I am a bit of a maths nerd – I enjoy using spreadsheets and graphs to analyse and illustrate. But I can’t claim much expertise – I did once obtain a Distinction in Statistics at Uni, but I’ve forgotten all of that now.

So while writing up some material on healing miracles (see Healing miracles around the world and Healing miracles and God) it occurred to me that miracles were a subject just asking to be looked at statistically. But it certainly wasn’t easy.

If you’re not a maths nerd, I suggest you read the summary only, which I’ve thoughtfully placed at the top.

### Let’s start with the conclusion

After I did a bit of reading, a lot of work on a spreadsheet, and an amount of head-scratching and re-calculation, I came to the conclusion that accounts of apparent miracles which occurred after christians prayed for healing provide good evidence for the existence of God. But the maths required a number of assumptions that really need to be better based before I would hang my hat on the results.

Non maths nerds can quietly leave now if they wish. For the rest, here’s how I came to this conclusion.

### Bayes Theorem

Bayes Theorem is an established calculation of probability that assesses how new information changes the probability of some fact. If we apply it to miracles, the calculation requires the estimation of the probability of a particular miracle occurring if we assume God does exist, and the probability of it occurring if we assume God doesn’t exist.

### The analysis of miracles

The question I wanted to consider was this. Do the many miracle accounts increase the probability that God exists? To consider this question, we need to consider probabilities for the following four cases:

Person is prayed for | Person is not prayed for | |
---|---|---|

Person is healed | ||

Person is not healed |

#### Estimating numbers

I don’t take these numbers all that seriously, but they are useful in giving an indication of my thinking and the evidence. So my estimates are as follows:

- The probability of someone recovering assuming there is no God, that is, by natural means, is occasionally reported. It is different for different conditions and diseases, but an estimate of 1 in 10,000 is reasonable. (It turns out this number isn’t critical, for the important thing is the ratio of this and the next figure.)
- The probability of someone recovering assuming God exists must include both this natural probability and the estimated probability that God might have intervened. I have assumed that if God exists, he might be as likely to heal someone as occurs naturally, so the total probability is 2 in 10,000. This isn’t a blind guess.

It is estimated from survey data that 300-400 million christians claim to have experienced or observed a healing miracle. If we make an estimate of how many people have seen more than one miracle, and how many miracles have been observed by more than one person, we may estimate the number of different miracles to be a smaller number, say 100 million. If we then eliminate 90% as not having occurred (a pretty severe estimate) we are left with 10 million unexplained healings experienced by 2 billion christians, a probability of 1 in 200, much more than the estimate I have actually used.

- We also need a starting probability of God existing, and to avoid any christian bias, I have used 1 in a million.

This then gives the probabilities shown in this table:

Person is prayed for | Person is not prayed for | |
---|---|---|

Person is healed | 0.0002 | 0.0001 |

Person is not healed | 0.9998 | 0.9999 |

#### Doing the calculation

We are interested in the results for people who pray for healing, on the assumption that these give an indication of the existence or otherwise of God. For every ten thousand people who pray for healing from a serious condition, we are assuming two are healed and 9998 are not. (Again I say that I believe the success of prayer is much greater than this, but I am trying to use the most unfavourable numbers.)

So we do a step-by-step Bayesian calculation, where the initial probability of God’s existence is reduced by a very small amount for each non-healing and increased by a larger amount for each healing.

### And the answer is ….

It turns out that it after we have considered 35,000 people, or 72 apparent healings, the probability that God exists has risen from 1 in a million to 50%. When we have considered 43,000 people and 83 healings, the odds have risen to 90%.

### So what does this show?

If we believe the numbers, it shows that it only takes a relatively small number of well-attested healings to make it highly likely that God exists. And that number of well-attested healings certainly exist. Even just using the ones I have documented as Healing miracles and God we reach that number.

Of course the numbers are very rough estimates, and undoubtedly could be contested. But I have been fairly conservative, and I have played around with other numbers, and while the numbers can change a lot, the conclusion doesn’t change much.

I have to admit that the whole approach is problematic – is it really valid to try to estimate the probability of God’s existence? But besides being a fun exercise, the calculation helps make clear the assumptions each of us make.

#### I’d love feedback

Perhaps there are errors in my assumptions, method or computation – if so I’d like to have them pointed out so I can improve it. Any other feedback is welcome.

#### Read more

- Healing miracles and God – a summary of my investigations so far.
- Can we scientifically test alleged healing miracles? – some thoughts on how we should go about this.
- Ten healing miracles – how a doctor investigated the medical facts.
- Healings at Lourdes – background information on one of the world’s most famous places of healing.
- More healing miracles – reports from around the world.
- Heart-starting action – a miracle in the emergency ward.

Photo: Wikipedia

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