Here is another tool for theodicy.
If the distribution of evil found in this world renders the existence of God improbable, there had better be some other world w* whose distribution of evil doesn't render the existence of God improbable. What is w* like? There are two options.
Option 1: w* is basically a variant on our universe, but improved by having fewer evils. For instance, maybe w* has 50% fewer murders, 75% fewer wars, etc. However, the problem with this option is that it is very difficult to draw the line between such a variant and our world so as to say that the w* is significantly more probable on theism but our world is not. For the admission that some such variant of our world would not render theism implies that the kinds of evils we have in our world are ones that God has reason to permit, perhaps for the kinds of reasons that theodicists have given, such as that various evils make various virtues possible. But then to claim that our world is improbable would require some sort of an argument as to just how much murder, war, etc. is needed for the requisite goods. And here the theist can reasonably make a skeptical move by pointing out that we have no way of estimating the right amounts.
Option 2: w* is radically different from our world, and does not contain the kinds of evil that our world does. For instance, maybe w* contains no beings capable of suffering or wrongdoing, but only mathematicians who feel varying degrees of elation at theorems they have proved. But now we have a diversity move available. Consider a world w** which contains both the sorts of beings that w* has as well as the kinds of beings, with the kinds of evils, that our world has. Such a world has a greater diversity of goods and virtues than w* does, and hence is better than w*. Therefore, at least prima facie, some such world is more likely to be created by God than w* is. Moreover, we do not have evidence against the claim that our world is such—for instance, for aught that we know, our world could be a multiverse that contains an island universe full of mathematicians incapable of suffering or wrongdoing. Now, one might worry that in such a world, there would still be fewer murders, fewer wars, etc. than in our world. But if that's the worry, then we're back to the considerations of Option 1.