Spending quotient (generally referred to as SQ) a method to quantitatively assess a player’s economic management in a game. Simply put, SQ is a measure of Macro skill, with higher numbers being better.
The term itself was created in a forum post on Team Liquid as part of a detailed analysis of Macro across all leagues in the Starcraft 2 ladder, and has quickly become a well-used tool for comparing economic management between players. The SQ of a certain player in a game is calculated using the following formula:
Where i represents resource collection rate and u represents average unspent resources. These values can be found on the score screen after a game. The result is usually a two-digit value, where a higher SQ means better economic management. While you can plug in your average income and resource collection rate manually, players may also wish to use automated tools, such as GG Tracker, to automatically track their SQ for each game.
During his research of score screen data from 2084 games between 2011-08-28 and 2011-09-15, TL.net user whatthefat noticed that "Surprisingly, there is a very close to exponential relationship between Average Unspent Resources and Average Income". He also noticed that players from all leagues spend their income in an approximately logarithmic fashion.
By assuming an exponential relationship with A and t as constants we get
Which is really close to the definition of SQ. The rest of the constants are put there to force SQ to vary between prettier numbers which makes numerical calculations more accurate and a lot easier for humans to comprehend. According to whatthefat "the value 0.00137 was picked as a compromise value to yield a good fit across all leagues".
There are a few limitations on the use of SQ as a measure of economic management:
- Firstly, it is not reliable to use in very short games. Most players will not have much problem dealing with their income in this case, which results in all players having very high and similar SQ. In order to avoid this, the inventor of the term is recommending not to calculate SQ for games where the average income is lower than 600 resources per minute.
- Secondly, the average SQ is somewhat dependent on which race is played. For example, Protoss players accumulate a lot of unspent resources before every Warpgate cycle, resulting in lower SQ compared to a Terran player of equal skill.
- Thirdly, SQ may unfairly punish players who purposefully bank resources in the late game when they reach max supply.
The following sites offer statistics including the SQ about Replays.
|Dusk Towers||TvT||Nathanias vs PuLSe||1.631||564||96|
|Ruins of Seras||ZvP||Dendroaspis vs Barry||1.969||649||108|
|Prion Terraces||PvT||NeoBlade vs GrandAdmiral||1.417||447||92|
|Ruins of Seras||TvT||hard vs naras||1.839||8.913||10|
|Ulrena||TvZ||Neckbeard vs Gui||921||2457||11|
- RCR = Resource Collection Rate or Income. Dendroaspis leads with 1.969. He was a top 30 GM, when he played this game.
- AUR = Average Unspent Resources. Hard has a good RCR with 1.839, but 8.913 AUR is way too much money in the bank.