Self-Spell Mechanics

Abstract

This report looks at some of the important mechanics of self-spells which have not yet been made public. The UtoLab team headed by myself investigated the duration of self-spells, the effects of exploding fizzles and their likelyhood to occur. It was found that all self-spells work with similar formulae, with their duration depending only on guilds/land, the given spells 'Duration Factor', and a random factor. A comprehensive formula for minimum and maximum durations was found with the limit at 20% guilds - Although with Mystics' Guilds counting for double that, they reach a cap at 10% raw guilds. Also the random factor was even and linear, an exploding fizzle occurs approximately 33% of all fizzles and kills 0.5% of your wizards, and you can still succeed spell at 0% guilds.

Introduction

We all use self-spells every day, and they do a fair bit to help our provinces, whether by adding 5% defense or decreasing the upkeep costs of our troops. This guide will aim to explain some of the mechanics behind self-spells. Some of this will be old news to some players, but much of it is a recent discovery and can be of great use to the dedicated player. Be careful though to use the formulae presented here correctly otherwise you will get disappointed results. Also as you well know there is a significant random factor active, so don't confuse a 50% success rate as "will work every second time".

All figures and formulae presented here are done so in good faith, and we have endeavoured to make them as accurate and correct as possible. If you find something here which needs correcting please contact us so we can rectify the problem. Thank you.

Spell Duration

We all know that there is a great deal of randomness in spell durations, but until now only a few have known how to optimise their self-spell potential. Like many research topics it often helps to start with extremes, so first off we set up provinces with zero guilds, and repeatedly cast certain spells to determine the minimum spell durations. The most interesting piece of information from this was that there was no randomness in spell duration with zero guilds - no matter how many successes (we used over 20), it always gave the same, minimum, duration.

The other extreme we used were very high guilds. These provinces were set up with 50% guilds, and recasted the same spells again and again (over 1,000 casts have been made in total). This gave results where the maximum effect was always (except for Paradise) twice that of the minimum effect. Just as importantly, the minimum for this was twice that of the minimum we had with zero-guilds, and the maximum was thus four times the zero-guild minimum. To establish the trend line the same was done again with 10% and with 20% guilds which confirmed a linear relationship with maximum durations from 20% guilds (i.e. over 20% gave no extra bonus to duration).

The formula for spell duration was postulated as:

Spell Duration = DF x [1 + (rand_between[1,3]) x MIN(1,G%/20)]

DF = Duration Factor
G% = Percentage Guilds

That is the duration of a self-spell is determined by the percentage guilds divided by twenty (with the maximum at 20% guilds). Which is then multiplied by a random number between 1 and 3, plus 1, then multiply by the Duration Factor of the spell.

Note that for mystics double the guilds percentage to account for their bonus.

For max/min duration with a certain amount of guilds:

MaxDuration = DF x (1 + 3 x MIN(1,G% / 20))

MinDuration = DF x (1 + MIN(1,G% / 20))

For example, if you have 10% guilds, and you want to cast MP - DF = 6

MinDuration = 6 x (1 + MIN(1,10 / 20))

MinDuration = 6 x (1 + 0.5)

MinDuration = [i]9

MaxDuration = 6 x (1 + 3 x MIN(1,10 / 20))

MaxDuration = 6 x (1 + 3 x 0.5)

MaxDuration = 6 x (2.5)

MaxDuration = 15

So you can expect to get between 9 and 15 hour casts.

Or at 20% (or higher) guilds:

MaxDuration = DF x 4

MinDuration = DF x 2

The Duration Factor for each spell is:
(Note: The numbers in brackets are the minimum and maximum duration with 20% guilds)

Note: All of these are presented in good faith, and are true and correct as far as the authors knowledge extends, if you find an error in this, please contact me so it can be rectified.

Note #2: None of those factors include Dark Elves 30% strength bonus, please remember to multiply all numbers by 1.3 for Dark Elves.

The two exceptions to this are Tree of Gold and Paradise which work under slightly different functions.
* For ToG use the same function, but instead of random_between(1,3) use (0,1) to give a range of 40-80% (as integers) which multiply by your current income (then by 1.3 for Dark Elves to give 52-104%).
* For Paradise also use the same function, but replace the (1,3) with (1,7)/2 or (0.5,3.5).

It was also found that the randomness is linear, with just as much likelyhood for any specific result over any other, but due to rounding the top result is often less common. Furthermore, if you cast a spell twice, the most recent cast overrides the previous - even if it has a shorter duration. So if you get a 22 hour MP and recast for 15 hours, you lose that extra 7 hours.

The effects of Building Efficiency and Magic Science were studied by using a province with low BE and one with high science (over 100% bonus) - in both cases it was found that there was no difference in the durations of the spells cast. That is, a province with 41% BE, no science and 20% guilds will actually get better durations on average than a province with 140% BE, +150.0% Magic Science and 15% guilds.

Fizzles

I'm sure we've all seen this message more than we would like:

Your wizards gather their runes and begin casting. The spell consumes 4273 Runes and ... fizzles. Alas, we were not able to fulfil your expectations.

Or the even more dreaded:

Your wizards gather their runes and begin casting. The spell consumes 4273 Runes and ... fizzles. Alas, we were not able to fulfil your expectations. Please forgive us. Sir Clampy the Awesome, something has gone terribly wrong with our spell. 45 of our wizards were killed in an explosion!

The successrates of self-spells depend on the spell itself with harder spells like Paradise with a difficulty of 249 failing much more often than Minor Protection with a difficulty of 45. The exact formula for self-spell success rates is still uncertain, but success rates of approximately 20% for Minor Protection down to approximately 5% for Paradise have been found with zero guilds. Having said this we have also seen over 100 casts in a row all fail - so it is advised to avoid running zero guilds if you still want to cast spells.

The other issue is the wizards lost, on approximately 33% of fails you will lose 0.5% of your wizards to explosions. This 33% slides with a higher frequency (up to 40-50%) for harder spells, and lower frequency (around 20%) for easier spells. Remember that unlike thievery operations this loss of wizards is relatively low, it takes 21 explosions to drop you to 90% of your wizards - but also remember that it takes a lot longer to replace them.

Offensive Spells

Our research into the effects of offensive spells is still inconclusive, if you would like to help please contact us (see end of report). For a sneak peak though we can tell you that durations work similarly - being determined only by guilds and networth difference. So if you want a high success rate you'll need wpa and sci, but if you want to actually do some damage make sure you build up to 20% guilds as well - a 4 hour Meteor Storm just isn't that scary :)

Also we should note that some of the spell descriptions in The Guide and other places are incorrect - for example storms doesn't affect population growth, it actually kills 1.5% of your peasants per hour change.

Conclusions

* Self-Spell durations are only affected by your guilds, and not wizards (you need at least one wizard though), not BE and not Magic Science.

* You get maximum gains at 20% guilds.

* You get minimum gains, but can still succeed with zero guilds.

* You lose 0.5% of your wizards on an exploding fizzle (Which occurs approximately in 33% of your fizzles).

* ToG and Paradise work slightly different compared to duration spells.

Acknowledgements

Special thanks to Lead_Pipe who got a lot of the data and helped me analyze it all.
Thanks also to Clarey, Catwalk, Grinch, Sully, Chuppa, Ryshad, sm0k, AquaSeaFoam and Idealist for testing and discussions, and Peppie for editing.

Future Research

We will continue to try to find success rates for self-spells, but it is a low priority for us at the moment. We are focusing more on offensive spells now to complete our knowledge base there before public release. Also we are nearing completion of our Overpopulation Experiment and you can expect public release of that within the next few weeks. Our research into thievery success rates and gains for some ops is still ongoing. Our main current research is focused on attacks - in particular troop losses, ME change, gains, oversend messages and peasants gained.

If you would like to help with any of this, or anything else on our never-ending list of topics to look at in the future, please contact us either in #utolab or by PM to myself - we'd be glad to have another opinion or province to help.