Simple stats for NaW and WaW85

When I play games I am always concerned with making the best use of the units I have. In some games this is quite easy to do because the game has fewer attack options. In a game like Nations at War and, to an even greater extent, World at War 85 you have more potential targets for your attacks because of the range of your weapons and the multiple attack types a unit might have. In NaW games where the ranges are often smaller there aren’t as many but in WaW85 with weapon attack ranges out to 11, or even more, hexes you need to be able to quickly determine where your firepower will be best used. 

I am the type of gamer who – when they see that they get to roll multiple dice for an attack – will assume, with no real evidence, that they will be doing a lot of damage. Empires will crumble before my mighty 4D6! Now we all know that this isn’t true and so I have helped myself by creating some quick mental tools to help me evaluate my chance of success and my opponent’s chance of thwarting me.  To that end, I offer this quick and probably statistically messy way of analysing odds in World at War 85.

The first edition of World at War had many expansions released for it but one of the first was the Gamer’s Guide and it included an article by Peter Bogdasarian, The Math of Eisenbach Gap, that analysed to-hit chances and modifiers with exacting detail.

I read through that article many times when I was playing the original World at War game and it was very informative but all those useful numbers would just fall out of my head when I sat down to play a game. I also do not find percentages very enlightening. I need to have statistics translated into something that I can use at the table.

Luckily for me, WaW 85 only uses single D6s for combat and event resolution. Some might say that this gives the game a lower level of granularity in its stats and effects (which is an entirely different discussion) but one benefit of this is that it is dreadfully simple to analyse potential combat results. No tricksy Bell curves for us! To begin our exploration, lets take a look at the delightful Warsaw Pact T-72 tank.

 The T-72 has an AP attack value of, ignoring the range for the moment,  3⁴.  The attack hits on a 4+. So this tells us that there are three sides of the dice that will give us a hit and three that will not. Given that there are six faces of the dice that means that 50% of the time a roll should be a hit. If we are rolling three dice we multiply that 50% value by three to get 150% which tells us that we should get 1.5 hits every time we roll the three dice for this attack.

The HE attack value is less effective and only hits on a 5+. So on the dice only two of the faces give us a positive result (2 faces of 6 on the die) which is a 33% chance of a hit on one dice and therefore a 100% chance on three dice. Or one hit. Now it is important to remember at this point that these are only averages. If we want to get specific (and put out a table with a header and everything) we would get these sorts of numbers. 

So looking at the 3⁴ AP attack we examined earlier, we only have a 12.5% chance to hit with all three dice, a 25% chance to hit with 2 and a 50% chance to hit with one. On average though the attack should give us 1.5 hits and it is this number that is easier for us to work with in a game setting. 

We can do the same with our opponent’s armour values as well. If our East German T-72 is firing at a West German Leopard-1 we can look at the counter and see that the armour value is 3⁶. The tank will, for an average armour roll, make 1/2 of an armour save.  One result from six on a die will be a single positive result so 1/6 multiplied by three is 3/6 which results in 0.5 saves.

 For an average shot from the T-72 we will get 1.5 hits and the Leopard-1 will save 0.5 of them to give us an average of one hit that is not saved. Now I hear what you are saying. “This is all fine but is there an even easier way to do this calculation all at once?”. And of course there is.

No matter what the attack or armour values are for units we can just add up the positive results for the attacker and subtract the values for the defender to give us a final net value. Every 6 net results is an unsaved hit. 

So if we take our original example, the T-72 shoots and gives us an average of three hits per dice and it rolls three dice so we get nine positive results. The Leopard-1 saves on a six which is one point per dice and it rolls three which gives us three potential saves. Nine minus three is six which is one factor of six. Or one hit. 

So let’s test out our newfound knowledge with an actual in-game example. Cue the educational music!

It is often easy to figure out your best target when the units are different but what if they are the same and there is only a modifier or two difference between them? What is the best target for the M3 Bradley CFV in the following situation? There are two T-62s that the Bradley can fire at. One is in the open and the other is in the Woods but it is at Point Blank range. Does the range bonus overcome the terrain effects?

The T-62 in in hex I10 is at a range of 6 hexes in the woods and the other, in hex J8, is at a range of 7 hexes but in the open. While firing at Point Blank range at the tank in I10 the Bradley has a 4³ firepower. This is four positive results per dice times four dice for 16 total. When firing at the T-62 in J8 it is a 4⁴ firepower which is three positive results on four dice for 12 total. So far so good. 

The T-62 in I10 has a base armour value of 3⁶. This is increased by 1 by the Woods and by another one for an ATGM firing into Blocking terrain. It also benefits from Concealment but a hard target can only get a maximum of two additional defensive dice. So the T-62 has a 5⁶ armour value in this hex which is 1 positive result per dice times five dice for a total of 5. The T-62 in the open only has its default 3⁶ armour which generates a total of 3.

The net result for the T-62 in J8 is 12 points from the attack minus 3 from defense for a total of 9. The result for the T-62 in the woods is 16 points minus 5 for the armour and terrain for a net result of 11. The T-62 in the Woods is slightly more protected than the tank in the open (5 points versus 3) but the range to the T-62 in J8 causes the attack to diminish more than the Woods protects the tank in I10. So the T-62 in I10 is the slightly better target.  

This also works in reverse. You can use this quick mental math to evaluate risks as well. How many hits will get through if an M1 shoots at your T-72? Is the Soviet Volley Fire going to do more damage? The system isn’t as precise as actual statistics but I find it useful to use in games to help me evaluate attacks and defensive options.