Revenue management at Liverpool Football Club

Liverpool Football Club, of which I’ve been a fan for nearly eleven years now, is in the midst of a storm with fans protesting against high ticket prices. The butt of the fans’ ire has been the new £77 ticket that will be introduced next season. Though there will be few tickets that will be sold at that price, the existence of the price point has been enough to provoke the fans, many of whom walked out in the 77th minute of the home draw against Sunderland last weekend.

For a stadium that routinely sells out its tickets, an increase in ticket prices should be a no-brainer – it is poor revenue management if either people are scrambling for tickets or if there are empty seats. The problem here has been the way the price increase has been handled and communicated to the fans, and also what the club is optimising for.

At the outset, it must be understood that from a pure watching point of view, being in a stadium is inferior to being in front of a television. In the latter case, you not only have the best view of the action at all points in time, but also replays of important events and (occasionally) expert commentary to help you understand the game. From this point of view, the reason people want to watch a game at the ground is for reasons other than just watching – to put it simply, they go for “the experience”.

Now the thing with stadium experience is that it is a function of the other people at the stadium. In other words, it displays network effects – your experience at the stadium is a function of who else is in the stadium along with you.

This can be complex to model – for this could involve modelling every possible interaction between every pair of spectators at the ground. For example, if your sworn nemesis is at the ground a few seats away from you, you are unlikely to enjoy the game much.

However, given the rather large number of spectators, these individual interactions can be ignored, and only aggregate interactions considered. In other words, we can look at the interaction term between each spectator (who wants to watch the game at the ground) and the “rest of the crowd” (we assume idiosyncrasies like your sworn enemy’s presence as getting averaged out).

Now we have different ways in which a particular spectator can influence the rest of the crowd – in the most trivial case, he just quietly takes his seat, watches the game and leaves without uttering a word, in which case he adds zero value. In another case, he could be a hooligan and be a pain to everyone around him, adding negative value. A third spectator could be a possible cheerleader getting people around him to contribute positively, organising Mexican waves and generally keeping everyone entertained. There can be several other such categories.

The question is what the stadium is aiming to optimise for – the trivial case would be to optimise for revenue from a particular game, but that might come at the cost of stadium “atmosphere”. Stadium atmosphere is important not only to galvanise the team but also to enthuse spectators and get them to want to come for the next game, too. These two objectives (revenue and atmosphere) are never perfectly correlated (in fact their correlation might be negative), and the challenge for the club is to price in a way that the chosen linear combination of these objectives is maximised.

Fundamental principles of pricing in two-sided markets (here it’s a multisided market) say that the price to be charged to a participant should be a negative function of the value he adds to the rest of the event (to the “rest of the crowd” in this case).

A spectator who adds value to the crowd by this metric should be given a discount, while one who subtracts value (by either being a hooligan or a prude) should be charged a premium. The challenge here is that it may not be possible to discriminate at the spectator level – other proxies might have to be used for price discrimination.

One way to do this could be to model the value added by a spectator class as a function of the historic revenues from that class – with some clever modelling it might be possible to come up with credible values for this one, and then taking this value into account while adjusting the prices.

Coming back to Liverpool, the problem seems to be that the ticket price increase (no doubt given by an intention to further maximise revenue takings) has badly hit fans who were otherwise adding positive value to the stadium atmosphere. With such fans potentially getting priced out (in favour of fans who are willing to pay more, but not necessarily adding as much value to the ground), they are trying to send a message to the club that their value (toward the stadium atmosphere) is being underestimated, and thus they need greater discounts. The stadium walkouts are a vehicle to get across this point.

Maximising for per-game revenue need not be sustainable in the long term – an element of “atmosphere” has to be added, too. It seems like the current worthies at Liverpool Football Club have failed to take this into account, resulting in the current unsavoury negotiations.

Now that I’ve moved to Barcelona, Liverpool FC need not look too far – I’ve done a fair bit of work on pricing and revenue management, and on two-sided markets, and can help them understand and analyse the kind of value added by different kinds of spectators, and how this can translate to actual revenues and atmosphere. So go ahead and hire me!

Bias in price signals from ask only markets

Yesterday I listened to this superb podcast where Russ Roberts of the Hoover Institution interviews Josh Luber who runs Campless, a secondary market for sneakers (listen to the podcast, it isn’t as bizarre as it sounds). The podcast is full of insights on markets and “thickness” and liquidity and signalling and secondary markets and so on.

To me, one of the most interesting takeaways of the podcast was the concept that the price information in “ask only markets” is positively biased. Let me explain.

A financial market is symmetric in that it has both bids (offers to buy stock) and asks (offers to sell). When there is a seller who is willing to sell the stock at a bid amount, he gets matched to the corresponding bid and the two trade. Similarly, if a buyer is willing to buy at ask, the ask gets “taken out”.

The “order book” at any time thus contains of both bids and asks – which have been unmatched thus far, and looking at the order book gives you an idea of what the “fair price” for the stock is.

However, not all markets are symmetric this way. In fact, most markets are asymmetric in that they only contain asks – offers to sell. Think of your neighbourhood shop – the shopkeeper is set up to only sell goods, at a price he determines (his “ask”). When a buyer comes along who is willing to pay the ask price of a good, a transaction happens and the good disappears.

Most online auction markets (such as eBay or OLX) also function the same way – they are ask only. People post on these platforms only when they have something to sell, accompanied by the ask price. Once a buyer who is willing to pay that price is found, the item disappears and the transaction is concluded.

What makes things complicated with platforms such as OLX or eBay (or Josh Luber’s Campless) is that most sellers are “retail”, who don’t have a clear idea of what price to ask for their wares. And this introduces an interesting bias.

Low (and more reasonable) asks are much more likely to find a match than higher asks. Thus, the former remain in the market for much shorter amount of time than the latter.

So if you were to poll the market at periodic intervals looking at the “best price” for a particular product, you are likely to end up with an overestimate because the unreasonable asks (which don’t get taken out that easily) are much more likely to occur in your sample than more reasonable asks. This problem can get compounded by prospective sellers who decide their ask by polling the market at regular intervals for the “best price” and use that as a benchmark.

Absolutely fascinating stuff that you don’t normally think about. Go ahead and listen to the full podcast!

PS: Wondering how it would be if OLX/eBay were to be symmetric markets, where bids can also be placed. Like “I want a Samsun 26 inch flatscreen LCD TV for Rs. 10000”. There is a marketplace for B&Bs (not Airbnb) which functions this way. Would be interesting to study for sure!

Charging for parking

In a potentially interesting move, the Delhi government has declared that starting from 2016, only half the stock of Delhi’s cars will be allowed on the road each day, based on the parity of the number plate.

While in theory it might work, the dependence of Delhi people on cars, ownership of multiple cars and possible number-trading might render it moot. Also, given that not everyone uses their car every single day, a simple car swap arrangement (like Zipcar; but we need to figure out liability properly) might defeat this regulation.

The more sure-fire way to reduce the number of cars on the road is to impose a congestion surcharge but it it is not an easy regulation to implement – given that you’ll need electronic modes to collect tolls, devices in cars, etc (not that it hasn’t been done, but given India’s scale it’s considerable effort).

A better way to implement congestion surcharge is to charge economic rates for parking. In most cities in India nowadays, parking is highly subsidised (in terms of money) which results in more people taking their cars out, not being able to park them, and creating further congestion by driving around looking for a place to park (Brigade Road in Bangalore is a good example of parking-led congestion thanks to slow-moving cars looking for a place to park).

The question is what an economic rate for parking must be, and that can be determined by looking at the prevailing real estate rates in that area. In the area I live in Bangalore, for example, the “guidance value” (rate used by the municipal corporation to determine the “fair value” of a property in order to tax sales) is about Rs. 8000 per square foot.

Assuming a price to earnings ratio of 20, this translates to Rs. 400 per square foot per year, or little more than a rupee per square foot per day. A parking lot is about 9 feet wide and 18 feet long (based on US standards, assuming India is the same). Let us assume a 50% overhead for space needed to move the car in and out of the lot. Based on this, the “fair rent” for one car parking space in my area is 18 * 9 * 3/2 * 400 / 365 = ~Rs. 270 per day, or translates to around Rs. 11 per hour.

Notice that all the calculations above were either multiplications or divisions, and hence the per hour parking price is directly proportional to the guidance value of property in the area. Based on the numbers above, a good rule of thumb for “economic cost” of an hour parking space is 11 / 8000 or about 14 basis points (a basis point is one hundredth of a percentage point) of the per square foot guidance value.

Of course, there are transaction costs (of putting the car in and out) and demand varies by time of day (so we might have an element of “surge pricing”). Yet, what we have is a good rule of thumb to decide the per hour parking rates.

Revisiting IPOs

I’ve written several times (here, here and here) that the IPO pop is unfair to existing shareholders since they end up selling the stock cheaper than necessary. Responses I’ve received to this (not all on the blog comments) have mostly been illogical and innumerate, talking about how the pop “increases the value of the entrepreneurs’ holdings”, and that the existing shareholder “should be happy that the value has gone up” rather than wondering why he sold his shares at the low value.

Thinking about this in the context of the impending Cafe Coffee Day IPO, I realised that a pop is necessary (though not maybe to the extent of the MakeMyTrip and LinkedIn pops), because investors need some incentive to invest in the IPO rather than buying the stock in the secondary market after listing.

Secondary markets have superior price discovery compared to primary markets since the former have several (close to infinite) attempts at price discovery, while the latter have only one attempt. Also, prices in the secondary market change “slowly” (compared to the price difference between primary and secondary market), so even if someone has invested at a price they later have dissonance with, they can reverse the investment without incurring a high cost.

For this reason, if you want to invest in a company and want to know that you are paying a “fair price”, investing in secondary markets is superior to investing in primary markets. In other words, you need a higher incentive in order to buy in primary markets. And this incentive is provided to you in the form of the IPO pop.

In other words, the IPO pop is an incentive paid to the IPO buyer in exchange for investing at a time when the price discovery is in a sense incomplete and cannot be particularly trusted. Rather than pricing the IPO at what bankers and bookbuilders think is the “fair price”, they will price it at a discount, which offers IPO investors insurance against the bankers having made a mistake in their pricing of the IPO.

And how much to underprice it (relative to any “fair price” that the bankers have discovered) is a function of how sure the bankers are about the fair price they have arrived at. The greater their confidence in such a price, the smaller the pop they need to offer (again, this is in theory since investors need not know what fair price bankers have arrived at).

The examples I took while arguing that the IPO pop is unfair to existing shareholders were MakeMyTrip and LinkedIn, both pioneers in some sense. LinkedIn was the first major social network to go public, much before Facebook or Twitter, and thus there was uncertainty about its valuation, and it gave a big pop.

MakeMyTrip was a travel booking site from India listing on NASDAQ, and despite other travel sites already being public, the fact that it was from an “emerging market” possibly added to its uncertainty, and the resulting high pop.

So I admit it. I was wrong on this topic of IPO pops. They do make sense, but from a risk perspective. Nothing about “wealth of existing shareholders increases after the pop”.

Social Reading

Feedly, the RSS Reader I’ve been using ever since Google Reader shut down, has announced a feature called “Shared Collections“. This is something like the Google Reader shared items (much loved by its loyal users including me, but something that apparently wasn’t good enough for Google to retain), except that it is available only for premium users.


While this is in theory a great move by Feedly to start shared collections, recognising the unfulfilled demand for social reading post Google Reader, their implementation leaves a lot to be desired. And I’m writing this without having used the feature, for, in an extremely daft move, it is available only for pro users. My problem is with the pricing model, which charges content creators (or curators or aggregators, if you like to call them that) for sharing content!

There are so many things wrong with this that I don’t know where to start. Firstly, if you charge people for creating content, that significantly increases the barrier to creating content. If there is an article I like and want to share with my (currently non-existent) followers, the fact that I have to create a premium account to do so means that the barrier to doing so is too high.

Secondly, if I’m going to be a consumer of shared collections from other people, I’ll need a certain critical mass of friends before I start using the feature. I won’t start using a feature only because one or two friends are curating content on it. The critical mass is much higher. And by putting barriers to entry to people who want to share, it makes this critical mass even more difficult to obtain.

Thirdly, Feedly doesn’t have a social network of itself so far (though I’m not aware what permissions they’ve taken from my when I used my Google account to log in to the service). And without having a ready social network for discovery (Google Reader leveraged the Google Talk network), how do they expect people to discover each other’s collections, once created? Are they relying on external networks such as Facebook or Twitter?

It is not easy to build a social network of curation. Google Reader had managed it quite well back in the day by first allowing people to share items without comment, then add external content, and then to add comments. It was an extremely powerful way for people to share blogs and other content, and discussion on that was rather active. I even remember quite a few people adding me on Google Talk for the sole reason of wanting to follow my Shared Items.

In recent times we’ve seen the news aggregator app Flipboard starting its personal collections feature. I have a collection, but don’t remember the last time I put something into it – for without any interaction on that, there’s absolutely no motivation. Flipboard, by the way, has access to your Facebook and Twitter graphs, and so has access to some sort of a social network. Yet, despite keeping the feature free, they haven’t been able to generate sufficient activity on it.

Feedly has got just about everything wrong with its Shared Collections feature. There is disincentive for content creators. There is no incentive for content consumers. They don’t have a ready social network. And there doesn’t seem to be any interaction.

If only Google were to bring back Google Reader and Shared Items, now that they’ve decided to dismantle Google+.


Market depth, pricing and subsidies

A few days back I had written about how startups should determine how much to subsidise their customers during the growth phase – subsidise to the extent of the long-term price. If you subsidise too much initially, elasticity might hit you when you eventually have to raise prices, and that can set you back.

The problem is in determining what this long-term sustainable price will be. In “one-sided markets” where the company manufactures or assembles stuff and sells it on, it is relatively easy, since the costs are well known. The problem lies in two-sided markets, where the long-term sustainable price is a function of the long-term sustainable volume.

A “bug” of any market is transaction costs, and this is especially the case in a two-sided market. If you are a taxi driver on Ola or Uber platform, the time you need to wait for the next ride or distance you travel to pick up your next customer are transaction costs. And the more “liquid” the market (more customers and more drivers), the lesser these transaction costs, and the more the money you make.

In other words, the denser a market, the lower the price required to match demand and supply, with the savings coming out of savings in transaction costs.

So if you are a two-sided market, the long-term sustainable price on your platform is a function of how big your market will be, and so in order to determine how much to subsidise (which is a function of long-term sustainable price), you need to be able to forecast how big the market will be. And subsidise accordingly.

It is well possible that overly optimistic founders might be too bullish about the eventual size of their platform, and this can lead to subsidising to an extent greater than the extent dictated by the long term market size. And some data points from the Indian “marketplace industry” show that this has possibly happened in India.

Having remained credit card only for a long time now, Uber has started accepting cash payments – in order to attract customers who are not comfortable transacting money online. This belated opening shows that Uber perhaps didn’t hit the numbers they had hoped to, using their traditional credit card / wallet model.

Uber has problems on the driver side, too, with an increasing number of its drivers turning out to be rather rude (this is anecdata from several sources, I must confess), refusing rides, fighting with passengers, etc. Competitor Ola has started buying cars and loaning them to drivers, perhaps indicating that the driver side of the market hasn’t grown to their expectations. They are all indicative of overestimation of market size, and an attempt to somehow hit that size rather than operating at the lower equilibrium.

So an additional risk in running marketplaces is that if you overestimate market size, you might end up overdoing the subsidies that you provide to build up the market. And at some point in time you have to roll back those subsidies, which might lead to shrinkage of the market and a possible death spiral.

Now apply this model to your favourite marketplace, and tell me what you think of them.

Elasticity and Discounted Pricing

The common trend among startups nowadays is to give away their product for a low price (or no price), and often below what it costs them to make it. The reasoning is that this helps them build traction, and marketshare, quickly. And that once the market has taken to the product, and the product has become a significant part of the customer’s life, prices can be raised and money can be made.

The problem with this approach is the beast known as elasticity. Elasticity means that when you increase your price, quantity demanded falls. Some products are highly elastic – a small increase in price can result in a large drop in quantity. Others are less so. Yet, it is extremely rare to find a product whose elasticity is zero, that is, whose quantity demanded does not vary with price. And even if such products exist, it is extremely unlikely that a product produced by a startup will fall in that category.

A good example of elasticity hitting is the shutting down of this American company called HomeJoy. As this piece in Forbes explains, the chief reason for HomeJoy shutting down is that it couldn’t hold on to its customers when it started charging market rates:

Not only did that kind of discounting make Homejoy lose significant money, it also brought in the wrong kind of customer. Many never booked again because they weren’t willing or able to pay the full price, which ranged from $25 to $35 an hour. Homejoy changed its pricing last year to make recurring cleanings cheaper and encourage repeat business. In response, some customers simply booked at the cheaper price and cancelled future appointments.

Based on the above explanation, it seems like subsidising customers to gain traction is a bad idea, and that a business should not be willing to make losses in the initial days in order to gain market. Yet, that would be like throwing out the baby with the bathwater, for subsidising at the “right level” can help ramp up significantly without elasticity hitting later. The question is what the right level is.

A feature of many businesses, and especially marketplace kind of businesses that startups nowadays are getting into, is economies of scale. This means that as the number of units “sold” increases, the cost per unit falls drastically. In other words, such businesses work well when they have built up sufficient scale, but collapse at lower levels. For such businesses, the thinking goes, it is impossible to bootstrap, and the solution is to subsidise customers until the requisite scale can be built up, at which point in time you can start making money.

The question is regarding the “sweet spot” of subsidy that should be given to the customer in order to build up the business. If you subsidise the customer too much in the initial days, there is the risk of elasticity hitting you at steady state, and things rapidly unravelling. If you subsidise too little, you may never build the scale.

The answer is rather straightforward, and possibly intuitive – start out by charging the price to the customer at which the business will be profitable and sustainable in the steady state. This will imply losses in the initial days, since your unit costs will be significantly higher (due to lack of scale). Yet, as you ramp up and hit steady state, you don’t have the problem of raising the price which might result in elasticity hitting your business.

What if, on the other hand, the subsidy you are giving out is not enough, and you are not willing to build traction? That is answered with the “Queen of Hearts” paradigm. The paradigm says that if the only way you can make your contract is if West holds the Queen of Hearts (talking about contract bridge here), you simply assume that West holds the card and play on. If he held the card, you would win. If not, you would have never won anyway!

Similarly, the only way your business might be long-run-sustainable is if you can generate sufficient traction at your long-run-sustainable price. If you need to drop the price below this in order to gain initial traction, it means that you will have the risk of losing customers when you eventually raise the price to the long-run-sustainable-price, which means that your business is perhaps not long-run-sustainable, and it is best for you to cut your losses and move on.


Now think of all the heavily-discounted startups out there and tabulate who are the ones who are charging what you think is a long-run-sustainable price, and who runs the risk of getting hit by elasticity.