In Warhammer Fantasy Battle the lizardmen army has a special rule known as ‘cold blooded’ which allows them to roll three dice instead of two for leadership, drop the highest and only sum up the other two. While this gives results similar to the basic two dice leadership roll (between 2 to 12), I’ve always known intuitively that the results are a lot better. Today I’m going to quantify the actual difference and compare them to a different high leadership army (the dwarves).
Firstly, I built a simple spreadsheet in Excel to represent the results of the rule. I know, I know, right about now you’re wondering why I didn’t write a program to solve the dice roll for me. Well to tell you the truth, I’m not that great of programmer. Actually, I’m a horrible programmer. I got through my dissertation on Labview and writing my monochromator automation program with goto statements…. yes the program was in Basic. But it worked, and I got the spectroscopy data I needed so it’s all win-win in my eyes.
With a simple Excel spreadsheet emulating the three dice roll drop the highest leadership rule, I decided to do some basic statistics to determine what the ‘cold blooded’ rule does for the army versus a standard leadership roll of 2d6. The average leadership roll is 5.54 (vs. 7) with a standard deviation of 2.22 (vs. 2.45). So you gain a base of 1.46 points in leadership and have a tighter spread meaning that what you’re troops end up rolling is closer to the average they should be rolling. All in all a plus for leadership and a deviation that definitely boosts them into a high leadership army (even though the numbers in the book don’t look to be that high). But that’s not all that happens. The distribution is left skewed also, meaning it’s really hard to roll a 10, 11, or 12 with the army and rolling a 2, 3, or 4 is more probable than it the numbers suggest. The two graphs below show what I mean. The solid fill is the relative chance of rolling a particular result, while the line is the cumulative chance of rolling the stated leadership value or less.
As you can plainly see there is a significant probability of rolling low numbers. For leadership, which happens to be the most important roll you make in a battle (other than cannon sniping shots), this actually skews the odds towards the lizardmen side. I’m also including the standard leadership distribution below so you can visually compare the two.
For a standard army testing on 7, you’ve got a 58% chance of passing. The lizardman army has a 52% chance of passing on a 5 (nearly 2 points lower). As you get a higher leadership the number becomes even more skewed. A lizardman leadership of 9 (which the slann has) has a pass rate of 94%, the equivalent standard leadership number is 11 (at 97%)! The same applies for saurus oldbloods and scar-vet characters, vanilla saurus and temple guard infantry, and saurus cavalry. Their leadership of 8 (90% pass rate) is equivalent to a 10 (92% pass rate) meaning that lone units can act as if they have leadership equivalent to other armies generals!! What this means for lizardmen troops, if your leadership is 5 or below you can safely say you add 1 to 1.5 points to it. As soon as you’re leadership is 6 and above, it’s as if your leadership score just went up by two points. That’s a fairly powerful leadership boost hidden within the cold-blooded rule.
FYI: Dwarf units and heroes are 9 with the fighting lord at a 10. A lizardman army made up of saurus units has a higher leadership than dwarfs, has a similar cost, strength and toughness. They do have a bit lower armor save, but a much higher movement speed. All in all, I’m thinking the ‘cold blooded’ rule isn’t priced correctly, if you consider a dwarf well priced (which they aren’t).