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But what about % of accidents/kilometer then? The same 1 accident per 0.5M miles would be 1 accident per 0,8M kilometers...
Precisely! One can use a number such as x accidents/mile — in the example above, if there is an average of 1 accident for every 500,000 miles driven, that number would be 0.000002, or 2 * 10^-6 — or y accidents/km, but it cannot be n%.
 
I agree, exactly what crash rate Elon considers "safe enough" for Robotaxis is a very important consideration for Tesla's valuation.

It's important to note the NHTSA data actually tells us there are 1.8 cars per crash on average so the actual NHTSA reported crash rate per car per mile is 498/1.8 = 1 per 277 miles. This is also a significant underestimate because many minor crashes are not reported for insurance reasons - the actual US crash rate per car is closer to 1 per 150 miles.

Elon said earlier this year he is assuming he can launch unsupervised Robotaxi's when he gets FSD to 3-4x the average human. But does this mean one crash every 150*3 - 450 miles, 277*3=831k miles or 498*3 = 1,494k miles?

I would guess they are aiming for around 1 per million miles which would in fact be 6.7x safer than the average human in the US. Of these crashes, only a very small % are likely to be the Tesla's fault.

Most likely Tesla's real goal is based on probability of injury per mile. In 2016 (i haven't checked updated data) in the US there was an accident with an injury every 794k miles and a fatal accident every 60.8 million miles.
There may be driving policy prioritisation decisions which make a minor crash more likely and a serious crash less likely for example.

Perhaps Tesla is aiming for a 10x improvement in accidents with injury as the threshold for Robotaxi launch (this will have added help from the safer design of Tesla's & EVs relative to the US fleet). This would amount to one accident with injury per 8 million miles travelled per car.

Totally agree with using probability of injury per mile. Probability of death is not going to be used because there is simply not enough data with EVs for that. Interestingly, there is a moral argument for allowing EVs as soon as they have a lower probability of injury than humans, because to not do so means you are essentially injuring more humans.
 
Does it make mathematical or statistical sense to you to describe that as 99,9998% reliability? Because that’s what my point was. If you read the rest of my post you discover that I agree this can be used as a comparison for relative incidence of traffic accidents, but it shouldn’t be expressed as that type of percentage. You correctly point out that an accident rate can be expressed as 1 accident / x miles driven. See how the unit is “accident/miles”. A percentage has no units.

I see, I misunderstood your comment - edited my original post to point this out.

You are right that accident/miles is not a percentage, but nevertheless we can normalize it by defining it as the "probability of no accidents per one mile driven" - which I think is how Elon used it.

If we define it that way, then:
  • one accident per 500,000 miles has a "one mile safety probability" of 499,999/500,000 = 99.9998%
  • one accident per 3 million miles has a "one mile safety probability" of 99.9999666, i.e. "four nines"
I.e. (N-1)/N, which is 1-1/N - or the 1/N calculation we used in prior comments.

Do you agree with this more precise definition?
 
Tesla is metric. SpaceX is metric. Whatever the definition of FSD reliability, it will be SI. No ‘miles’ in sight.

No we wont.
Our Dear Leader has spoken !


"The voters spoke," Trump told reporters afterward. "They voted for change, OK? They voted for putting America first, and that means using American ways to measure things. Not foreign."

"The metric system is a disaster," he continued. "Look at the countries using it. France. Germany. South America. They're failing, big league. They're falling apart. Not us. Not us. We're going back—and by the way, when I was in military school I was a tremendous athlete, everyone said it, I used to run the 440, won many awards, probably could've gone to the Olympics, decided not to—but the metric system, all these meters and kilowatts and K's and all of these things, they're going away, OK? They're going away."

Edit:
Source
With Executive Order, Trump Bans Metric Race Distances
 
It's important to note the NHTSA data actually tells us there are 1.8 cars per crash on average so the actual NHTSA reported crash rate per car per mile is 498/1.8 = 1 per 277 miles. This is also a significant underestimate because many minor crashes are not reported for insurance reasons - the actual US crash rate per car is closer to 1 per 150 miles.

You mean 1 per 277 thousand miles and 1 per 150 thousand miles, right?

Human drivers are bad, but not that bad. :D
 
  • Funny
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No, traffic accident statistics generally use "miles driven", and the number simply means that if a driver is driving 500,000 miles then the average number of traffic accidents he will be involved in during those 500,000 miles driven will be around ~1.

Edit: as you later point out I misunderstood your argument and only quoted a small part of your post out of context.
Why are you setting your minimum at 10M for FSD then? That’s 100 years of 10k/yr driving with 1 accident. Do you let other people drive you? They are surely not that good. I want 10M too, but 500k sounds like flip the switch to me, that’s better than me (I backed into a car 3 years ago).
 
I see, I misunderstood your comment - edited my original post to point this out.

You are right that accident/miles is not a percentage, but nevertheless we can normalize it by defining it as the "probability of no accidents per one mile driven" - which I think is how Elon used it.

If we define it that way, then:
  • one accident per 500,000 miles has a "one mile safety probability" of 499,999/500,000 = 99.9998%
  • one accident per 3 million miles has a "one mile safety probability" of 99.9999666, i.e. "four nines"
I.e. (N-1)/N, which is 1-1/N - or the 1/N calculation we used in prior comments.

Do you agree with this more precise definition?
The SI world will be happy, as their “one km safety probability” will always be higher than the “one mile safety probability”. We will need probability conversion tables.

In fact, the SI pedantics will insist that the correct unit is “one meter safety probability” which far exceeds all the above…
 
Totally agree with using probability of injury per mile. Probability of death is not going to be used because there is simply not enough data with EVs for that. Interestingly, there is a moral argument for allowing EVs as soon as they have a lower probability of injury than humans, because to not do so means you are essentially injuring more humans.

This is not only a moral but also an economic argument: for a modern national economy at large the cost of traffic accidents with personal injuries is huge: material damage, lost productivity, health care costs, family disruption, emotional distress. All of these have direct price tags and various external costs.

But a single car manufacturer cannot simply unilaterally declare that because it's already safer it should be used, due to legal liability reasons as @neroden pointed it out. It will require policymakers to declare FSD safety technologies mandatory under certain circumstances - which will limit liability. This process will likely require many years, possibly decades though.

So pretty much the only way forward for Tesla is to be scientifically safer by a factor of 5x-10x: "10 times safer" is probably much easier to argue in courts (and to regulators/policymakers) than "2 times safer".
 
Tesla is metric. SpaceX is metric. Whatever the definition of FSD reliability, it will be SI. No ‘miles’ in sight.
There is no real problem as miles *are* defined upon a metric system ... international mile is exactly 1609.344 meters, no ambiguity.

And that is the last post on miles versus kilometers. Removed some more already. Sorry I to have to butt in so much, but geez, how hard is it to stay on topic?...

Mod
 
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Semi-OT:

TLDR: Germany is continuing to do everything in its power to not commit to EVs.

This post was motivated by my deep frustration with the disinformation being spread around and wanting to provide you with more insights about one of the biggest car markets worldwide: Germany.

Three days ago, the Frauenhofer Institute for Solar-Energy released a new report comparing the lifecycle CO2 impact of battery-electric vehicles vs. hydrogen vehicles. The Frauenhofer Society is the 'biggest organization for applied research and development services in Europe' - its significance, especially in Germany, cannot be understated.

The conclusion of the report is that for vehicles with a battery of up to 45 kWh, electric vehicles are better for the environment. If the battery is larger than that, this effect reverses. Skimming through the report, I noticed some very weird assumptions:

1) They assume a lifecycle of 150,000km. As we all know, Tesla's batteries easily last a lot longer than that. Just recently, someone passed the 900,000km mark and they apparently only swapped out the battery once.
2) They ignore that a battery has a use case after being used in a car. Stationary storage is an excellent way to make the most out of the used resources.
3) They make some, in my opinion, questionable assumptions about the energy density of battery cells and packs in the future: link removed because it was corrupted - mod

Technologies such as Maxwell should accelerate the development of energy density further than what is displayed here. Maxwell already validated 300 Wh/kg and has a path to 500 Wh/kg, so the 2030 case seems off to me.

Some caveats:
I have to be honest and say that I do not follow the development of hydrogen fuel cells as closely as I follow the electric vehicle development. Therefore, I cannot evaluate the assumptions they use for hydrogen vehicles.

This study was, of course, immediately picked up by some news outlets. Some examples of how it was reported:

- Süddeutsche Zeitung (highly respected newspaper) writes: 'And the recent findings [about hydrogen cells] will not amuse Elon Musk'
- taz uses the headline: 'Hydrogen fuell cell beats Tesla'
- Other smaller outlets reported on it; it got a lot less coverage than I would normally expect from such news. I'm showing these examples as the German news media loves to use every opportunity to bash Tesla and/or Elon Musk.

Fun fact: the study was commissioned by H2 Mobility, a consortium of gas firms (Air Liquide, Linde), Daimler, and gas stations (OMV, Shell, Total). I cannot/don't want to believe that that there is a causality - Frauenhofer Institue is of such high reputation - but still, this seems very odd.

The study then suggests to conduct more research in regards to fuel cells and synthetic fuel. It also concludes that fuel cells and battery electric vehicles perfectly complement each other (as shown by the different CO2 impact depending on the needed range).

Why am I highlighting this conclusion? This fits exactly to the current trend that can be observed in Germany. There's a strong emphasis on "Technologieoffenheit" (openness to technology). Germany is doing everything it can to not fully commit to electric vehicles.

Some examples:
- BMW and Daimler are very upset with VW's strong lobbying effort to stop Diesel and advance electric mobility
- Politicians keep on stressing that we have to be open to new technologies:
- The liberal party FDP released a statement today stressing that we cannot focus on e-mobility
- The biggest party (CDU & CSU) wants to focus on synthetic fuel instead of electricity in order to
'keep the competitive edge'
- The main channel (ARD) of our public broadcasting network recently released a whole documentary where they spread misinformation about EVs (e.g. they cited the infamous Swedish study).

One last tidbit: There was recent political conference with the title 'the future of the automotive industry' There, the three ministers of the states where VW, BMW, and Daimler are located, were asked whether there is just a single topic where they do not agree with the strategy of the respective auto OEMs. The politicians weren't able to come up with a single thing where they did not agree with the OEMs.

In conclusion: Unfortunately, I do believe that Germany will severely lag behind regarding EV adoption and I'd model Tesla's impact here accordingly. Sorry for the long post, I hope it at least provided you with some new information.
 
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I agree, exactly what crash rate Elon considers "safe enough" for Robotaxis is a very important consideration for Tesla's valuation.

It's important to note the NHTSA data actually tells us there are 1.8 cars per crash on average so the actual NHTSA reported crash rate per car per mile is 498/1.8 = 1 per 277 miles. This is also a significant underestimate because many minor crashes are not reported for insurance reasons - the actual US crash rate per car is closer to 1 per 150 miles.

Elon said earlier this year he is assuming he can launch unsupervised Robotaxi's when he gets FSD to 3-4x the average human. But does this mean one crash every 150*3 - 450 miles, 277*3=831k miles or 498*3 = 1,494k miles?

I would guess they are aiming for around 1 per million miles which would in fact be 6.7x safer than the average human in the US. Of these crashes, only a very small % are likely to be the Tesla's fault.

Most likely Tesla's real goal is based on probability of injury per mile. In 2016 (i haven't checked updated data) in the US there was an accident with an injury every 794k miles and a fatal accident every 60.8 million miles.
There may be driving policy prioritisation decisions which make a minor crash more likely and a serious crash less likely for example.

Perhaps Tesla is aiming for a 10x improvement in accidents with injury as the threshold for Robotaxi launch (this will have added help from the safer design of Teslas & EVs relative to the US fleet). This would amount to one accident with injury per 8 million miles travelled per car.
Yeah, FSD/RT should go by probability of injury, not crash rate. If RT gets into fender benders just take the $ out of it’s pay and put it back on the street. If RT is really earning $30k/yr do you really hold it back because of a $10k fender bender every three years?
 
Why are you setting your minimum at 10M for FSD then? That’s 100 years of 10k/yr driving with 1 accident. Do you let other people drive you? They are surely not that good. I want 10M too, but 500k sounds like flip the switch to me, that’s better than me (I backed into a car 3 years ago).

See my other comment for the reasons, it's a "Prisoner's Dilemma" game theory scenario:

This is not only a moral but also an economic argument: for a modern national economy at large the cost of traffic accidents with personal injuries is huge: material damage, lost productivity, health care costs, family disruption, emotional distress. All of these have direct price tags and various external costs.

But a single car manufacturer cannot simply unilaterally declare that because it's already safer it should be used, due to legal liability reasons as @neroden pointed it out. It will require policymakers to declare FSD safety technologies mandatory under certain circumstances - which will limit liability. This process will likely require many years, possibly decades though.

So pretty much the only way forward for Tesla is to be scientifically safer by a factor of 5x-10x: "10 times safer" is probably much easier to argue in courts (and to regulators/policymakers) than "2 times safer".

But there's at least two existing precedents:
  • ABS brakes, while they are a big overall safety feature, do kill people: for example ABS braking on ice increases stopping distance by a factor of 5.
  • Likewise, airbags can seriously injure or kill people too, if they go off during light collisions that would have been injury-free without airbags.
Does anyone know the safety metrics of ABS brake and air-bag accidents and how manufacturers were able to standardize on them, despite them killing people in some situations?

Maybe that's the mystery public data @mrmage noticed and which Elon might be relying on as well?
 
Does it make mathematical or statistical sense to you to describe that as 99,9998% reliability? Because that’s what my point was. If you read the rest of my post you discover that I agree this can be used as a comparison for relative incidence of traffic accidents, but it shouldn’t be expressed as that type of percentage. You correctly point out that an accident rate can be expressed as 1 accident / x miles driven. See how the unit is “accident/miles”. A percentage has no units.
True, but I don't quite understand your point. At some time for a percentage to have meaning it has to be correlated with units of some type. (e.g. accidents/mile, accidents/km, accidents/nanometre, or accidents/hour, accidents/minute, etc.) Typically when referring to the number of nines, time is used as the unit (X outages per time period). However, because cars drive at different speeds under different circumstances, distance is usually used. So correlating the number of nines to the accidents/mile doesn't seem to me to be far fetched. And then because people don't want irrelevant complexity, the number of nines alone is used as a kind of shorthand.
 
True, but I don't quite understand your point. At some time for a percentage to have meaning it has to be correlated with units of some type. (e.g. accidents/mile, accidents/km, accidents/nanometre, or accidents/hour, accidents/minute, etc.) Typically when referring to the number of nines, time is used as the unit (X outages per time period). However, because cars drive at different speeds under different circumstances, distance is usually used. So correlating the number of nines to the accidents/mile doesn't seem to me to be far fetched. And then because people don't want irrelevant complexity, the number of nines alone is used as a kind of shorthand.
Maybe an example would help.

Say that Tesla looks at the AP performance and realises they have one accident for every 800,000 miles driven with AP on. They then look at the accident rate of Tesla cars driving in the same conditions (type of road, speed, etc.) with AP off, so human-driven, and the number is 500,000 miles before an accident occurs. They can then conclude there’s an improvement in safety due to AP of 60%. That 60% is a miles/miles result, but it’s the same for km/km. So one can say that AP is 60% more reliable than the average human, but one cannot say it is 99.999% reliable in absolute terms, because we cannot measure that. You can only compare one thing to another.
 
See my other comment for the reasons, it's a "Prisoner's Dilemma" game theory scenario:



But there's at least two existing precedents:
  • ABS brakes, while they are a big overall safety feature, do kill people: for example ABS braking on ice increases stopping distance by a factor of 5.
  • Likewise, airbags can seriously injure or kill people too, if they go off during light collisions that would have been injury-free without airbags.
Does anyone know the safety metrics of ABS brake and air-bag accidents and how manufacturers were able to standardize on them, despite them killing people in some situations?

Maybe that's the mystery public data @mrmage noticed and which Elon might be relying on as well?


Quick Google search: Effectiveness of motorcycle antilock braking systems (ABS) in reducing crashes, the first cross-national study. - PubMed - NCBI

Basically they did a cross-national study of how ABS for motorcycles reduces crashes (and mitigates severity of injuries) AFTER the EU made it mandatory in new motorcycles.

I quote:


RESULTS:
The effectiveness of motorcycle ABS in reducing injury crashes ranged from 24% (95% confidence interval [CI], 12-36) in Italy to 29% (95% CI, 20-38) in Spain, and 34% (95% CI, 16-52) in Sweden. The reductions in severe and fatal crashes were even greater, at 34% (95% CI, 24-44) in Spain and 42% (95% CI, 23-61) in Sweden. The overall reductions of crashes involving ABS-equipped scooters (at least 250 cc) were 27% (95% CI, 12-42) in Italy and 22% (95% CI, 2-42) in Spain. ABS on scooters with at least a 250 cc engine reduced severe and fatal crashes by 31% (95% CI, 12-50), based on Spanish data alone.

CONCLUSIONS:
At this stage, there is more than sufficient scientific-based evidence to support the implementation of ABS on all motorcycles, even light ones. Further research should aim at understanding the injury mitigating effects of motorcycle ABS, possibly in combination with combined braking systems.


So 99,9999% should be fine IMHO.

As not all companies will achieve FSD at te same time, the laws will change gradually.

Now:
handsfree driving is illegal;
Once Tesla or a competitor proves reliable FSD statistically:
handsfree driving is allowed with certain vehicles that are equipped for it;
Once the majority of car companies achieve reliable FSD:
handsfree driving is mandatory on public roads.

Now let's get back on topic. I think the whole FSD discussion is re-hashed way too many times, especially since we have no new information in that regard. (Except the FSD price increasing, woopteedoo).
 
This is not only a moral but also an economic argument: for a modern national economy at large the cost of traffic accidents with personal injuries is huge: material damage, lost productivity, health care costs, family disruption, emotional distress. All of these have direct price tags and various external costs.

But a single car manufacturer cannot simply unilaterally declare that because it's already safer it should be used, due to legal liability reasons as @neroden pointed it out. It will require policymakers to declare FSD safety technologies mandatory under certain circumstances - which will limit liability. This process will likely require many years, possibly decades though.

So pretty much the only way forward for Tesla is to be scientifically safer by a factor of 5x-10x: "10 times safer" is probably much easier to argue in courts (and to regulators/policymakers) than "2 times safer".
Eh, depends on how you word it. The public is number stupid. Just say it’s 100% safer. It sounds super impressive. Once you get past twice as safe it might as well be infinity. In court I bet you could argue 10% safer just as well as 10 times safer and get similar outcomes even though those are vasty different numbers.
 
  • Disagree
Reactions: neroden
See my other comment for the reasons, it's a "Prisoner's Dilemma" game theory scenario:
I don’t get it. Someone else's binary choice to use or not use FSD at 1/500k has almost 0 impact on your binary choice to use FSD at 1/500k (unless somehow you get hit by them in FSD). If FSD stopped improving at 500k I would see your point (and if FSD was ANYONE other than Tesla I might believe you), but Elon won’t stop at 500k if that’s where Tesla gets approval.
 
Basically they did a cross-national study of how ABS for motorcycles reduces crashes (and mitigates severity of injuries) AFTER the EU made it mandatory in new motorcycles.

Yeah, that's useful data, but what I meant is a bit different: for literally decades ABS (and airbags) was invented, available in some cars, but ABS was not mandatory by law.

How did Volvo and the other high end manufacturers treat the resulting liability, for example the fact that braking distance with ABS on ice increases 5-fold, which unarguably created some crashes which would not have happened without ABS - while also obviously massively reducing the average rate and severity of crashes? Or the fact that short, fragile elderly ladies being hit in the face by a deploying airbag designed for ~80 kg healthy males in an otherwise relatively low-energy and injury-free collision might seriously injure or even kill them by breaking their neck? Standard size for crash test dummies: 175 cm (5'9") tall and a mass of 77 kg (170 lb).

And note that ABS, once present in a car, was basically unconditional, the driver couldn't turn it off even if they expected icy conditions and knew about the limitations of ABS braking. So the liability of any injuries caused by ABS rested solely on the shoulders of the car manufacturer. What is the historic precedent for treating such risks?

Does this make it clearer?
 
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