, that is the ‘E’ value in the formula.
Working out B
Now, you need the ‘B’ value, and this one is so much easier to work out. All you need for the ‘B’ value is your corresponding Attack or Defence bonus. So, if you are calculating Defence against a Ranged, it is your Ranged Defence bonus in the equipment stats. If you calculating the Attack Roll for someone using a Whip, so, a slash weapon, you get their slash Attack bonus. Strength bonus has no effect here at all. So, now you can work out your roll for Defence or Attack, and vice versa for your opponent.
How Defence Affects Opponent’s Accuracy
Now, to work out the chance of hitting something, like I said before, you need the Defence Roll of player 1, who is taking the damage, and the Attack Roll of player 2, who is dealing the damage.
Now, one of these values that you get is going to be higher than the other. If the Defence Roll is higher than the Attack Roll, then this is the formula you have to use. Your accuracy of hitting, or the opponent’s accuracy of hitting, is your Attack Roll divided by 2 times the Defence Roll plus 1 [ATK/ (2 x DEF +1)].
Now, if the Attack Roll is higher, then the formula is the Defence Roll plus 2, divided by 2 times the Attack Roll plus 1. Then, you do 1 minus all of that value (1 – [(DEF + 2) / (2 x (ATK + 1))].
The value that you get from this accuracy calculation will be a decimal between 0 – 1, and this is the probability decimal. So, this is your chance of hitting. So, for example, I calculated my own Defence level with my own Defence bonuses to get a Defence Roll, then I did my Attack level with my Attack bonuses, and I worked out my Attack Roll. Then, I worked out that my accuracy was 0.403, which means that I have a 40.3% chance of hitting something.
So, in terms of Defence, this value that you get from this calculation can be really, really useful to work out how much a couple of Defence levels will change the chances of you getting hit.
Magic Defence, as I said, is a little bit different, and if you are interested in the process in that, just leave a comment, and I will reply and I will explain everything that you need to do to work that out. It is a little bit longer, so I am not going to go into detail in this article. But, I am happy to help anyone that is trying to calculate it. Now, this process that I have been talking about here is really complicated. But, the whole point of this article was to kind of just give you an idea of how your Defensive stats and your bonuses affect the chance of getting a successful hit on you and I’m hoping it made a bit of sense.
So, to summarise, your Defence level determines the chance of taking a successful hit, and does not affect the Max Hit at all. Defence also has its own impact on your Combat Level, which means that gaining Defence levels really, really increases your Combat level in comparison to the other stats.
Anyways guys, I hope you learned something pretty helpful today or enjoyed. If you did, be sure to leave a like, and make sure to subscribe if you are new. If you have any suggestions, make sure you leave them in the comments. If you have any questions or just want to chat to me, you can join the Theoatrix friend chat in game. As always, thanks for reading this article, and have a nice day!