There is only anecdotal evidence either way.
Hard Dog put up a lot of photos of rolled cars with roll bars and without. Convincing until you realise they don’t post photos of where one of their rollbars failed.
The death of a Miata owner at first was taken as definitive proof of the Mousetrap; the idea that the twin hoop style bars would fold forward over the drivers head. Photos were published showing the German made style bar neatly folded forward. It panicked the manufacturer, a small company, to the extent they were commssioning rolltests, The company went under, not sure because of thic, but it didn’t help/
In the end, it transpired the style bar was bent forward by the tow truck, when righting the car. The driver’s passenger walked away with barely a scratch. The car hit a rock in the road at about 40mph, and rolled, and the driver instantly killed when his had struck that rock. A roll bar would not of helped him. Perhaps having the windows rolled up up might have (top was down). Pure bad luck.
I only know of one person killed in a car crash, and he was driving a Mk1 MX5, and he turned it over. I probably shouldn’t use that anecdote to conclude that the Mk1 MX5 is the most dangerous car known with a 100% fatality rate.
The drop test is convincing, until you look look carefully and notice the car is springy; it visibly compresses and rebounds. If your car fell off the 1st floor of a multistory, the rollbar isn’t going to save you. But its a test specified by the MSA-RAC, though is actually meaningless. The Blue Book doesn’t give strength requirements for road cars, just the standard of construction (don’t use scaffolding poles). The main issue is no matter how strong the rollbar is, the MX5 wasn’t designed to have a rollbar. That’s why the the race cars have cages and not bars. Plus welded in…
I’ve haven’t found data to show if you are more or less likely to crash a MX5 compared to any other car.
I found this:
And extracted this:
Some caveats in this data. Its expressed as deaths per million cars registered, so normalised. Rollovers are a subset of single vehicle deaths; single vehicle accidents are when no other car is involved, like running into a tree, driving over a cliff, rolling after clipping a kerb. But this doesn’t include the number of accidents a particular model is involved in. I’ve selected cars most in the UK would be familar with, and which are comparable to cars in the UK
Looking at the data, its important to understand that you not twice as likely to die in the Ford Focus as in a NB MX5. Likely, there are more vehicle miles attributed to Ford Foci.
Possibly you could infer that the death rate in MX5s was similar to the Focus, if, say, the annual average mileage of a MX5 was about half of a Ford Focus.
But its a reminder there are other ways to die in a car besides rolling it over.
Roll over deaths are hard to find as a stat. A EU report, which I think was based on GB states (as GB was the only country to collate such data) suggested 10% of all accidents where there was serious injury involed a rollover, but 25% of seriously injured occupants were in a rollover.
For most cars, being in a roll leads to a worse outcome, generally for the occupants.
So the US data should be interpreted not how likely you are to be killed in a roll, but how good a job a car was protecting you elsewhere.
So taking the NC MX5 (06-08). On the face of it, its the car to be in if you drive into a tree, because everyone who was killed in a single vehicle crash, in that data set were in a rolled car. The NC has multiple airbags, probably a strong shell
Where the NB falls down (and the NA will be worse) is not what it will do when you roll it, but when you crash into that tree. Two thirds of single vehicle MX5 deaths are not involving a rollover, compared to 20% for the very safe, strong Volvo. The NA/NB are floppy cars. Their doors will cave in, maybe that PPF doesn’t help things as far as crash impact (more energy transferred to the driver).
The distribution (US, but likely similar in the UK) of types of car accident:
Front/rear impacts, with the driver flopping around like a demented crash dummy. Either a face full of Nardi-Momo steering wheel a bash on the back of the head with a powdercoated bar. .
A well padded Carbing bar with door bars I had for a well
Went into sprints, wuth a bucket seat. Oops, the padding slipped
A fun day at Curborough resulted in me writing off a borrowed Shoei helmet because of that bolt (it left a hole).
The UK bars are mostly copies or very similar to the HardDog rollbars from the US, so they sit back a bit further than the Jap bars (resulting in them offering less height than the Jap bars, because of how the hood is), Which means its less likely your head will hit it.
But back to anecdotes
I can hardly recall when I ever saw a UK car with a padded rollbar. When it happens, it tends to be B&Q pipe lagging. I ordered supposedly proper padding, and got 6 foot of very nicely soft pipe lagging,
I can understand why some want a rollbar for trackdays; they may have no choice. My days of trackdays are over, maybe the odd little sprint. So in my personal risk assessment (Hazardx Likliehood), I’m leaving a rollbar off. But I miss the look of it.