1) The information should benefit from being in a chart (rather than text), typically because that makes it clearer.
2) The chart should accurately represent what you're trying to say.
For instance, PHD Comics did a chart for Vacation v. Stress. That works well: you can get the basic gist at a glance (stress levels go up and down over time), then look at the peak/troughs to find out what caused them. xkcd has also done several of these, e.g. Ninja Turtles and Cat Proximity. The "Ninja Turtles" one is significant because the colours of the pie chart match the turtles' colours (limbs/shell), so that's funnier than just having a table of percentages. Also, I don't know how he assessed each name (e.g. by doing Google searches and counting results), but I don't really care whether the underlying data is factually correct; the important point is that the diagram should match what he (comic creator) thinks. Another example is SMBC, e.g. dirty dishes and The Graphvella.
The latest Dork Tower strip is also chart-based, but I don't think it really works, since it fails both of my rules above:
1) The message is "The nearer you get to a comics deadline, the more likely you are to use a chart". That's easy to understand, and the chart doesn't convey any extra information, so it would be better off as a tweet. The author maintains a Twitter account for one of his characters (@DrBlinkShrink), which is quite funny, so he could have done the same thing here. In fact, it would be easier to read the plain text, rather than untangling the negatives: "Inverse of time left" means that the bottom of the Y-axis is when there's loads of time left and the top of the Y-axis is when there's very little time left. The only advantage of the chart is meta-humour; I don't object to that, but I don't think it's enough to outweigh the other problems.
2) Taking the chart as presented, the probability increases rapidly while very little time has passed, then the probability doesn't change much in the final deadline panic. I assume that this is the opposite of what he's trying to say! It seems more likely that he means "The probability starts low and then shoots up at the end when you run out of time".
It may be significant that the other 3 comics I mentioned are all made by people with a scientific background, so they understand how charts work. They have also done comics about poor charts, e.g. xkcd's Convincing and SMBC's How to infuriate a Math major. In this case, I suspect that John Kovalic (the Dork Tower creator) started out with a standard exponential chart and then tried to fit the axes around it.
Thinking back to my Physics A level, we were taught that the X-axis on a line chart should normally be time, because that's where you have regularly spaced points; the Y-axis points tend to be a lot more scattered. If the Dork Tower strip had put time on the X-axis and probability on the Y-axis, the line would then match the message (slow growth initially, fast growth later). The "inverse time" thing is confusing, but here's a line chart that avoids that: Harry Potter and Tumblr. Just put a couple of marks on the X-axis for "start point" and "deadline", then you're sorted. As for probability, it can be expressed as a number (between 0 and 1) or as a percentage (between 0% and 100%). So, he should either put "(%)" after the axis label or change the markers to say "0, 0.25, 0.5, 0.75, 1".
I don't like to sound negative here, because I like reading Dork Tower and playing Munchkin. I also realise that it may be difficult to deal with deadline pressure, which is why I only create comics sporadically. Realistically, I don't expect him to redraw that comic just to fit in with what I think. However, I think it's useful to understand how charts work, whether you're creating them or reading them, and that doesn't just apply to webcomics.