OK, seeing as literally none of you asked, I made a graph of 18 years of bus fares in Edinburgh (on Lothian Buses - nobody really uses First Bus) 
Until 2013, it's almost as if you could set the bus fares by the increasing cost of diesel. Then something else happens... 
(I should declare that this is not a pop at Lothian Buses whom I think are by and large, fabulous, they pay their staff well, provide a comprehensive service and have invested massively in a modern, accessible fleet with increasingly improved emissions)
I found the recent history of passengers carried (not including trams), which since '95 has seen a long term increase of 48% over 20 years 
Although since the first tram-free year I could get figures for (1958), bus use in Edinburgh (for which read "public transport use) has halved. P.T. use peaked in 1956 at 286.6 million journeys. Tram use peaked in 1947 at 192.9M 
And going back to 1922 (when the Leith and Edinburgh Corporation transport systems were merged), there's a quite fascinating trend (yes, I know trains and "other" bus companies not included, but in the scheme of things they are largely a rounding error in urban PT in Edinburgh) 
Notice that even when the Corporation were mooting closing the tram system (1952), passenger numbers were high and only marginally down from the 1947 peak, then fell off a cliff as 25% was cut from the system as an economy measure
The system was rapidly cut back until only a few tram routes remained, then quickly closed by 1956, yet total P.T. figures continued to increase after "bussification"; the demand was clearly there for it.
4 things happened; 1 - too many buses lead to great congestion, so stops on the main routes (Leith Walk, Bridges, Princes St., West End) were spaced out. Interchange became harder and they were further from the street intersections so less convenient
2 - the Corporation couldn't buy enough new buses to replace both trams and older buses, so tram passengers often found their trams replaced by clapped out old buses. The novelty was not appreciated.
3 - The middle-to-upper class passenger segment who had patronised the trams well (and also trains) apparently did not take to buses. They quickly shifted to motor cars which became readily affordable to them at this time
4 - cars. Cars became ever more available. The council widened roads and spent lots of money on signals and plans for urban motorway schemes, car parks sprung up on gap sites and were formalised on most streets in city centre. You know the rest...
Cars, eh? I wonder how they are doing these days. Fortunately the DfT takes traffic counts all over Edinburgh. Let's look at some of the count points in the city centre. In fact - just for fun - let's look at the 5 closest to Picardy Place 
(foot of Lothian Road, London Road, Waterloo Place, South Bridge and mid Leith Walk)
What's that you say, the car/taxi count is down 24% in the last 16 years? Yes, you read that right; that's almost exactly down a quarter. I know this isn't a fancy, proprietary transport model but if counts are significantly down in all directions... 
This is the real elephant in the room for Edinburgh's fact-blind planners and transport engineers who seem to have convinced their bosses that a honking new gyratory is needed just to maintain the status quo
I mean anyone would think it's a coincidence when you overlay bus passenger growth since 2000 against car/taxi decline. So remind me again why the new design for #PicardyPlace features no obvious bus segregation? 
And as I previously managed to extrapolate, car occupancy is incredibly low (and falling), in fact for commuting it is to all intents and purposes 1 car = 1 person
Now, it should be possible to create a pretty map of traffic count points and the trend in traffic at each, but the eastings and northings provided by DfT are junk and locate the count points in Morocco!
So I'm doing it by hand, which is a pain in the teeth given the way the DfT site presents the data and refers to road sections, but I'm getting there. In the meantime, here are the top 20ish count points by overall decrease 
And here are the bottom 20ish by increase in that period, unsurprisingly these are all on the main commuter routes into town from the commuter belt OR in proximity to a large drive-to shopping mall/park 
So spare a thought for the residents in a 2 or 3 mile radius of "Fort Kinnaird", or Straiton who are absolutely drowning in cars as a result of rubber-stamping expansion of those shopping parks
Thanks to some spreadsheetery and some intermediate geo-coding tools, I have now managed to plot the CfT Count Points on a map and colour them by increase and decrease (darker = larger change) from 2000 to 2016 
Zooming in... Remember, this is the change in car and taxi traffic, and with 2 spot exceptions it's entirely negative for the city, and significantly so! The only road engineering schemes the city needs are road diets 
We can also see what a self-fulfilling prophecy and ultimate failure all that road engineering in the west has been. Cars will fill the capacity you create much faster than you can build it. 
And we wonder why they've managed to find a spare £120m down the back of the sofa to build a stonking new junction at Sherrifhall 
Reminder - public transport in West Edinburgh beyond the A8 bus corridor largely sucks (or can be totally absent). There is no realistic public transport alternative to the bypass if you're trying to go around Edinburgh.
There will also be an element of the "Donut City" going on here, as families and long-term residents are forced out of the centre by prices and the air-bnb-ification, the more transient residents who replace them less likely to go by car
Back to bus ticket prices, the collective memory of what a day ticket a.k.a. "daysavers" cost seems a bit vague. They started out in 2005 at £2.50 peak times, dropped to a flat £2.30 all times in 2006 and are now £4. Proportionately cost has tracked that of singles 
h/t to @julial49 for pointing out the day ticket started in 2002 at £2.30 (peak time, there was a fab £1.50 version travelling after 9:30AM), which alters the graph slightly but not fundamentally 
Er. 2001. At £2.20... It's getting late and one bus fare is beginning to look much like another.
