1. One line of evidence for God's existence involves examples of special providence. This might include modern miracles and answered prayers. Likewise, there are things we will need in the future, but we don't know that in advance. We'd pray for it if we knew we were going to need it. So in some cases God might provide for us as if that were an answer to prayer, because we don't know ahead of time that we need it to happen, and by then it would be too late to pray.
Now in some cases the windfall might be consistent with special providence or luck. Chances are, you will get lucky every so often. Coincidences happen. But I have in mind examples that are highly resistant to naturalistic explanations. Where it's too specific, unlikely, and opportune to be sheer luck.
2. However, "skeptics" discount this evidence as sample selection bias. The distribution is random. It averages out, when you take everything that happens to you into account. For instance, sometimes you get what you pray for, and sometimes you don't. Some people are healed, and some are not. If you only compare healings, it looks impressive. If you add dissimilar outcomes, it all blends into the undifferentiated background. Or so goes the argument.
3. There are, however, at least two major problems with the "skeptical" objection. To begin with, it backfires.
Suppose there really is a pattern. If, however, our sample is too small, then there's no reason to expect a discernible the pattern. If all we have to go by are anecdotes and isolated incidents, then it would hardly be surprising if the pattern entirely escapes our notice, for it only emerges if we have a much larger sample. In that case, apparent randomness is perfectly consistent with a deeper, broader pattern. So the very thing the "skeptic" mentions to show it's really random is the same thing that's consonant with its nonrandomness.
In terms of reported miracles, answered prayers, and other special providences, our provincial knowledge is only skimming the surface. We know next to nothing about what most other Christians experience at different times and different places. So even if there were a pattern, how would we be in any position to perceive it?
To take a comparison: suppose I'm a Martian who's assigned to study human behavior. I see a family of four load the trunk of their car with luggage and drive away. If their objective is to reach their destination, then they will take the shortest route. Depending on the length of the journey, they will drive as far as they can each day. Their route will be determined by the location of motels, gas stations, and the distance between the starting-point and the end-point.
Yet my Martian logic is confounded by their actual behavior. They don't travel in anything like a straight line. They constantly veer off. They may stay in a town or campsite for several days before they resume the trip. To all appearances, their behavior is random.
But from a human perspective we know that's probably not the explanation. Rather, this is typical tourist behavior. Their objective was never to simply reach their destination. Rather, it was always more about the journey than the destination. They are sightseers. They drive on scenic routes. They visit historic towns. Far from being random, their trip is meticulously planned. Where they will go. How long they will stay. Each day is accounted for.
In addition, our Martian can't tell from where they begin what their destination will be. He doesn't know if they plan to drive 50 miles, 500 miles, or from coast to coast. They might head east to west for most of the trip, then turn south during the final leg of the trip. Our Martian observer might have no inkling three-quarters of the way through the trip where their intended destination is. To register the pattern, you need to begin at the end and work backwards.
And it could be the same way with providence. The pattern defies recognition if all you have are isolated data-points.
4. However, the "skeptic" might object that this only shows, at best, how the phenomenon is consistent with either randomness or nonrandomness. Mind you, even if that were the case, it greatly attenuates the original objection. According to the original objection, what we really have is evidence of randomness, once you take all the evidence into consideration. But now the "skeptic" must concede that the distribution pattern isn't evidence for randomness–appearances to the contrary notwithstanding.
5. But it's not just parity. As I noted at the outset, what if you have examples of special providence which are not plausibly susceptible to naturalistic explanations? Then that's positive evidence for special providence.
To take a comparison, suppose a group of ten Caltech students or MIT students decide to break the bank. They figure out how to cheat casinos. They do it as a test of ingenuity. Perhaps they hack into the security cameras so that they can actually see the poker hands, and they devise some undetectable signaling system.
They divide up into teams of two and hit five casinos in Las Vegas. The same team never goes to more than one casino, so there's nothing to directly connect the group of ten cheaters.
It doesn't take long for each casino to catch on to the fact that something is afoot. A player is beating the odds way too often for that to be coincidence. Yet these are isolated incidents.
Suppose each casino is ignorant of the fact that four other casinos are encountering the same thing. Or even if they knew it, they have no background information on the players to connect them. Even if they were aware of a larger pattern, they can't account for the pattern. It seems to be random, although there must be some hidden connection.
But their inability to identify the collusion in no way obviates the evidence of cheating in the individual cases. By the same token, even if the distribution of special providences appears to be random, that doesn't affect or cancel out the evidence in specific cases.