14.7 Investor returns at Just-Dice.com

Other posts in series

18th November 2013

0. Introduction

I was very interested to hear that bitcoinproject.net was producing charts of Just-Dice statistics, with data updated every five minutes. The charts are useful, easy to read and interactive - I recommend you look at the site's charts before continuing.

I also think there are some other statistics that would be useful to chart (well, useful for me, anyway), and in this post I present those charts - I think at least some of them would be useful charts for bitcoinproject.net to include.

Below I've reproduced the original charts for context.

1. Intensity functions - change in cumulative statistics 
Bar charts are quite useful for showing changes in a cumulative variable per time period. However because data is binned, changes within that time period are obscured. For example, if you wanted to know what time of the day in the past most trades have occurred, if the bar chart binned the data by day that data would be obscured.

For these sorts of uses I prefer an intensity function of the cumulative statistic, calculated by taking the derivative of the kernel smoothed cumulative statistic. The next charts are the intensity functions of the charts above (smoothed using a twenty four hour bandwidth) , and if they were interactive you'd quickly be able to find the times of day when most bets occurred, or when the largest bets occurred.

Further, it's not easy to show expected values on a bar chart - side by side bar charts can be hard to read, whereas the expected change in profit line in the chart below is quite easy to compare to actual change in profit.

2. Other profit performance indices
There are a few other ways to process the data to find useful information that describes the performance of the site, and this section introduces some of them.

2.1 Cumulative wagered per bet and change in cumulative wagered per bet
The amount wagered per bet is an indicator of how much you can expect to earn from your investment, and also how much variance you can expect. The larger the amount, the larger your expected profit and the larger your expected variance. As you can see, this amount is mostly decreasing, with recent jumps due to a few whales betting over the last two days.

The constant decrease is probably due to regression toward the mean after Nakowa's betting spree, which does not appear in this data. I expect that over time this line will flatten, with jumps when a whale is betting.

The intensity function (change in cumulative wagered per bet) will show nice spikes when a whale is on board. Currently it seems to be increasing toward zero, another indication of the "flattening out" of the cumulative wagered per bet chart.

2.2 Cumulative profit per bet and change in cumulative profit per bet
If the amount wagered per bet is constant, the cumulative profit per bet should be a fairly flat line. In combination with the wagered per bet charts, the cumulative profit per bet and change in cumulative profit per bet charts can be useful in detecting trends in betting, and also in planning your own investment.

2.3 Cumulative profit per amount wagered and change in cumulative profit per amount wagered.
This is simply a chart of the site's percent profit. The figure given on Just-Dice.com is fine, however I personally like to be able to see how the profit percentage has changed over time.


2.3 Cumulative profit per amount invested and change in cumulative profit per amount invested.
If you're wondering why your profit is not what you expected when there hasn't been a large increase in the site profit, it's probably because of a change in the amount invested. Profit divided by amount invested shows the effect of the changing amounts of investment on profit. Note the recent downturn on the cumulative chart (last negative spike on the change in cumulative profit per amount invested chart). This was due in large part to a return of 10k btc of funds to site investment, combined with lacklustre profits. The positive spike just before that was due to one day of large betting, with less investment.

3.0 Investor returns
  This section introduces charts that investors will probably find the most useful - a report of the site percentage increase in site profit compared to expected, and the percentage increase of a "buy and hold" investment. "Buy and hold" simply means no "day trading".

3.1 Continuous percentage increase in investment over time.
 The expected percentage increase since October 11th (the start of data) is about 6%, however the "buy and hold" investment percentage increase is about 7.5%, which is a nice result.

3.2 Weekly and daily investor returns
Although there's not yet sufficient data to work from, weekly investor returns can be used to help quantify the risk of the investment. For example the Sharpe ratio could be calculated, using the expected return as the "risk free rate of return"

3.3 Difference between expected and actual investor returns
This chart shows how your investment has changed in daily and weekly increments.

4. Summary
I hope bitcoinproject.net decides to produce some of these charts. The investor returns chart would be very handy indeed, but the others also have merit. I like the change in site profit (intensity function) chart especially, since it allows me to see what's been happening on Just-Dice.com while I've been asleep, or at work.

A big thank you to bitcoinproject.net for collecting the data. It's a big job, done professionally and in a way that is easy to read. Please consider donating a small amount to them:

1Av1sFhiWVzhcgxPMsZXni4q5fYCMtR2jE

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