Winning percentages crop up in a couple of places, in the game graph and in the wpar (win percentage added per round) player stat. These stats were born out of the realisation that not all kills are created equal. The 4th kill by a fully stacked team cleaning up the opposition during their eco round is a lot less important than the first kill between two teams full buying towards the end of the game and facing economic ruin if they lose.
To establish exactly to what extent I returned to the study dataset and looked at various scenarios, using both large scale data like round scores and comparative economies and the smaller details of round kills and relative equipment values.
This took some time to unpick, and eventually broke down into two broad groups – the round scores with a linear relationship and the in-round kill stats and all economic stats that were a lot more subtle.
To start with round stats, there is a straightforward linear relationship between having a round lead and the chances of victory with each round having the same value in comparison to eachother. This varies by how far through the game the lead is established. A 3 round lead after 17 rounds predicts the result a lot more strongly than a 3 round lead after only 5 rounds. One of the interesting results of this reasoning is that the 2nd pistol round is more important than the first not just on eco grounds but in terms of the value of the round itself, as the swing in round score it produces is more predictive of the final result. The exception is if one team already holds a massive round lead making dropping a handful of 2nd half rounds less important.
When examining in-round win chances, kills start to become more complex. This is down to how there is a diminishing return in terms of the winning chance a numbers advantage gives a team. There are only so many ways the team with the extra players can maneuver to improve their chances of winning, particularly given the limitations of the timer.
It boils down to the first 2 kills giving a very large advantage, and after that they become a lot less important to the outcome of the round. An interpretation of this information could be that rounds are often decided when multiple players are killed and I’m just seeing that it’s very common to win a round by a margin of two kills. However checking specific scenarios, 5 vs 3, 4 vs 2, etc, seems to bear out the general conclusion. However if the players left in the smaller team can bring things back to an even contest then they have regained a lot of win percentage.
As with economic considerations in the PAE stats, the economy affects win chances in a more complex way. If we start with game level economy that goes hand in hand with round scores I’ve found that this affects win chances in two ways. Firstly an advantage in economic resources (like in PAE stats) need to be explained by a polynomial, which essentially means that the initial advantages are much more important. The first 10 and 20 thousand eco advantage is much more important to winning chances than any amount that is acquired on top of that.
The second part is that like round score advantage, the economic advantage has more impact over time – a $20,000 budget lead with only a few rounds left in the game can be worth many times the same lead established at the start of the match. And like round advantages it shows that the 2nd pistol round is more important because the eco advantage it secures (or gives the opportunity to secure at least) will probably take affect during more important rounds. The exception to this if a match so one sided that one team already holds a massive round advantage – in that case it’s almost certain that at some point the economy will swing around and give the leading team the chance to close out the map.
The economy at the round level isn’t quite as important, but it does provide us with some interesting insights. Once again a polynomial is required to explain it, so once again the initial advantages are more important in terms of who secures the win – the first $20,000 dollars of advantage are by far the most influential in determining the round win. But we know that teams will stack their loadout way above this when facing an eco. Why?
The answer is that the larger the equipment value advantage the larger the likely margin of victory in terms of players surviving, which cements the long term economic advantage because they don’t lose equipment and they don’t give eco to the opposition. My study shows that for roughly each $7000 of equipment value advantage a team is expected to win by an extra player, so a $35,000 advantage should produce a 5-0 wipe. Anything short of that indicates a sub optimal use of economic investment, but given the headshot potential of weapons in CS it’s always a possibility.
Win Percentage in action
Taking Envyus vs Faze in January’s Eleague major on de_nuke as an example we can see how the game winning chances change based on the circumstances
The left axis measures win percentage from Envyus’s perspective (spoiler: they lost the map) and is shown by the green lines on the graph, and the right axis measures the relative economic advantage shown by the red line on the graph once again from the perspective of Envyus, so negative numbers show that advantage to Faze.
- Faze get out to a solid 3 round lead and establish a solid eco advantage as well, but as it’s early on in the game so the relative influence of that is fairly small.
- Envyus come back with a run of rounds and flip things in their favour, establishing a small eco advantage.
- Faze go on a long run establishing a big 12-6 lead. Something to note though is that they don’t secure a very large eco advantage to go with it (partly due to the half time reset), Envyus manage to continue to be competitive enough to stop that long term persistent advantage going too far against them. This is what good eco management by the team behind looks like interacting with the team ahead going heavily for big anti-eco buys. Even so Faze are very heavily favoured here.
- Envyus mount a comeback to get to 11-12, but although they never get the round lead they establish a clear eco lead which at this stage of the game gives them an advantage going into the key final quarter of the game. Faze are one round loss from having their economy broken at a critical stage.
- Faze come through in the clutch and never lose another round, two rounds after having their back against the wall they flip the eco situation and ride it home to victory. Envyus’s economy ends in tatters as they desperately try to survive and fail.
Ultimately in this game Faze’s mid round run gave them enough slack that they could absorb the Envyus comeback, just avoid losing the lead and finish the map strongly. Did they get complacent and nearly let the map slip? They were certainly in mortal danger from a position of nearly assured victory.
Win percentage for players: WPAR
For players win percentage is measured as Win Percentage Added per Round or WPAR. It’s split over rounds as games that go on longer may result in larger values for players giving a misleading comparison between maps. The values for all players usually add up to around zero as you might expect, but there are sometimes macro considerations that don’t interact neatly with the value so it can be off a little.
Sometimes players that have a good PAE will also have a good WPAR, but often times they won’t. The reason for this is that there’s an element of clutchness to WPAR, not just how many kills you got but when you got them and how much impact they had.
A player with high PAE and low WPAR is probably getting a lot of cleanup frags in already won situations, or is giving up their life in the least favourable way possible – usually being the kill that breaks the team equilibriums or loses them a lot of eco investment.
A player with both high PAE and WPAR is not only out-performing their equipment value, they’re doing it at key times as well, getting key kills and advancing their team’s objectives at a bargain price.
A player with both low PAE and low WPAR is having a really bad day. An example of a player this might happen to is a team Awper who is eating up a lot of the team’s budget and is expected to get kills, but is being dominated by the opposition snipers instead.