In our quest to understand the business, I use a lot of statistics. I run up charts to understand where we are and where we need to be and one of the more recent charts I did was on Quantity & Price chart (with a secondary ‘Revenue’ figure approximated). After some internal debate, I’ve decided to post it to the blog – but without any actual numbers for quantities & revenue. I think the graph by itself even without those numbers can be quite useful.

Disclaimer – the following is from Starlit Citadel’s numbers only. These aren’t industraty statistics, nor am I a statistical whiz.

**The Graph**

## The Graph Explained

The entire graph is plotted on 3 axis for Revenue and Quantity on the two Y-axis & on the X-Axis; Sale Price in our store. I ‘bucketed’ a lot of our price points (e.g. everything that sold at $2.01 – $2.99 became a $2.95 price point) to get the Quantities. In addition, Revenue is a basic Price Point (bucketed) multiplied by Quantity (bucketed); so there’s obviously some obvious overstatement of numbers there. Also, the entire graph is excluding some scatter points that are significantly above the norm (i.e. I cut the axis short so that we could focus on the graphs). In addition, the graphs come from using Excel’s Polynominal Graph function (set to 5 intervals) to create the trendlines.

## Quantity Sold Graph

Not surprisingly, we sell a lot of items in the <$3 price range (that’s Sleeves for the most part). In fact, you can’t even see the marker for it because we had to cut the entire graph short. However, even from the trendline you can see the huge swing down as we move from $1 to $10 range, and this is all within the accessories side of our business.

Between $10 – $20; we sell mostly smaller expansions or cheaper card games and again, the slide is significant but beginning to moderate. In our experience, expansions always do sell less than base games. I don’t have any numbers, but a guess it’d be between 2 to 3 to 1 (i.e. 2 to 3 copies of a base game to 1 expansion sold).

We start seeing ‘full’ board game sales in the >$20 range; and that seems to run a more straight line graph til it hits $80. It’s much steeper in the $20-30 part; but after that you can almost say things like ‘every $10 increase in price sees a drop of 25 copies sold’.

After $80 though, we have bundled products where for example; we sell both Twilight Imperium & its Expansions together which creates a bump in the Quantity Sold since we only really create packages for popular products.

## The Revenue Graph

The Revenue Graph is where things get interesting. For example, we might sell a lot of items for <$10 – but revenue wise, it’s a small part of the business. When it comes to revenue, you can see that we do most of our actual revenue from products in the $30 – 45 price range. This seems to be the ‘sweet spot’ for our revenue / sales and I’d assume for publishers as well.

Interestingly, overall the entire revenue graph doesn’t move as much as you’d think. Sure, quantity sold seems to be affected (which is important for how much you order / print) but revenue you generate not as much. The other interesting aspect of the revenue graph is how sharply it begins to move up as we reach the higher end of our price points as even a small movement in quantity sold is significant in terms of revenue.

## Last Comments

Correlation isn’t causation. So for example – are our sales in the $30 – 45 range because that’s the price cutsomers will buy at or because Settlers of Catan, Dixit, Ticket to Ride & Dominion are all in that range? They are our bestsellers, so they are definitely going to influence the demand graph significantly.

The thing that you need to realise is that these numbers are all consolidated including the trendline graphs. Each game is going to be different. Sales of Eclipse for example is way above what is normal for that range.

Very interesting, thanks for sharing.

You should be cautious reading too much into these lines. You sell more cheap games and less expensive ones, this seems natural. So let’s just say that the quantity as a function of price, q(p), is a straight line,

q(p) = mp + b

where m is the slope and b is the y-intercept. Let’s say you make a fixed percent on each game sold, probably close to reality. So your revenue is,

r = fpq

where f is the percent you make on each game. Your revenue is equal to the price of the game times the percent you make times the quantity you sold.

Now substitute the above for q and we get,

r = fp(mp + b) = fmp^2 + fbp

a quadratic equation similar to the one you have above. Remember that m, the slope, is negative so at very small or very large p this goes to largely negative values. That is, it looks like a fun hill to run up and have a picnic on, instead of the maybe more familiar quadratic that looks like a yummy bowl for soup 🙂

Of course you don’t have a perfect straight line and the devil’s in the details but naively this overall behavior is exactly what you would expect.

I think I followed that… however, it’s not revenue you create a graph for but profit. Profit = % we make * price * quantity. Still,I see your point and internally, we have a profit graph too 🙂

While interesting, more often than not what we use the above graphs for are y-o-y comparisons. That way, we can track changes over a period of time in an ‘apples to apples’ mode; rather than trying to understand the graphs in isolation.

“Profit = % we make * price * quantity”

That’s exactly what r=fpq represents

I misunderstood your use of revenue, I thought you meant net not gross. That just removes the factor of ‘f’ from the equations but it’s still quadratic.