# Can We Make Density Make Sense?

When commentators argue about the importance of density to public transit, it’s common to hear a range of density figures thrown around.  These figures are almost always averages over a large area, and as I argued on my recent post on the perils of average density, averages are simply useless for describing the kind of density that determines public transit outcomes.

As Paul Mees’s new book shows, you can easily run numbers that show that metro Los Angeles is denser than metro New York. If you want to sow confusion, you’ll use those numbers to imply that since Los Angeles has far lower transit ridership than New York, density must not matter to transit after all.  In fact, density matters, but average density doesn’t.  What matters to public transit is the density right around its stations and stops, and this can be quite unrelated to the average density of a whole urban area.

The post is still worth a look for its excellent comment thread.  Several commenters proposed alternative ways of talking about urban density that would better describe the way density matters to transit.  They all seem to have the same theme:

The conventional idea of density is about comparing units of area to each other: this patch of land is denser than that.  Instead, compare the densities of units of population.

There seem to be two ways of asking a population-centered density question:

1. What percentage of the population lives at densities above x?
2. What’s the average density at which people in this city live?

On the blog We Alone on Earth, Fedor Manin took a shot at the question “what percentage of the population lives at each density?”  Here are his graphs:

The second graph is a distribution of the population by density, showing what percentage of the population is in each density range.  Unlike the average densities of metro Los Angeles and metro New York, which I discussed in my last post, these graphs get closer to what matters for transit.  In New York, (the pale blue line) you have a lot of people living at very high density — inevitably right next to a subway station — and these are what drive the city’s high transit needs and performance.  In Los Angeles (the dark blue line that peaks in the center of the graph) you have an overwhelming predominance of a moderate density figure.  That moderate density corresponds to development forms ranging from the townhouse to the four-story apartment building, but this form requires long travel distances and more spread-out access needs than New York does, so it yields much lower transit performance.

Notice how this graph corrects common stereotypes of Los Angeles, stereotypes that you might find reinforced by Google Earth.  A lot of the area of metro Los Angeles is large detached homes with swimming pools, a very low density.  So if you’re thinking in terms of area — as anyone looking at a map must implicitly do — that development pattern seems to dominate the city.

Yes, but although those stereotypical homes cover a lot of area, they don’t represent all that many people!  That, after all, is what low density means!  So if you look what percentage of the population of Los Angeles that lives in these low-denstity homes, it’s not much.

Now here’s the point that’s easiest to miss:   All that area covered by relatively few people is not really a problem for transit, so long as we don’t give it more service than its relatively small population (and low ridership potential) deserves.  Transit outcomes don’t really depend on how much of this low density stuff there is in a city.  They depend on how much high density stuff there is, and the average density of the whole city will tell you nothing about that.

Fedor Manin’s distributions of population by density, charted above, still don’t get us exactly to a citywide assessment of “density as it matters to transit,” but they are much, much closer than any citywide average density.  On the other hand, a distribution can’t be reduced to a single quotable number, and in many conversations, if you don’t have a single quotable number, you don’t get a word in.

So the answer, as several commenters have suggested, is probably to talk about the average density per person rather than per unit of area.  It may seem that density is intrinsically a “per unit of area” concept, but you can certainly ask:  “At what residential density does each citizen live?”  Here, residential density is ideally the density of a single parcel: one house or apartment building.  What percentage of the population lives on detached homes on quarter-acre blocks?  What percentage lives in buildings taller than five stories?

Then, you can ask “What’s the average residential density at which people in this city live?”  Again, this is an average over the population — not, like conventional density, an average over the area.

This is probably still too much averaging, and likely to mislead, but at least it takes out a lot of the noise that contaminates citywide averages, and focuses on fine-grained parcel-level patterns that are more likely to reflect proximity to transit.  Readers are encouraged to play with this idea!

### 29 Responses to Can We Make Density Make Sense?

1. Phil LaCombe October 2, 2010 at 8:58 am #

This is a very thought-provoking post, especially your perspective on the no-problem of transit in the low-density areas of Los Angeles. I’d be interested to see Baltimore, having a different typology than these cities–the rowhouse city, added to these graphs.

2. anonymouse October 2, 2010 at 9:31 am #

Yes, I think this is a much more useful way of looking at density. The numbers clearly show that a large part of LA’s population lives in moderate density areas, and that this makes for “long travel distances”. But this alone is not quite enough to explain the poor performance of LA’s transit network. You also need to look at the network itself. And LA’s system consisting primarily of buses running in mixed traffic on local streets is not well suited to competing with driving long distances on freeways. Neither are freeway express buses, because the decentralized nature of LA makes it difficult to provide the “one seat ride” that would make such buses useful. But neither is NYC’s system where many people commute exclusively by subway (as opposed to a combination of subway and bus), because the existing density just wouldn’t support such an extensive subway network.

3. Eric Doherty October 2, 2010 at 9:34 am #

If “What matters to public transit is the density right around its stations and stops” Then this seems like a problem best tackled with GIS (Geographic Information Systems) analysis.
But perhaps what matters even more is the density of potential transit riders, and where they live in relation to transit (I say live because that is what there is census data for). For example, adjust the figures for income and immigration status (the longer you live in Canada and the more money you make, the less likely you are to ride transit).
In either case, you should be able to do a buffer analysis of the area around each stop (or route for frequent stop service). I don’t know what you would find, when I tried to do this for Metro Vancouver I could not get the data for the transit routes.

4. David Marcus October 2, 2010 at 11:30 am #

By most of these measures, Boston has a low density, yet I think of it as one of the better transit cities. Perhaps what it lacks in density it makes up for in walkability

5. SpyOne October 2, 2010 at 12:00 pm #

I can see this being distilled down to one quotable figure that still has meaning: the number of people (or percentage, if that will sway your audience more) who live at or above a certain threshold of density. “See, we can support a transit service, because 100,000 people live in areas over (x) people per square mile.
Pair this with a similar figure for jobs. “Further, (y)% of the city’s jobs are in an are where there are (z) jobs per square mile, so transit could easily take people from those homes to those jobs.”
And the wheels come off the cart when someone realizes the homes are all half-million-dollar brownstones and the jobs are all in the food court at the mall, but you get the idea.
I cam from a rural town that used similar reasoning to put in transit: There was a university campus that ran its own bus service in the middle of rural housing and farmland, and about 12 miles away there was a tiny city with a business district about a block-and-a-half wide and three miles long. The city couldn’t support a bus on its own, and the town didn’t think it would be possible to run a profitable bus when the houses were 4 to a mile, but between them the three entities cam up with a bus that ran every hour, from the university down a state highway that ran down the middle of the town, then ran along the main street to shopping center and then returned.
And it turns out a surprising number of teens will walk 2 miles to a bus stop if the bus will take them to a mall, and if the alternative is to watch the trees grow. And college students are less likely to flee campus every weekend if there is some way to get to a Kmart without a car, or to a grocery store that doesn’t charge 50% extra because it is close to the campus. They even extended the bus service to run beyond the campus in the opposite direction, as they realized the bus could turn an impossible walk into a possible walk, if not a convenient one, for a large number of people.
Now most folks would have said you can’t do an effective transit system for a town of 15,000 people spread over 45 square miles. Heck, folks said the city couldn’t do transit, and its 15,000 people were in 4.5 square miles. But it worked.

6. Alon Levy October 2, 2010 at 3:07 pm #

Boston has the fifth highest perceived density in the US, trailing NY, SF, LA, and Chicago. It also has the second highest ratio of perceived to standard density, which by itself is also a correlate of transit use.

7. Steve Lax October 2, 2010 at 5:46 pm #

Does DENSITY need to make sense? We know that many factors lead to the success/failure of transit, both in general and at the route level. Density is an important factor; but only in the context of many other factors that have been discussed in this forum often (access to the transit, income levels, connectivity to jobs, etc.)
One of the more successful new routes I was partially associated with connected three small cities (about 25,000 to 50,000 population each and within 15 miles of each other) to a city with about 40,000 population about 35 miles from the closest of the first three cities (total route length of fifty miles). Most of the land between was farmland or environmentally protected land. However, the three small cities had lost industry and had a population that could and was trained to take jobs in a growth industry in the fourth city. The service started with six round trips a day seven days a week. At its peak it had 45 round trips a day and now has 38 round trips (due to a decline in the growth industry.) But the service succeeded despite low density along the route (even in the three small cities) because a need was identified and the transit service was tailored to meet that need.

8. Matt October 2, 2010 at 6:09 pm #

I looked into perceived density following Alon’s link to a great report published by Minnesota DOT in 2001 (http://www.lrrb.org/pdf/200124.pdf). The report makes a strong argument for perceived density over average density. However, the report also finds that perceived job density and residential concentration are more important than perceived residential density when explaining transit mode share.
I did find one problem with the calculation of perceived density. The perceived density of any city will vary, depending on what size geographic unit you select. This was raised by Richardson, Brunton and Roddis in 1998 (http://www.tuti.com.au/Publications/1998/1998Density.pdf). They applied the perceived density approach to various sizes of Australian Census boundaries and the smallest geographic unit (Collector District) provides the highest perceived density.
This makes a comparison of perceived density between different cities a little more complicated, as you would always need to specify the size of the geographic units when you quote a perceived density. It also makes comparisons across countries problematic (for example US traffic zones are larger than Australian Collection Districts).

9. jarbury October 2, 2010 at 8:04 pm #

I agree this is a far better way of measuring density. I’d be fascinated to see a similar graph for Auckland, and how it compares with other cities in Australia most particularly.
Relatively little of Auckland seems to be particularly high densities, so I think we’d be something similar to Los Angeles, if not a bit lower in densities.

10. F October 2, 2010 at 9:56 pm #

Here’s a graph with DC and Baltimore:

If you find me data for Australia and New Zealand (or any other country — ideally it would be over units comparable to US block groups) I’ll make the graphs.

11. Alon Levy October 3, 2010 at 12:58 am #

Matt, the link you posted is precious, and is something I’ve wanted to see for a while. I was thinking of doing the adjustment on a population basis and not on an area basis, but it seems that the authors found a reliable adjustment factor coming from area.
For US-Australia comparisons, I’m not sure what to do about area. But I can tell you that US census tracts (used in the Austin Contrarian’s table, but not in Gary Barnes’ more granular table) have on average about 5,000 people. Urban tracts tend to have somewhat more – in New York City, they have about 10,000.

12. Alon Levy October 3, 2010 at 1:02 am #

Sorry, the AC table I linked to in my previous comment is much coarser than I said. It uses municipalities, not census tracts. Here is the census tract table.

13. ws October 3, 2010 at 5:52 pm #

Matt touched on “job density”, which I feel is also a good indicator of overall metropolitan transit use, but often not discussed much.
Are high job densities something major metropolitan or medium metropolitan areas should strive for?

14. Alon Levy October 3, 2010 at 6:07 pm #

WS: I think everyone agrees that the more jobs are located right next to stations, the better. But beyond that, views differ, especially on the question of whether job concentration in the CBD is good or bad. The basic tradeoff is that CBDs’ high job density and traffic congestion make them easier to serve by transit, but then travel would be unidirectional so trains and buses would be empty going in the other direction.

15. J October 3, 2010 at 9:51 pm #

Ha, I was having a conversation similar to this last week.
Someone was saying that transit doesnt work in the US because “not everyone lives in new york”. He was implying that the vast majority of the country is not dense enough for transit.
Well yeah, thats why it’s low density, because few people live there. And high density places are dense because so many people live there….thats how they get dense!
More people take the bus in a single major city like LA than live in a state like south dakota.
Thats why you get to ignore all those low density places. The majority of the population lives in areas dense enough for transit.

16. voony October 3, 2010 at 9:54 pm #

Yes, Matt is right job density pattern is probably more important than residential density pattern.
Cities with strong CBD usually achieve very high ridership, and if I remember correctly Seattle perform better than Portland i term of modal split, and if a reason is to find, it is the job density. We could say the same of Calgary in Alberta.
Since Jarret was mentioning Paul Mees’ last book.
Having read it, I could have a less indulgent opinion than Jarret on it. I understand that the Paul Mees thesis is to say “you don’t need high density to provide transit” because the number given in the book “prove it”, and so “we can happily continue to live our suburban life as is” is the conclusion of the book.
As discussed here, density pattern is very important, and rough CMA data have little value (Tokyo by that token, is also low density), and I have found hat Paul Mees was not going beyond it, and you need to go beyond it:
It is what I have try to do for Zurich, since provided as an example of low density region achieving high transit market share, by Paul Mees. http://voony.wordpress.com/2010/04/26/thezurichmodel/

17. M1EK October 4, 2010 at 6:37 am #

Jarrett, a local blogger friend of mine wrote on some of this stuff a couple years ago:
http://www.austincontrarian.com/austincontrarian/2008/03/weighted-densit.html
You might find it interesting.

18. francis October 4, 2010 at 10:00 am #

Regarding LA (and other places)…
Single family house does not necessarily mean single family occupancy. There are numerous examples of informal garage units, extended families in one house, etc. On the flip side highrises are not necessarily high density if most residents aren’t full-time.

19. SpyOne October 4, 2010 at 10:06 am #

There’s density and then there’s density.
For instance, “is high job density something cities should strive for?” Maybe.
Too much density can be a bigger problem than too little. As the job density goes up, you have more and more people commuting each day to a smaller and smaller area, and that will cause traffic problems. 50,000 people trying to get to, or from, a 50,000 seat stadium create traffic snarls: it’s just too many people and too concentrated an area.
However, 50,000 people spread over 50,000 square miles is also a problem, as they require far more infrastructure per person. If they lived closer together, their homes could be served with fewer miles of roads, for example.
There is probably an “ideal density”, or at least an “ideal density range”: something that maximizes sharing of infrastructure balanced against minimizing traffic problems caused by large numbers of people all trying to go to the same region at once.
Better for transit, too: you’d rather have riders who want to get off along a stretch of a route than have them all want to get off at the end, I’d think.
Same goes for “we can’t all live in New York”. In 1900, something like 5% of our population lived in cities, although many of the “rural towns” had transit, as every town with a population over 5000 had a streetcar line. And although a much higher percentage lives in cities today, much of the population still lives in areas where transit is impractical. States like Alaska and Wyoming have populations so spread out that even connecting their communities, by bus or train, isn’t very practical.
But much of our population DOES live in areas where transit is possible. For example, the population of Washington DC is pretty close to that of Wyoming. Suggesting that transit will only work in big cities is ignoring how big some of our smaller cities have grown.
To see the flaws of “average density”, one need look no farther than Virginia Beach. Our average density (from wikipedia) is 1,712.8/sq mi (661.3/km2), but that ignores the fact that almost noone lives in the southern half of the city. And I don’t mean “nobody important”, I mean less than 1000 people, as it is all rural farmland.
Transit looks a lot more doable when you realize that most of the population and almost all of the businesses are along a couple of major arteries.

20. Tebici October 4, 2010 at 1:48 pm #

I also found it interesting that Chicago, Boston, and the Bay Area, look a lot more like Los Angeles than New York based on these graphs. My intuition (having been to all of those cities except SF) is that the answer is basically what you addressed quite well in your previous post in your discussion of Las Vegas (https://www.humantransit.org/2010/09/the-perils-of-average-density.html) “The Las Vegas way is to build utterly car-dependent apartment buildings on a vast scale”, “typical Las Vegas urban fabric is designed for motorists and hostile to pedestrians.” L.A. might not be quite as bad as Las Vegas and does have some functional pedestrian neighborhoods, but there is no guaranteeing these are where most of the density is; a great example is Melrose Avenue, a popular shopping street which is surrounded by single family homes. I’m not sure how you would measure that difference with available data. One possible metric may be mix of uses on a fine scale. Though they have a lot of inverted corner shopping plazas which are actually 2 story. The design seems very car oriented but I wonder how they have enough parking for two stories in that space unless they get walkup traffic.
Having lived in Cambridge and Somerville, MA, you will find that very few areas are over 4 or 5 stories, there are many detached single family and “triple deckers” (3 stacked flats in a detached building) and yet it is very multi-modal. (Granted all of these are _very_ small lot and mostly likely “underparked”.) So I wouldn’t want to leave people with the impression that you have to reach Manhattan densities to have good transit service.
On the other hand Atlanta is exactly what I expected with the “bump” occurring at a much lower density. While they’re implementing some good things now they’ve got a challenging starting point.
The Atlanta Smartraq study had some interesting grid analysis of the city highlighting which neighborhoods had a combination of street grid density, mixed use, and residential density. One interesting element of the study was that the score of one grid block also took into account the performance of it’s immediate neighboring blocks so it accounted for whether it was isolated or part of a larger walkable neighborhood. The grid blocks were 200m square. I would have to talk to a local to find out whether they thought it matched their perception of the city. Note: their interest was walking; not specifically transit.
The other question of course is how these densities are arrayed within a city. Is it a bullseye metro with the densest parts in the middle in close proximity to one another or strung along axes easily served by transit? Or is the density completely scatter-shot?

21. Alon Levy October 4, 2010 at 2:33 pm #

@SpyOne: as I said, there’s a tradeoff. You have the Tokyo CBD, with around 2 million people working within an area of about 20 km^2. This CBD is served by nine subway lines and seven commuter lines, which are busy at all times and generate profits to their operators. On the other hand, those lines are severely overcrowded; some are running at twice over capacity.

22. The Overhead Wire October 5, 2010 at 9:16 pm #

I don’t want to do too much self linking but I also didn’t want to write all these posts over again in the comments. I will say that there has been a bit of research on employment density but not as much as residential density. Because 60% of transit ridership comes from work trips, I think that employment plays a much larger roll than residential, though both ends of the trip are important. But considering nimbyism in the suburbs and the lack of ability to change densities there, the focus on employment centers without these types of barriers become more important points for intensification. Additionally, if you read Zupan’s work, transit ridership increases when the density of housing is closer to the intensity of employment, which you saw in the last housing boom where areas just outside of downtown where filling in (ie South Waterfront, LODO, South End Charlotte etc) These places took pressure off the exploding market for downtown which was expanded a few stops away by the transit access.
For those discussing employment density and the importance of employment, you might want to check out a few of my previous posts:
Pushkarev and Zupan on Employment
Employment Incentives Near Transit
Station Locations and Employment
Importance of Employment Centers

23. stephen October 19, 2010 at 9:55 pm #

I feel like I must take issue with this presentation of density for two reasons; first because it discounts the travel needs of people in low density areas and second because it leads us to thinking that the majority of people live in dense areas and this is simply not true, at least not in King County, WA.
As shown in the data below only approximately 18% of the county’s population lives at a density that is supportive of 30 minute service or better. Jarrett, your statement that low density areas are only a problem if you allocate more than the appropriate amount of transit to them is all fine and good until you realize that 63% of the population will be paying for service that provides really very little utility to them. And there is no weighting formula that will change the absolute majority of people living at low density areas compared to higher density areas.
Population within King County living in block groups with population densities over given dwelling unit per acre thresholds, shown as (Threshold; Population; % of Total Population)
<4; 1,186,014; 62.9%
>=4; 367,254; 19.5%
>7; 125,393; 6.7%
>9; 205,538; 10.9%
Levels of Transit Service by Density Thresholds DU/Acre as suggested by Transit Capacity and Quality of Service Manual
<4 = Non/Fixed Route
>=4 = 1 bus/hour
>7 = 1 bus/30 min
>9 = Frequent service
Focusing on density is divisive because it says, we count and you don’t. If pushed too far, you will either dilute your density thresholds to include more of your taxing region or you risk alienating a majority of you tax base. If you want transit to have broad appeal, you need to find a way to take suburban transit seriously.
What is really at play here is not who do we serve and who do we not, but that the cost of meeting transit demand varies by land use. Despite the circuitous routing, the auto oriented development and the dismal farebox recovery of suburban services, unlike many other utilities, as density and demand increase the service cost per capita also increases, see the second chart below. If that is the case either denser areas must recover even more of their operating expenses through the farebox, (the West would need to generate another \$104 million in fares, or a 124% increase) or we would need to explain that the usefulness of transit increases as density increases and in order for transit to meet that increased demand the public should pay more for it.
2009 Public Investment in Transit Per Capita by Subarea*
Shown as (County Subarea; Population; Perceived Population Density – by gross acre**; Total Non-Fare Revenue Operating Expense; 2009 Public Investment per Capita)
West; 699,140; 18.09; \$182 Million; \$260.00
East; 539,705; 5.85; \$60.4 Million; \$112.00
South; 700,375; 7.27; \$78 Million; \$111.00
*Based on documents prepared for the 2010 Regional Transit Task Force and Suburban Council Population figures.
**Based on 2008 Population Estimates
One solution would be to require denser areas recover more of their operating costs through their fare box to offset the increased cost in operations. They already do you say, yes but not nearly enough to offset the increased level of service. For the West Subarea to afford the level of transit service that they currently have, without having a disproportionate public per-capita expense, they would have to generate another \$150 million in fares, or about double what they already collect.
Thoughts?

24. Jarrett October 22, 2010 at 9:59 pm #

@Stephen. Re the uselessness of aggregate density figure see here:
https://www.humantransit.org/2010/09/the-perils-of-average-density.html
The relationship between density and transit ridership is overwhelming if you focus on density right around stops and stations.
Transit is intrinsically an unevenly distributed service. If you believe that its purpose is to meet needs regardless of ridership, you’ll spread it out everywhere. But if you believe that its purpose is to maximize ridership, then you’d do just what a business would do and focus on the best markets. And for transit, localized density around potential stops and stations is the best indicator of a good market.
For more on that tradeoff and policy tools for understanding it see here:

25. stephen October 22, 2010 at 10:30 pm #

@Jarrett,
Actually the more I’ve looked at the charts, in the article you reference the more I realize I must be talking about some other kind of equity.
The point I’m trying to make is that often dense areas do not represent the majority of the taxing area. This whole issue of where transit should be provided is only a question because people from all development areas, transit friendly and transit averse, contribute to it.
What’s more the service cost per captia increases as the density increases. Even when people can admit that service costs are inherently different based on the land use etc. I will still be resistant to taxing myself when I have no way of knowing whether my level of taxation is appropriate.
I’m only arguing that if transit is so much more productive for dense areas (which it is) then why can’t those dense areas pay for the difference? Which maybe it could if fares were taken seriously in the US as funding stream (I’ve heard many people suggest we should get rid of them all together). There must be something that makes sure dense areas are being cost effective and they are not simply using their transit superior land use as an argument for more money.

26. stephen October 22, 2010 at 10:32 pm #

Errata, I meant to say that the dense areas often to do not represent the majority of the population within the taxing district.

27. Joseph November 27, 2010 at 1:23 am #

Why should people who live in dense areas pay for the many more road-miles per capita in the less dense areas?

28. Jackie January 5, 2011 at 6:42 pm #

A number of responses arguing for more transit operating costs to be recovered through fare box, suggested that it was unfair to subsidise transit operating costs. These responses do not take into account the contribution of transit to reduced road congestion, health and accident costs, and reduced emission. These responses correspondingly fail to recognise the multi billion dollar subsidy of road cost externalities. Indeed, the Indpendent Pricing and Regulatory Tribunal (NSW) concluded that the external benefits from rail and bus use in reduced congestion, emissions and accidents, was around 70% of revenue requirements. Thus IPART determined that fares were required to fund only 30% of transit revenue requirements.
If the full externalities of road use are accounted for – spatial land use, parking, costs of social exclusion, the adverse health effects of sedentary travel and consumer operating costs – there is a sound economic case for free transit. Not that I would argue for the latter, but proper costing of road use compared with transit is absolutely essential to understand the full costs to society of not providing transit.
This is more critical to understand than arguments on density. To argue whether or not density is required for transit involves somewhat of the traditional chicken and egg argument on what comes first. Transit combined with land use planning around rail stations, provides the basis for higher density to evolve!

29. Nick February 25, 2012 at 5:25 pm #

Regarding what kind of densities most Angelinos live at, it’s probably single family homes. However, the single family homes are on smaller lots than in other cities. Most of Los Angeles lives at densities of 3000-9000/km2 mostly. Here’s roughly what each density levels look like at a neighbourhood level:
1000/km2: Really large lots like Atlanta’s suburbs
3000/km2: Single family on lots of about 1/6 to 1/8 acre
5000/km2: Typical 20th century streetcar suburbs, think Chicago’s bungalow belt
7000/km2: Townhouses or single family on very narrow lots
10000/km2: Rowhouses and townhouses, or 2 storey apartments in the case of Los Angeles
15000/km2: 2-3 storey apartments like in Montreal’s Plateau Mont Royal
20000/km2: 3-5 storey apartments like the centre of Koreatown
30000/km2: 4-8 storey apartments like in the Bronx or Harlem
50000/km2: 10-20 storey apartments (not tower in the park) like in certain parts of Manhattan … OR 4 storey apartments with very narrow streets and very small courtyards like parts of Barcelona
80000/km2: 20-80 storey apartments, think Hong Kong but with more spacious units
I think one way of getting good results for transit share would be essentially compining the density gradient and weighted density. I have a hard time seeing how a city that has a small core at 5000/km2 and the rest at 1000/km2 would have a higher transit ridership than a city that’s uniformly 10000/km2, even though the less dense city has a higher gradient.
The advantage of a city like Boston compared to San Diego, which has a similar weighted density but less steep gradient might be that the average for both cities is not dense enough for high transit ridership, but Boston has more very high density, which generates most of the transit usage. Basically, you could look at it like this (example)
30000/km2: 70% chance of using transit
10000/km2: 40% chance of using transit
5000/km2: 10% chance of using transit
3000/km2: 5% chance of using transit
1000/km2: 3% chance of using transit
Of course, you should be looking at both residential and employment density, maybe even retail density.
There are a few other factors, like where the highest density is located (ideally all in one place), which puts LA at a disadvantage.
I would suggest that another disadvantage LA has over a city like Seattle, which has a lower weighted density and gradient, but still has higher transit usage, is related to size. If you assume a bus takes twice the time to get from A to B than a car, a trip from a typical Seattle neighbourhood to downtown might take 15 minutes by car and 30 minutes by bus, so people might be willing to take the bus since 15 minutes is not that much time. However, LA is so huge that it might take 40 minutes by car and 80 minutes by bus, fewer people are willing to make that 40 minute sacrifice, especially when their commutes are already longer.
What LA would need is more rapid transit, which would require very high densities, or commuter rail, which I find works better in centralized cities. Commuter rail where I live is not very frequent, so it doesn’t work well if you have to transfer from one commuter rail line to another, hence why you need all commuter rail lines to end downtown somewhere.