### Lifeboats on the Titanic

Should RMS Titanic have carried more lifeboats? Yes, probably. But it took me a few minutes to convince myself.

Roughly 1500 died on the Titanic; according to Wikipedia, it would have cost about \$16,000 to equip her with additional lifeboats sufficient to save them all. Call it \$10 per life saved. The price level today is roughly 22 times what it was in 1912, so in today’s terms that’s \$220 per life.

Now, if I were boarding a ship for a luxury cruise, and was offered the chance to pay an additional \$220 for a guaranteed seat on a lifeboat in the event of a sinking, I’m quite sure I’d take a pass — and I’m quite sure so would virtually all of my fellow passengers. So if the Titanic had been designed to cross the ocean once and then spend the rest of its days in a museum, it would have been insane to equip her with extra lifeboats. But of course if the Titanic had been designed to cross the ocean once and then spend the rest of its days in a museum, it would have been insane to build her in the first place. So that’s not the right calculation.

The right calculation accounts for the fact that a single lifeboat provides security to passengers on multiple voyages. How many voyages? Well, the Titanic was intended to make the round trip between Europe and America every three weeks; that’s two voyages per three-week period. I’m not sure how long the sailing season was, but we know it was underway by mid-April (and perhaps earlier; it’s often mentioned that if the Titanic had been ready earlier she would have sailed earlier) so (assuming sailing conditions are roughly symmetric around the solstice) it must have lasted till at least mid-August. That’s time for five round trips at a minimum, and I’m guessing this is a quite conservative assumption.

If a lifeboat lasts a year, then, it does its job at least ten times. If it lasts five years (which is, I suspect, another quite conservative assumption), it does its job fifty times. Now we’re in the vicinity of \$4 per passenger (and of course much less if my assumptions are indeed quite conservative).

Okay, now if I were boarding a ship for a luxury cruise, and was offered the chance to pay an additional \$4 for a guaranteed seat on a lifeboat in the event of a sinking, I might still take a pass, though it’s not quite as easy a call at \$4 as it is at \$220. But a good rough empirical rule of thumb, for low-probability disasters like this, is that most people value their lives at something a bit south of \$10 million. So for most people to want the lifeboat, you’d have to believe that the chance of sinking was better than one in two -and-a-half million. Those are roughly the same odds you face when you board an airplane today, and I’m inclined to doubt that a 1912 ocean cruise was substantially safer than a 2012 airline flight.

So yeah, it seems like they should have had more lifeboats. But all the people to whom that was instantly obvious must sure be a lot quicker at mental arithmetic than I am.

#### 60 Responses to “Lifeboats on the Titanic”

1. 1 1 Roger Schlafly

The Titanic was a victim of bad luck and unforeseen circumstances. They thought that even if the hull were damaged, the ship would stay afloat long enough for all passengers to be rescued. So they thought that there was no need for lifeboats. In retrospect it seems as if the Titanic should have spent more money on lifeboats, but maybe that money would be been better spent on higher-grade rivets or improved safety procedures. There are a lot of things that might have saved those lives.

2. 2 2 Mike H

In fact, they cut corners on safety in many many ways, from the initial design through to operations, even through to mitigation of the disaster after the iceberg had been struck. They could have, for example, gone more slowly in the icefield at night.

Cynical Question : if the company had retained rights to the story of their ship, would they have made a profit, even after compensating the victims and their families?

3. 3 3 T M

This post only considers the benefit to the passenger – isn’t there a benefit to the ship owner?

Would the damage to the White Star Line company’s reputation have been quite as bad if all passengers had survived?

4. 4 4 James

Steven: are there any papers that talk about the 10 million figure?
Thanks

5. 5 5 Daniel Hewitt

The \$16k appears to be a fixed cost. Would there not also be a variable cost component? Maintenance on the boats, lost revenue due to the weight and volume they take up, etc.

6. 6 6 Harold

I suspect a lot of people assume they have a guaranteed seat in a lifeboat. If they were offered a guaranteed seat for a small fee, perhaps some would stay at home. This would be irrational.

White Star should also have considered the effect of bad publicity. I suspect it would have been well worth \$16,000 to have saved all the passengers.

I wonder how they decided on the number of lifeboats they did. If they believed the ship would not sink, then zero would be the best number. If they felt it might, then enough for all would be the best. I can’t quite see how they came up with enough for half the people to be the optimum number.

Possibly your estimates are overly optimistic in one way: one seat = one life saved. Just because I have a reserved lifeboat seat somewhere does not mean I am going to find it, let alone survive. The ship is sinking, after all!

8. 8 8 Steve Landsburg

James:

are there any papers that talk about the 10 million figure?

Google for papers by Kip Viscusi.

9. 9 9 Keshav Srinivasan

Steve, I know economists tend to make the assumption of rationality, and indeed they’ve had great success working from this assumption. But do they also assume that people have perfect knowledge of the risks they face? I for one did not know that the chance of dying in an airplane was 1 in 2.5 million, and I suspect most people do not know this either. You would have to make a hard argument to say that I somehow subconsciously knew the statistics.

Another problem is that I think people often round off probabilities: they don’t distinguish between 99.999% and 100%, and similarly between .00000001 and .00000000001. Intuitively, it seems to me that the human mind just classifies risk into categories like “certainty”, “pretty big chance”, “small but significant chance”, “negligible chance”, etc. I don’t know how many such risk categories there are, but I have a feeling that people won’t distinguish between, say, a 1 in 500,000 risk of dying and a 1 in 2.5 million risk of dying. Is there any way to confirm or refute my intuition?

10. 10 10 Ron

Harold:
They decided on that number of lifeboats as a number that satisfied
the relevant regulations. From a recent Wall Street Journal article:

Yet the Titanic was fully compliant with all marine laws. The
British Board of Trade required all vessels above 10,000 metric
tonnes (11,023 U.S. tons) to carry 16 lifeboats. The White Star
Line ensured that the Titanic exceeded the requirements by four
boats. But the ship was 46,328 tonnes. The Board of Trade hadn’t
updated its regulations for nearly 20 years.

11. 11 11 Neil

Since the Titanic’s lifeboats were only half full, there must have been an excess supply of lifeboats.

12. 12 12 Jimmy

Steven, you are overlooking the \$1,843,201,268 the film has made in revenues, presumably only possible due to the loss of life. After deducting the cost of the ship this leaves a net gain per life of over \$800,000. In 1912 money, no passenger would have paid an extra \$36,000 to cover this benefit and secure a seat in a lifeboat.

13. 13 13 nobody.really

They thought that even if the hull were damaged, the ship would stay afloat long enough for all passengers to be rescued. So they thought that there was no need for lifeboats….

My own boat – a Honda Odyssey Touring model – was designed on a similar principle. It does not have a spare tire; instead, it has “run-flat” tires that, in theory, will enable to driver to continue driving on a deflated tire 100+ miles – presumably far enough to find help.

But there’s still a place to install a spare as an emergency emergency back-up measure. If we can calculate the value of adding lifeboats to the Titanic, can we calculate the value of adding a spare to an Odyssey?

14. 14 14 Kirk

I think it’s worthwhile to note that the culture at the time of the Titanic valued lives differently, particularly on a luxury liner like the Titanic. I can’t help but think that the ability to evacuate the higher class passengers contributed to the number of lifeboats. Under Ron’s discussion of the regulations, there must be some other explanation for the extra 4 boats – hell – it might have been aesthetics.

15. 15 15 Greg Linster

Steven, that last link (“same odds”) doesn’t seem to be working.

16. 16 16 Steve Landsburg

Greg Linster:

Fixed. Thanks.

Roger Schlafly,
They got the best, the problem was steel metalurology wasn’t up to modern standards, they used the best steel at the time, but unknown to material scientests then:
http://www.sciencedaily.com/releases/1997/12/971227000141.htm

18. 18 18 joe

Hi Professor,

I am wondering what governs if a comment is published or not?

I submitted a comment last night, using the name anon, no spam, no flames, no links, just text, and it said it needed to be approved.

Today I don’t see it.

???

Thanks,

Joe

19. 19 19 Steve Landsburg

Joe: Comments need to include a valid email address (which is never published). I am almost sure the comment you’re referring to was disapproved because the email address was something like anon@anon.anon, which didnt look terribly valid.

20. 20 20 Roger Schlafly

Adam, other articles say that the Titanic did not use the best rivets available at the time. See:

There are also several other safety measures that could have been taken, in hindsight.

21. 21 21 Ron

My thought about the four extra lifeboats was that it was so that
the company could publish something like this:

At White Star Line, we care deeply about customer safety. Despite
being unsinkable, our new Titanic liner is equipped with 25% more
lifeboats that required by regulation.

22. 22 22 John K Berntson

I have a slightly different, unprovable, long-held take on the disaster. I just wrote it down on my own blog, so I won’t repeat the whole thing here, but the two things the ship had in abundance that night was 1) wood and 2) manual laborers. With a little imagination and leadership, many more lives could have been saved.

http://vanguardobserver.wordpress.com/2012/04/16/titanic-waste-of-wood/

23. 23 23 Andy B

“Should RMS Titanic have carried more lifeboats?”. If you pose the question a little differently to say “Ex ante, should RMS Titanic have carried more lifeboats?”, I think you come up with a different answer.

The ship was thought to be unsinkable. Obviously we know that to be wrong but that was the prevailing thought at the time. So unlike a modern airplane, where we do expect a very small number of them to crash before we board, people didn’t fathom it was possible for Titanic to founder. On that basis one in two-and-a-half million is clearly far too rich a price to pay for something whose expected odds of being useful are closer to infinity.

24. 24 24 iceman

Anyone know the % of non-fliers in the ‘population at large’? Seems like the imputed odds here could actually be a fair amount better than for *boarding* a plane. Also interesting per the link that deaths per vehicle mile appear to be similar for planes and cars; I guess based on the relative capacities that would make air travel around 100 times safer per passenger mile (which seems like the most meaningful # for most people), but I would’ve guessed the difference was much greater still.

The broader discussion is starting to sound like “Unsafe At Any Speed”. Of course in hindsight there’s always something more that could’ve been done, but sometimes people do their best within reasonable limits and unexpectedly bad things (or a confluence thereof) still happen. Anyone seen the famous old video of the twisting bridge? I believe we learned some fascinating things about harmonics from that. I’m sure the aesthetics of an ‘unsinkable’ ship covered with lifeboats weren’t too desirable, but if their expected purpose was primarily to offload passengers onto other ships that would have more time to come assist, I can at least imagine how some # between 0 and 100% capacity seemed optimal. I recently read there was in fact a ship just ten miles away that was confused by what we now call “cold mirages”. Some also speculate the icebergs were much worse than normal due to unusually high tides (possibly following a low sunspot cycle). That could be all hogwash, but before jumping straight to negligence I at least find it helpful to have some notion of who might’ve had an *incentive* to take excessive risk.

25. 25 25 Harold

I often doubt that safety per passenger mile is the best comparison for different modes of transport. I am sure that for many people safety per journey would be a better metric to compare the risks.

26. 26 26 Mark Draughn

I hope that \$16,000 cost of extra lifeboats includes additional crew or better rigging, because merely having additional boats on board wouldn’t have helped: The last two boats were never launched, although they were left afloat after the Titanic sank and a few people saved themselves by climbing on board.

27. 27 27 Bob Murphy

Awesome post, Steve. I’ve often wondered about this myself. As some others have asked, would it ever make sense for a ship not to “fully insure”? Or, would it make sense for an airplane to only have parachutes for half the passengers, etc.?

28. 28 28 Tushar

Extra lifeboats sank the “Eastland”
Some history from Edward Tenner, Historian:
Adding extra lifeboats on “The Eastland” (post the Titanic sinking) resulted in it’s sinking killing more people than the Titanic disaster.
Law of unintended consequences
http://www.ted.com/talks/edward_tenner_unintended_consequences.html

29. 29 29 Alex

Interesting idea but your numbers are not quite right. There’s a false presmise because the total cost of a lifeboat doesn’t need to be recouped in a single trip. Typically, it would be spread over the anticipated period of operation. The company could presumably also claim depreciation on the lifeboats to offset against tax, lowering the total cost somewhat.

30. 30 30 David

Since most boats sink by capsizing to one side or another, it would be unreasonable to assume more boats would make a difference. In this case the ship sank without capsizing, but that was in it self an extraordinary event no doubt due to the training of the engine crew.

A problem with modern boats is that the passenger count goes up by adding decks to the ship. I doubt that there was room for significantly greater number of lifeboats since the distance around the ship does limit this. Remember it is the passenger lifeboat capacity and not the quantity of lifeboats that really matters. So would lifeboats that took on more passengers have made a difference? Probably not if one of the prior posts remarking that the boats were not filled to capacity.

@Jimmy,
the revenue of the subsequent commercial exploitation of the disaster did not accrue to passengers or the cruise line, so it would be irrelevant to the decision about lifeboats.
Also, even if the profits from movie HAD accrued to the passenger’s descendants or to the cruise line’s legal successor, a claim to a large amount of money 80 years in the future is worth very little as you have to discount it.

32. 32 32 Harold

I think that many boats were not full because there were not enough women and children ready at the time to fill them. Women and children first became women and children only. This may have been for a good reason, to prevent a rush from swamping the boats.

33. 33 33 John Faben

@Harold – if you want to go from New York to LA, then deaths per passenger mile is most definitely the relevant safety statistic for you. If you just want to go *somewhere* then deaths per journey might be relevant. So first you need to ask: how often do you make a journey where you actually have a specific destination in mind, and how often do you just want to travel somewhere?

Personally, I am much more likely to have a destination in mind before I decide to make a trip (I’m going to see friends, going for business, etc.), but I realise this might not be true for everyone (e.g., people who are going on holiday might not be too picky about their destination).

34. 34 34 Steve Landsburg

Alex:

There’s a false presmise because the total cost of a lifeboat doesn’t need to be recouped in a single trip.

This is explicitly addressed in the post.

35. 35 35 Steve Landsburg

John K Bernston: You wrote:

http://vanguardobserver.wordpress.com/2012/04/16/titanic-waste-of-wood/

What an interesting and novel take on this! Thanks for sharing it.

36. 36 36 Steve Landsburg

Advo: The entertainment value is certainly relevant to the social cost-benefit analysis.

Steve,

what I think is missing with regard to the Titanic is an analysis of whether “women and children first” makes any economic sense.
Also, while it would obviously make more economic sense in general to rescue rich people rather than poor people, I wonder whether this holds true for, say, a rich person of 55 years of age vs., say, the character of Leonardo Di Caprio, since a retired rich guy would likely consume a lot of capital that might better be invested (referring to the recent estate tax discussion).

38. 38 38 Harold

John Faben: I agree, for a specific journey passenger miles is the relevant statistic. I was thinking of general claims such as air travel is safer than car travel.

39. 39 39 Ken B

Women & children first make sense in terms of a tribal history. You don’t even have to go that far back in history to get to where it makes a lot of sense.

40. 40 40 NC Lawyer

John Faben – I agree. I’d definitely want to use the deaths/mi statistic in most circumstances. The other statistic might be more valuable on high risk trips such as to Everest.

Roger,
Thanks! That was interesting, always neat to see the power of the internet.

42. 42 42 iceman

I guess SL’s link does suggest most airplane accidents involve problems associated with takeoffs and landings = ‘per trip’. People also claim most car accidents occur close to home but I presume that’s just where most of the miles are. Then Superfreakonomics tells me walking (or at least drunk walking) is the worst. Gawd why is everything so complicated?

43. 43 43 Henri Hein

@iceman:

A simpler universe would also be more boring.

44. 44 44 John K Berntson

I had forgotten until I read David’s post above, but there was plenty of capacity for more lifeboats. Titanic and Olympic had special, reusable davits, designed to launch four lifeboats per station. So, 64 boats in all, enough for 4000 people, I think. They would be stored in two stacks, two high, between and behind the davits.

Yes, it would have taken more deck space and there was the aesthetic issue, but they had given themselves that option. Why they chose not to use it? Many of the reasons discussed above, I suspect.

45. 45 45 NC Lawyer

Giving this some more consideration, should we not evaluate why 400 people died when there was available capacity for them in the lifeboats that were launched? I’ve heard that lack of lifeboat training was a factor.

46. 46 46 iceman

Henri Hein – the one unassailable truth in all of this is that if you want to get plastered while getting to point B air travel is the way. I’m reminded of this everytime I fly.

47. 47 47 Seth

I often say I’d pay extra for an ejection seat on an airplane, of course I never say how much extra.

48. 48 48 Finance Lawyer

Here’s the question that I’ve always had:

Why have more than, say a half-dozen lifeboats (to deal with minor incidents) but not enough to save everyone on board? Either she’s going to float, or she’s not.

49. 49 49 Steve Landsburg

Finance Lawyer: I believe the answer to your question is that the lifeboats were intended to ferry people to rescue ships, and it was presumed they could make several round trips to the rescue ships before the main ship went down. Nobody foresaw that no rescue ships would arrive, so nobody expected the lifeboats to have to hold all the passengers.

50. 50 50 iceman

On the design incentives per Wikipedia: “Cost considerations were relatively low on the agenda and Harland and Wolff was authorized to spend what it needed on the ships, plus a five precent profit margin.”

51. 51 51 Al D Phillips

Even guaranteeing a physical seat on a lifeboat might not have saved your life. There would not have been enough time to launch them all. Even though it took over two hours to sink,they barely got the last few in the water upright.

If I were travelling on Titanic 3rd class I probably would not have spoken English and been woken up at midnight by a crewman speaking incomprehensible. I would’ve had to understand English and figure out how to get through hallways up top to the lifeboat deck. But also been blocked by locked gates.

Had the ship sitting ten miles away had been listening to its radio, it would have arrived in an hour to rescue the poor souls

52. 52 52 MIke

I would be willing to pay a substantial amount to avoid experiencing the horror of listening to thousands drowning in the waters surrounding my lifeboat. Apparently many Titanic survivors were permanently scarred by this experience, which is easily understood.

53. 53 53 Shel

There is an information asymmetry between the company and the passengers. The company obviously makes more profits by hiding the risk to sell more tickets than showing it to charge for extra lifeboats.

54. 54 54 kiapita

One thing that some historians have pointed out is that the lifeboats on a ship the size of an ocean liner of the time were not intended to hold the entire passenger list and crew afloat for an indefinite period of time. Their main purpose was to ferry passengers to whatever ships came to aid. Remember that that the sea lanes were crawling with ships at all times. One of many aspects of bad luck that struck the Titanic that night (struck, get it?) was that the nearest ship was the Carpathia, 4 hours away. Except, of course, for the nearby mystery ship that some have speculated was the California, although this has never been proven. If an ship of any size had been within 2 hours or less, the number of lifeboats would not have been an issue.

55. 55 55 Stephen Karlson

Mightn’t the higher first class fare have included an implicit premium for faster access to the boats? (A colleague with some expertise in the history of ocean shipping suggested this years ago.)

56. 56 56 Al D Phillips

Had the officer in charge of the bridge not reversed the engines and tried to turn at full power, or even hit the iceberg head on, the Titanic probably wouldn’t have sunk.

The Titanic’s sister ship Olympic rammed a U-boat during WWI and survived.

57. 57 57 Jim Glass

Late comment on this thread, with some things not mentioned above.

I don’t think anyone noted that the lifeboats they had sailed off 40% empty. They’d have done better to have lifeboat drills.

Also, the definitive 100-year review of the sinking pretty much debunks all the popular stories about low-quality steel, money-saving shortcuts that sacrificed safety, etc. The Titanic was actually extremely well built, over engineered re specifications, the safest of ships of the era.

In fact, during the CSPAN (so you know how dry and detailed it was) program on the review one of its authors said White Star line “overcompensated” by building in very expensive but pointless safety improvements in its other ships after the Titanic sinking.

The fact is that Titanic sideswiped a berg that sliced through five of its watertight compartments. No ship was going to survive that. But it was an extremely low probability event.

Now, if the bridge officers had steered directly *into* the berg (rather than away from it, leading to the sideswipe) it would have kept sailing right on home with a dented bow, and today be the answer to a trivia question: “What famous ocean liner steered straight into an iceberg on its maiden voyage?” But who making an instant decision is going to decide to steer a ship *into* an iceberg?

BTW, Titanic’s sister ship Britannic *also* sank on its maiden voyage(!) — even after all the extra safety improvements were built into it. It was serving as a hospital ship in WWI when it either hit a mine or was hit by a German torpedo.

The thing is, such a small explosion should have done little damage to such a big ship with so many (more!) water-tight compartments … but Britannic sank like a stone with serious loss of life. Why it sank so quickly is to this day a much bigger mystery than the causes of the Titanic’s sinking … though it’s never gotten the public’s attention.

58. 58 58 Jim Glass

Had the officer in charge of the bridge not reversed the engines and tried to turn at full power, or even hit the iceberg head on, the Titanic probably wouldn’t have sunk.”

Here’s the video on the report I mentioned in my prior comment:
http://www.c-spanvideo.org/program/SSTi

It concludes the bridge officers made the optimum turn, anything else would have been worse (e.g. by slashing the stern as well) apart from steering directly *into* the berg. The bow of the ship was by far the strongest portion because the highest risk of collision was head-on. Also, only the forward water-tight compartment (or two) would have been ruptured. The ship and people on it would have been fine — except for the unfortunate crew members who had living quarters in the bow. But who steers directly into an obstacle?

“The Titanic’s sister ship Olympic rammed a U-boat during WWI and survived.”

Ramming a U-boat would have been like squashing a grape for Titanic. But remember how Titanic’s other sister ship Britannic also went to the bottom on its maiden voyage in WWI, in a near inexplicable manner.

59. 59 59 Al D Phillips

I’m sorry I did not intend to imply they should should have hit the iceberg on purpose, but rather to suggest that had they accidenally hit it without seeing it the results would have been better.

1. 1 Potpourri