NYC taxi meter and options pricing

https://questdb.io/blog/2020/10/16/taxi-drivers-are-options-traders

by bluestreak • 6 years ago

125 56 6 years ago

hardtke• 6 years ago

Some economists at Vanderbilt used the introduction of Boro cabs (green cabs) to estimate the effect of an additional for hire vehicle on traffic congestion. They claim that most of the increase in Midtown Manhattan traffic congestion is due to Lyft/Uber[1].

[1] https://www.danielmangrum.com/docs/Boro_current.pdf

Xavdidtheshadow• 6 years ago

PBS Newshour reported on the same thing in SF: https://www.pbs.org/newshour/science/how-uber-and-lyft-might...

adwww2• 6 years ago

Same in London - it feels like almost every vehicle on the road is a private hire Uber in central London.

chrisseaton6• 6 years ago

That's a good thing though, right?

We want more people using taxis rather than their own cars.

iso9473• 6 years ago

I was walking through parliament square yesterday, and was shocked by how few private cars there were. Vans, black cabs, busses made up 80%+ of my limited sample

SilasX3• 6 years ago

There’s a good deep dive on options there, but I’m just stuck on the formula they use for cab fare. $.50/minute of below 12 mph, $2.50 while over.

What?? Why would you do it like that? That incentivized jerking up to 12 mph whenever possible.

Uber got this right early on: the rate for the time and mileage are separate.

H8crilA2• 6 years ago

The rate per mile can be translated into the rate per minute via the current speed. That's why the option payout formula appears.

dannyw• 6 years ago

But why make it an option payout, instead of time + distance?

thescriptkiddie• 6 years ago

You have it the wrong way around. It's $2.50/mile, but not less than $0.50/minute. Pricing is normally by distance not time, but to protect the driver in the event that heavy traffic prevents them from covering much distance, there is floor on the charge per minute. Nothing special happens when you accelerate past 12 mph.

SilasX3• 6 years ago

Then explain the first graph.

marcinzm• 6 years ago

That incentivized jerking up to 12 mph whenever possible.

No it doesn't. Driving 12mph translates to 12 * 2.50 = $30/hour. Driving under 12mph translated to 60 * 0.5 = $30/hour. It's a smooth transition.

tozeur• 6 years ago

Second QuestDB PR piece today.

imgabe• 6 years ago

My (admittedly limited) experience in NYC taxis did involve a lot of rapid acceleration and speeding. This makes a lot more sense now. Might explain some of the NYC cabbies reputation for reckless driving if they are incentivized to be going above 12mph as much as possible.

jedberg• 6 years ago

driving customers faster earns the driver more.

I always knew this, but I always assumed it was because of the value of the $2.50 meter drop. I didn't realize how much of an incentive it was built into the meter fare.

This explains why they always drive so crazy.

tomglynch• 6 years ago

Further down the article, he draws the conclusion that the start fee is probably not enough to incentivise the drivers to drive fast, but to drive slowly to make the most of the current customer.

A slow-earning loaded cab makes more money than an empty one.

onlyrealcuzzo• 6 years ago

Is that why a lot of cabs used to drive fast... but take the long circuitous route?

diebeforei485• 6 years ago

This pricing model is weird. I'm not sure where it comes from, but isn't Uber's model (a per-minute rate PLUS a per-mile rate) clearly easier to understand for everyone?

isatty• 6 years ago

I think this is a PR piece but they simplified everything so much (both options and their db operations) that it completely missed the mark.

bern44442• 6 years ago

When the Hourly Fare rate is noted as 30 + max(0, Speed - 12) that's missing the 2.50 multipler right? Really it should be Hourly Rate = 30 + (2.50 * max(0, Speed - 12)).

Or if you prefer Lispy stuff :)

(+ 30 (* 2.5 (max (0 (- speed 12)))))

This then means if you drive at 22mph for 1 hour, you earn 30 + (2.50 * max(0, 10)) or $55 which you also get from 2.50 * 22

Is this just discounting the constant multiplier since it applies to everything and can be pulled out?

Retric• 6 years ago

A simpler formula is Max(30, Speed x 2.5).

bern44442• 6 years ago

Right, thank you. There seem to be a few instances in the article where there's either more complexity than needed or missing/incomplete information

teraflop• 6 years ago

We can see that a higher mean and a higher standard deviation result in higher option value.

This is a pretty unconvincing argument, because increasing the standard deviation increases the expected value of a lognormal distribution, even without any weird option payoffs being involved.

smabie• 6 years ago

Increased volatility of the underlying always increases option prices.

Moreover, a higher standard deviation decreases the compounded returns of a log normal distribution, not decreases it. This is called volatility drag, and is closesly related to the AM-GM inequality: the geometric and arithmetic means of a series are only equal if all terms are identical. If this is not true, an arithmetic average will always be greater.

nobody99993• 6 years ago

Going through more than 10 years worth of NYC taxi data, I analyse how the antiquated meter system impacts the livelihood of NYC cabbies by drawing an analogy with stock options trading. Interestingly, this approach allows us to show that drivers have progressively been worse-off, independently of competition from Uber.

The author ignores significant issues with the data. These include time of day, where time-specific surcharges increase the fare independent of distance or time spent in the taxi. The author also ignores the shift system for fleet cabs. As a general rule, fleet cabs operate two twelve hour shifts, with the day shift generally being less lucrative than the night shift. What's more, the author ignores the fact that Thursday evening through Sunday morning are significantly more lucrative than the rest of the week.

If you ignore the above and just average everything together, you'll miss important differentiators in revenue.

I get that the author normalized the data to enable his analysis of revenue. But given that he ignores important variables makes the results suspect.

Many drivers only drive at night. Many drivers only drive during the day. Some drivers only drive Thursday-Sunday. Some only drive Monday-Friday.

So a Monday-Friday day shift driver will generate less revenue than an Monday-Friday night shift driver. Similarly, a Wednesday-Sunday day shift driver will generate less revenue than a night shift driver.

And those who work Wednesday-Sunday will generate more revenue than those who work Monday-Friday.

And the author focuses only on the revenue side and ignores the costs. The last time I checked, a day shift lease is ~$95+full tank of gas, while a night shift lease is ~$120+full tank of gas, with a premium charged Thursday-Sunday.

However, there are other kinds of leases as well. A weekly lease, generally shared by two drivers, will run ~$900-$1000 split between them. And a monthly lease can be even more cost-effective.

And those leases include maintenance on the vehicle, insurance and vehicle storage.

While it's interesting to see the analysis of how the fee structure generates revenue, the author ignores a whole raft of other variables which directly impact on revenue generation.

Lastly, the author asserts that it's the "antiquated" taxi meter fee structure that has caused drivers to be "progressively worse-off."

I don't see how he was able to draw that conclusion from the data presented.

Edit: Fixed typos and edited for clarity

howlgarnish• 6 years ago

All the factors you cite impact driver earnings, but do they impact the analysis? At the end of the day the argument boils down to "drivers make more money when they can drive faster", which seems pretty indisputable. So if overall traffic speeds are slowing down, then in aggregate all drivers will suffer as well, although the daytime driver suffering through rush hour gridlock will be comparatively worse off than a driver who focuses on long airport rides in the middle of the night.

As for the taxi meter fee structure, Uber/Lyft can work around this with surge fees during those congested peak hours, while taxis cannot. This too is quite clearly in the Uber drivers' favor: if you're going to be sitting around in traffic, better to be paid more for it. (Unless Uber takes all the extra revenue for themselves, but that's another story.)

nobody99993• 6 years ago

All the factors you cite impact driver earnings, but do they impact the analysis?

Probably not. However, if the analysis doesn't provide enough nuance WRT revenue generation, how useful is that analysis, except as a primer on using those particular techniques in a novel fashion?

At the end of the day the argument boils down to "drivers make more money when they can drive faster", which seems pretty indisputable.

Absolutely a fair point, although ignoring the time-based variations in the demand curve likely has a measurable effect on revenue generation.

To illustrate that point, during the pandemic, overall traffic volumes are down at least 50%, presumably allowing even day time drivers to drive faster. However, some estimates of taxi driver revenue have it down 80+%.

Even more, traffic lights on one-way avenues (at least in Manhattan, where the bulk of medallion taxis operate) are generally set at slightly less than 25 miles/hour (the citywide default speed limit), so "driving faster = making more money" isn't really correct. "Driving faster than 12 miles per hour usually results in higher revenue" is probably more accurate.

So if overall traffic speeds are slowing down, then in aggregate all drivers will suffer as well, although the daytime driver suffering through rush hour gridlock will be comparatively worse off than a driver who focuses on long airport rides in the middle of the night.

That absolutely applies to day time drivers, and night-time drivers can (and usually do) generate more revenue. However, some of that difference is unrelated to speed. Rather it's related to demand. Because people know that traffic is bad during the day makes them less likely to use a taxi during the day and more likely to do so at night.

However, your example of airport rides is flawed, as rides between airports/Manhattan are a flat fare and not based on time and distance.

I don't use Uber or other FHV services, mainly because I find their business model offensive, given the huge fees they charge are way out of proportion to the services they provide -- and that's fundamentally unfair to the drivers.

Which is also why I always pay cash when using a taxi, as there's usually a fee of at least 5% on credit card transactions in the taxi, and drivers often don't receive their money for days -- yet the fleet owners require up-front payment for leases, and the drivers must fill the gas tank before returning the car.

willyg123• 6 years ago

Some drivers only drive Thursday-Sunday. Some only drive Monday-Friday.

I lived in NYC prior to Uber and when Uber was first making inroads (for 9 years until 2016, so this totally could have changed since). Often, I'd chat with the driver to pass time/reduce awkwardness. A common complaint was drivers being required to lease a cab for a full-week for 12 hours each day.

As a general rule, fleet cabs operate two twelve hour shifts, with the day shift generally being less lucrative than the night shift.

Taxi shifts are scheduled and designed so each shift is equally attractive, so that each shift gets a rush hour [1].

As an aside, as someone who works on the software side of the options trading business, I found the article to be quite interesting.

[1] https://www.nytimes.com/2011/01/12/nyregion/12taxi.html

nemo44x• 6 years ago

Wow, $120 for a premium shift today is so much cheaper than 10 years ago. I could be wrong but I remember reading back then cabbies we’re paying around $220 and in some cases not even getting a cab to drive as they were all taken.

That market really changed from a sellers to a buyers over the years.

nobody99993• 6 years ago

Wow, $120 for a premium shift today is so much cheaper than 10 years ago. I could be wrong but I remember reading back then cabbies we’re paying around $220 and in some cases not even getting a cab to drive as they were all taken.

Note that I didn't say it was $120 for a premium lease, I said $120 for a night shift lease Sunday-Wednesday, with premiums on top of that for Thursday-Saturday nights.

What's more, the Taxi and Limousine Commission (TLC) that regulates Taxis and For Hire Vehicles (FHV), has capped the maximum lease rates, since every time the fares increased, fleet owners would raise lease rates to take almost all the additional revenue.

I'm not claiming that folks make lots of money driving medallion taxis in NYC (in fact, the bottom has pretty much dropped out during the pandemic).

Rather I don't think that the analysis in the article is nuanced enough to make any comparisons with Uber/Lyft and other FHV drivers.

[0] https://www.nycitycab.com/Business/FleetTaxisforleaseList.as...

JackFr• 6 years ago

Cabs are paid by the minute below a certain speed and by the mile above a certain speed. Cab drivers will earn more by completing trips faster. Thus congested traffic costs costs cab drivers money.

The introduction of option pricing theory, terminology and various forms of hand waving does nothing but confuse the central argument with gross misapplication of theory.

Cancan82• 6 years ago

Agree that all that is needed is a “more pay per time period for more efficiency” but think it’s hard to get right.

The cab driver is constantly playing bird in the hand is worth two in the bush - do I take less per minute with this customer but take a long time, or take the customer quickly, get paid more, but then also have the risk I won’t pick anyone up for long enough that I am worse off?

I think most people go for bird in hand is the issue.

JumpCrisscross• 6 years ago

Cab drivers will earn more by completing trips faster

Medallion owners earn more when their cabs complete trips faster. What they pay their drivers is a matter of their contract.

I make this clarification because it has muddied policy waters before. Some cabbies own their medallion. But most are independent contractors to a corporate owner.

kgwgk• 6 years ago

Medallion owners earn more when their cabs complete trips faster. What they pay their drivers is a matter of their contract.

In general medallion owners do not "pay their drivers". Most drivers pay the medallion owners to lease the taxicab (or the medallion alone).

TheTank• 6 years ago

Author here. You are right this is convoluted and confusing.

I wanted to write an informal introduction to options using a more tangible example for those who are put off by the maths but still would like to gain an intuitive understanding. At the same time I wanted to show things I found were interesting in the data.

It may have been better to separate the two ideas. As you rightly say, one is confusing the other in the current form.

srtjstjsj• 6 years ago

Cab drivers will earn more by completing trips faster.

Only if supply is saturated by demand. I'd rather get paid to sit in traffic than be idle.

PaulHoule• 6 years ago

That article would benefit from editing.

He's covering a lot of ground and might have done better to lead with the graph that he made with his product, which shows that the average speed of cabs has gone down a lot.

The options curves that he talks about then involve: (1) how does slower driving impact the earnings of cab drivers and (2) is a cab driver motivated to drive faster or slower?

If log-normal distributions, greek coefficients and such were really relevant they should be realized to something like "delta was 0.2 in 2011 and 0.4 in 2012 because of X and with the consequence Y"

I am still left wondering how do the following factors combine:

- increasing traffic from increasing population and economic activity

- increasing traffic from increased ride hailing competition (those yellow cabs have a quota, but the challengers don't)

- increasing traffic from deteriorating conditions on public transit

- cab drivers deciding to drive faster or slower because of what they learned at the Chicago School of Economics

and that's were "gross misapplication of theory" comes in. When profit is the small difference between two large numbers it is easy to lose a whole basketball team's worth of shirts pricing options -- every crisis a new generation of quants learn the hard way that Marx had a point about the "declining rate of profits".

juskrey• 6 years ago

This is intuitive since taxi has much more chances to arrive late than to arrive early, because no taxi driver have ever arrived before departure.

Shivetya• 6 years ago

FWIW, a nice article covering how the current pandemic affected cabbies[0] also reveals some of the costs they pay out. While the article has a bit of fluff what many don't understand that under normal conditions a driver of a regular cab leases their car per shift in addition to credit card processing and more

[0]https://www.marketwatch.com/story/all-hail-new-york-citys-ta...

vaccinator• 6 years ago

When the cab drives above 12mph, $2.50 per mile
$2.50 x their average speed if they drove above 12mph

Seems like those arent the same... hopefully it isnt both...

OneTwoPetitFour• 6 years ago

Let's assume a cab is driving a customer at a constant speed during one hour.
$30 if they drove below 12mph ($0.50 a minute)

Average speed: 30mph => $2.50 * 30 miles = $75

It is the same, because it was already assumed to be based on exactly one hour.

NYC taxi meter and options pricing

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