Outliers
This morning I happened to watch the highlights of the final day of the 2nd Test Cricket match between India and England (which India have won by the way!) on YouTube, and then somehow went into the rabbit hole of cricket as it often happens with me.
I came across this wonderful documentary from ABC Australia about Don Bradman and Sachin Tendulkar. For those who knows me know the fact that I am a cricket buff! I am surprised how I missed this wonderful piece of documentary.
I obviously know all about this story in gory details, and collected every single details when this event was happening live, but somehow I missed this documentary. The story here is 1 hour long and worth a watch even if you are not a fan of cricket, as it is well made. The main item that caught my attention was a plot discussed at 9:40 of the video. That is the plot I re-created above (data from ESPNcricinfo).
This is a scatterplot showing runs scored by batsmen in Test cricket along the X-axis, with their batting average along the Y-axis. This is an extremely simple plot, but it reveals two players, Don Bradman, plotted as an outlier along the Y-axis, and Sachin Tendulkar, plotted as an outlier along the X-axis. The pattern is so obvious there there won't be any argument about it.
Outlier Analysis
The most common statistical measure of an outlier (other the visual) is called a Z-score. It is basically a normalized departure from the mean. As defined, a Z-score is a statistical measure that describes how far a data point is from the mean of a dataset, in terms of standard deviations. It's commonly used in outlier detection to identify values that are significantly different from the rest of the data.
Formula for Z-score:
Z = (X − μ)/σ
Where:
X = the data point
μ = the mean of the dataset
σ = the standard deviation of the dataset
- Z-score of 0 means the value is exactly at the mean.
- Z-score of +2 means the value is 2 standard deviations above the mean.
- Z-score of -2 means it's 2 standard deviations below the mean.
Usually a Z-score of +3 or -3 and beyond is considered statistical outliers. So, I made a list of 223 test cricket batting average data spread randomly across time and space. I calculated the Average of the Batting Averages. I calculated Z-score of both Tendulkar and Bradman, both on the Total runs scored and Batting Average categories. The two tables below summarizes the result.
| Metric | Value |
|---|---|
| Batting Average | 37.98 |
| Standard Deviation | 12.96 |
| Max Average | 99.94 (Bradman) |
| Tendulkar’s Average | 53.78 |
Z-Score
| Name | Runs | Average | Z-Score Run | Z-Score Batting Av |
|---|---|---|---|---|
| Sachin Tendulkar | 15921 | 53.78 | 3.53 | 1.22 |
| Don Bradman | 6996 | 99.94 | 0.72 | 4.78 |
As expected by visual inspection of the plot. Both Tendulkar and Bradman scores above 3.0 in their respective axes. Bradman's batting average of 99.94 earns him a Z-score of 4.78. Tendulkar's Z-score of Total runs scored, earned him a Z-score of 3.53.
Outliers works in other cases too
| Company | Employees | Revenue (M USD) | Revenue Z-Score |
|---|---|---|---|
| CD Projekt | 1200 | 210 | -0.10 |
| Valve | 360 | 4000 | 4.79 |
| Remedy Entertainment | 330 | 150 | -0.18 |
| Paradox Interactive | 600 | 200 | -0.11 |
| Frontier Developments | 500 | 100 | -0.24 |
| IO Interactive | 200 | 90 | -0.25 |
| Behaviour Interactive | 1000 | 300 | 0.02 |
| Bohemia Interactive | 350 | 110 | -0.23 |
| GungHo Online | 600 | 800 | 0.66 |
| Krafton | 2000 | 1700 | 1.82 |
| Playdead | 50 | 30 | -0.33 |
| Supergiant Games | 40 | 25 | -0.34 |
| Team Cherry | 35 | 20 | -0.34 |
| Facepunch Studios | 60 | 50 | -0.30 |
| Larian Studios | 200 | 300 | 0.02 |
| Double Fine | 150 | 100 | -0.24 |
| Housemarque | 80 | 60 | -0.29 |
| Moon Studios | 70 | 40 | -0.32 |
| Campo Santo | 30 | 15 | -0.35 |
| Thatgamecompany | 90 | 55 | -0.30 |
| Zachtronics | 25 | 10 | -0.36 |
| Subset Games | 20 | 8 | -0.36 |
| ConcernedApe | 1 | 50 | -0.30 |
| Inkle | 10 | 5 | -0.36 |
| Stoic Studio | 15 | 12 | -0.35 |
| Red Hook Studios | 25 | 18 | -0.35 |
| Klei Entertainment | 100 | 90 | -0.25 |
| DrinkBox Studios | 30 | 20 | -0.34 |
| Vlambeer | 5 | 3 | -0.36 |
| Roll7 | 20 | 7 | -0.36 |
The did the same scatter plot of these 30 gaming companies.
A company with only 360 employees and 4B in revenue is something very special and the Z-score of 4.79 reflects that. Valve has developed some of the most influential and critically acclaimed video games, including:
Half-Life series
Portal series
Left 4 Dead
Team Fortress
Counter-Strike
Dota 2
Half-Life: Alyx (a flagship VR title)
Valve is also the creator and operator of Steam, the largest digital distribution platform for PC gaming. Launched in 2003, Valve is known for its unique flat organizational structure, where employees choose their own projects. The company emphasizes experimentation, iteration, and playtesting in game design, treating it as a form of experimental psychology.
Web-3 Games
Data for the web-3 games in difficult to verify. I know this from Splinterlands revenue and employee numbers are not updated. However, it still fits the profile.
| Company | Employees | Revenue (USD) | Revenue Z-Score |
|---|---|---|---|
| Sorare | 100 | $150,000,000 | 4.15 |
| Axie Infinity | 120 | $110,000,000 | 2.94 |
| Splinterlands | 43 | $11,800,000 | -0.02 |
| Illuvium | 150 | $5,000,000 | -0.23 |
| The Sandbox | 200 | $37,000,000 | 0.74 |
| Decentraland | 100 | $15,000,000 | 0.07 |
| Gods Unchained | 80 | $3,000,000 | -0.29 |
| Star Atlas | 120 | $2,500,000 | -0.3 |
| Big Time | 90 | $4,000,000 | -0.26 |
| Ember Sword | 60 | $1,500,000 | -0.33 |
| My Neighbor Alice | 70 | $2,000,000 | -0.32 |
| Alien Worlds | 50 | $2,200,000 | -0.31 |
| CryptoBlades | 40 | $1,000,000 | -0.35 |
| Mobox | 60 | $1,800,000 | -0.33 |
| Zed Run | 55 | $2,300,000 | -0.31 |
| Chainmonsters | 30 | $900,000 | -0.35 |
| Guild of Guardians | 45 | $1,200,000 | -0.34 |
| Aurory | 50 | $1,700,000 | -0.33 |
| Skyweaver | 65 | $2,100,000 | -0.32 |
| Neon District | 35 | $850,000 | -0.35 |
| Blankos Block Party | 85 | $3,500,000 | -0.27 |
| Crypto Raiders | 25 | $600,000 | -0.36 |
| Nine Chronicles | 40 | $1,100,000 | -0.35 |
| Upland | 90 | $6,000,000 | -0.2 |
| DeFi Kingdoms | 70 | $2,400,000 | -0.31 |
| Pixels | 30 | $750,000 | -0.36 |
| World Eternal Online | 45 | $1,300,000 | -0.34 |
| Crypto Unicorns | 55 | $1,900,000 | -0.32 |
| Revv Racing | 60 | $2,600,000 | -0.3 |
| MetaSoccer | 35 | $1,000,000 | -0.35 |
I know for a fact that Splinterlands revenue is currently not $11.8M! I wish! However, that is what is reported at compworth.com. So take this data with a grain of salt. However, it does proves the point, that Sorare and Axie Infinity are probably outliers in terms of revenue, while Splinterlands is above the background, but not an outlier.