The Old World, magical effectiveness and the problem of cumulative advantage, or, time to get the calculator out.

 

 

Having played a few games of the Old World now, learning the rules, a few issues have been nagging me, and I’m going to address one in particular here, the Magic system. The system in itself is just about OK, it works, to some degree, but the disparity in wizard’s magic levels is painfully obvious. It feels like higher level wizards very easily dominate lower level ones, the advantages are huge and very impactful on the game’s outcome (too much so in my opinion). So, I’ve been looking at the underlying maths and probabilities of the system, and hence if that feeling is justified. The issue is ‘cumulative advantage’. As a games designer this kind of thing interests me – why is this happening, what in the game is making this feel wrong or frustrating or over-powered, and thus, later, how can it be fixed for better balanced and/or more challenging play?

To do this, I’ve looked at wizards at the two extremes in the game, 1st level vs 4th level, and split this into two actions, the two most common to wizards in the game (their point really), casting spells and dispelling spells. Then, these numbers have been translated into the game’s own measure of ‘effectiveness’, points values. Interesting and telling results. Let's get into the weeds...

Casting Spells
First, lets look at a wizard’s chance of actually casting one spell in the Old World. 1st to 4th level, with casting values of 7+ (the lowest required on 2D6+1 to +4) to 10+. It isn’t complex probability, and it is summarized in the table below, as a % chance that a wizard will actual succeed in casting a spell. Bit of real maths-hammer follows...

% chance to successfully cast
               2D6 Result or more
Level      7+       8+       9+      10+   
1            72%    58%    42%    28%
2            83%    72%    58%    42%      
3            92%    83%    72%    58%    
4            97%    92%    83%    72%    

So, a 1st level wizard casts on a 7+ 72% of the time. A 4th level wizard 97% of the time.

                                                           7+    8+        9+      10+
4th to 1st as a factor for success -     1.3    1.58    1.97    2.57    - times more likely to succeed   
                        average = 1.85 times more likely to succeed at casting


From these numbers, on average, a 4th level wizard is on average x1.85 more likely to succeed in casting any one spell. So nearly, not quite, twice as often. The probabilities actually skew to the top end heavily, as shown above.

Number of Spells
In the course of a 6 turn game, a 1st level Wizard with 1 spell could, at best, cast 6 spells (the same one 6 times). That is their maximum. A 4th level wizard with 4 spells, at best, could cast 24 spells, each spell 6 times. This is the very extreme result (unlikely a wizard will pass all rolls but possible), but, the 4th level wizard has 24 opportunities to cast in a game, the 1st has 6, so that is, easy maths, 4 times as many possible attempts in a game.

So, for casting alone (we’ll get to dispelling next), the 4th level is 1.85 times more likely to succeed in over 4 times as many attempts. In overall effectiveness 1.85 x 4 = 7.4. In casting alone, a 4th level wizard is 7.4 times more 'effective'. I’ll call that the 'average casting effectiveness coefficient'.

Dispelling
Casting is only half of what a wizard does in the game, the other half is dispelling. Going through the same system as above, but the scale gets longer, as the results required can get higher, 16 being the maximum (12+ level 4 = 16)  without magic item assistance, which I'm ignoring here to use the base mechanics.

% chance to successfully dispell
                  Result required or more
Level        7+        8+       9+      10+     11+    12+    13+    14+    15+    16
1               72%    58%    42%    28%    17%    8%    3%      3%    3%     3%
2               83%    72%    58%    42%    28%    17%    8%    3%    3%     3%
3               92%    83%    72%    58%    42%    28%    17%    8%    3%    3%
4               97%    92%    83%    72%    58%    42%    28%    17%  8%    3%

So, a 1st level wizard will successful dispelling on a 9+ 42% of the time, a 4th level wizard will succeed 83% of the time (almost double, we can agree).

4th to 1st as a factor for success -     
8+        9+      10+     11+    12+     13+    14+     15+    16
1.58    1.97    2.57    3.41    5.25    9.33    5.66    2.66    1    times more likely to succeed

average = 3.71times more likely to dispell.

On average, a 4th level wizard is 3.71 times more likely to successful dispell than a 1st level wizard.

These numbers aren’t the only factor though, in yet another advantage, as a 4th level wizard dispells over a 24” radius (or 1809” squared of tabletop), whilst the 1st level dispells over 18” radius (or 1018” squared of tabletop), or 1.77 times the area they can actually effect.

The 4th level and 1st level are equal on the number of times they can dispell per game, so for once, no advantage to the higher level here.

So, 3.71 x 1.77 = 6.57 times more effective. We’ll round to 6.5, so a 4th level is on average roughly 6.5 times more effective at dispelling than a 1st level wizard. I’ll call that the 'average dispell effectiveness coefficient'.

 

Effectiveness Coeffiecents applied to current Points Values
7.4 times more effective at casting and 6.5 times more effective at dispelling. That could be averaged to 6.95 times more effective overall. Actual, not, because you don’t just get to do one or the other, the wizard gets to do both, so they should be added together! For 13.9 times more effective overall, as an average.

There is a scale to measure ‘overall effectiveness’ for units in the game, this is points values (love them or hate them, it’s what the game uses).

Let's take a basic wizard, level 1, Empire human, with those stats and nothing extra, just a basic human wizard with their 1 spell, as our starting base line. The game scores it at 60 points. Fine. So a 4th level wizard should probably come in, (on a points calculator that actually rates their overall effectiveness), with all the 4th level wizards' cumulative advantages, at something like 60 x13.9 = 834 points!. The game actually score it at 160 pts. The disparity is, well, huge. IMHO, high level wizards are currently vastly, vastly, under-point and therefore able to dominate magic in any game (and why every army brings a 4th level wizard as a no brainer pick, and many bring 2). 60 points to 834 points are the two ends of the ‘wizard points scale’, with the others sitting evenly spaced at 2nd level = 318 points and 3rd level = 576 points. Ouch! On that scale, only 1st level wizards could practically be taken in most games. Bit dull that, why bother with higher levels? It would result in very little magic in the game, which isn't what is wanted. Magic has to be in the game and do something. The opposite is currently true. Notably, only 4th level wizards appear.

Given 834 points for a 4th level wizard means they won’t appear in any game, except really, really, big ones (which might not be such a bad thing), we could just reverse the equation instead, with a 4th level human wizard still at the current 160 points, then the first level one should roughly = 12 points, 2nd level = 61 points and 3rd level = 110 points. On the current points measure, low level wizards are seriously over pointed, if we begin with the assumption that the higher ones are in the right points ball-park for actually getting them used in games (over-used one might posit).

This calculation doesn’t take into account that the low level wizard also has a worse stat line as well, less survivibility, less attacks, etc. That’s another (far smaller) factor, but, here, I’m just looking at pure magic effectiveness. OK, this is the extreme and assumes perfection in dice rolls, a wizard can’t always cast (due to a miscast or say, not on the table yet, or being dead) or dispell (out of range, or likewise, already dead or other unknown factors like scenario, arriving late to the tabletop, etc.)… so being super generous, let's say they are only actually doing half of all these casing and dispelling actions (your 1st level wizard then gets off 3 spells per game, the 4th gets off 12, still pretty good, probably too good, and dispells not withstanding). That still leaves the 'average effectiveness coefficient' at roughly 7…

So, our 60 point 1st level wizard actually means a more realistic, 420 point 4th level wizard. That puts them out of the running in all but the largest games. 2nd level are then 180 points and 3rd level are 300 points.  I think, that might be a closer 'points to effectiveness' reflection of their abilities on the tabletop.

Conclusion
The problem with the current system is the cumulative advantages just keep stacking, and not just for 1 turn, but for all 6 turns of the game. You can feel that when you play the game. Higher level wizards easily dominate, to the point that, as it stands, 4th level wizards are the most effective purchase from any army list, never fight without 1, probably take 2 or 3… they are a points value bargain, and for me, this is so far from balanced it just breaks the game’s magic system. 

There is no in-game mechanic that attempts to correct this, or adds some other re-balancing element into the rules, another random factor say. Obviously, dice rolls vary, you can be unlucky or luck, but this is the results on average. A 4th level wizard isn’t just 4 times better (and even this most basic arithmetic obviously isn’t recreated in the game's current points calculations), but maybe up to 14 times better, being generous, with a 'higher level bias' (so more, better wizards and spells are being used in the games more often), it is still at least 7 times more effective… they know more spells, have more chances to cast them, have a better chance to cast them, can dispell enemy spells over a wider area, with a higher chance of success – cumulative advantages, for every turn of a game… it never stops being that big advantage, wizards don’t weaken turn by turn (just for one example of a possible in-game re-balancing factor). The current magic system just hammers the lower level casters, and player's will (already do) notice. The game's best solution to this? Take your own level 4 wizards back. How dull! – unless you enjoy a magic system dominated by only top end wizards (in which case what is the point of including low level wizards?). I’d prefer all four levels to have their place and usefulness in my games. Why can't two level 2 wizards match a single level 4 in game? The maths says they won't in the current system, far from it, they'll get dominated.

Well, now I know this data, so I can think about some house rules that start to fix this disparity and game balance issue, for a better gaming experience and more fun with magic that isn’t just repeatedly level 4 casters duking it out, game after game. Something to work on in my side project of getting the Old World rules to play the way I'd like them too for my games. Simplest solution, as ever, fix the points... but there must be something better, in-game rules mechanics-wise, rather than the blunt points cost tool. Probably, you actually need to do several things. Thinking hat on (it's no doubt tall and pointy).

PS - Of course, most are happy to play rules as written, and given its the same rules for everybody, its impact is mitigated, but it feels unsatisfactory to me for my games. The mechanics of the magic system needs to work better than this, it's sub-par games design, unless the intention was to allow 4th level wizards to be ubiquitous and dominant, but I don't believe it was. 

 The first thought I have is to make it harder to cast multiple spells each turn... which effects the higher level casters more than the lower (given they are the ones doing more casting), or limit the amount of spells being cast, such as 1 of each type each turn... so 1 hex, 1 vortex, 1 magic missile, etc... I prefer an in game mechanic over a points correction.We'll try just +1 to a spell's casting number for each spell cast to start with. Second spell +1, third spell +2, etc. That'll help a bit... but not enough.

The second thought is that the previous dice pool system at least acted as in-game mechanic check on casting, you had a finite resource of dice for casting and dispelling, and players made the choice of how to spend that resource, which is at least a decision point for the players, rather than atm, were there isn't any decision to make, all wizards just try and cast every spell every turn, because why not?. Back to some form of dice pool might be an answer.