Written by on Aug. 17, 2018 .

Released in 2017, HLTV’s Rating 2.0 is the second iteration of the only advanced metric designed to sum up player performance into a single value. However, in a previous blog post, Chris demonstrated its shortcomings and the necessity for a new player rating system.

While Rating 2.0 does incorporate many other ways a player can contribute to a game besides kills and deaths, we feel like there are more important aspects of a game that currently are not accounted for; aspects that many in the community, including Astralis’ in-game leader, have been asking for.

Stats/Rating which is based on how much money the opponent spent LETS GO 😁.

It is a little crazy that it is almost impossible to have a rating below 1 if you make an ace against glocks/usp. But I believe you guys have been trying to figure something out about that already right — Lukas Rossander (@gla1ve_csgo) July 30, 2018

So today, we at SixteenZero are introducing Player Round Impact (PRI), an early-stage metric that measures player performance by incorporating the context of each player's kills and deaths.

The Importance of Context

Consider the following rounds with virtually identical stats from ESL One New York 2017.

Player Opponent Round Map Kills Deaths Damage Watch EliGE Astralis 23 Mirage 5 0 500 Link s1mple EnVyUs 16 Cobble 5 0 408 Link nitr0 Virtus.pro 7 Nuke 5 0 358 Link

Rating 2.0 and KDR would give similarly high scores to all three of these rounds. Watching the clips, though, it is clear the context of each round is very different. But how do we quantify that context?

Win Probability Model

The first step is to develop a win probability model: a tool utilized by analysts in other competitive fields to track how likely each side is to win a game/match, given a game state. Our initial model predicts which side is likely to win a round given the map and the weaponry brought into the round, then adjust its estimate each time a player is killed.

For example, entering a gun round on Cobblestone, the CT side is 53% likely to win the round. If the T side gets the opening kill, the CT side is only 31% likely to win (a -22% change), however, if the CT side should get the opening kill, they would be 69% likely to win (a +16% change).

So, how do we use this model to get PRI? By assigning the attacker and the victim the change in win probability of each kill.

Applying the Win Probability Model – PRI

Revisiting the Ace Rounds

Now, let’s revisit the aforementioned ace rounds through the lens of our win probability model.

Team Liquid vs. Astralis, Mirage, Anti-eco Round Event Attacker Victim Liquid Win Probability Win Probability Change Start 89% 5 v 4 EliGE Kjaerbye 94% 5% 5 v 3 EliGE device 99% 4% 5 v 2 EliGE dupreeh >99% 1% 5 v 1 EliGE Xyp9x >99% 0% Win EliGE gla1ve 100% 0%

EliGE PRI Calculation: 5% + 4% + 1% + 0% + 0% = 11% or 11 PRI

Based on the weaponry each team brings into the round, Team Liquid has a significant advantage, and with each kill, Astralis' chances only get worse. As a result, each of EliGE's kills become increasingly less valuable, to the point that each of the last two are virtually unimpactful. Let's see how EliGE's PRI of 11 compares with the other rounds.

Natus Vincere vs. EnVyUs, Cobblestone, Pistol Round Event Attacker Victim Na`Vi Win Probability Win Probability Change Start 50% 4 v 5 ScreaM Edward 34% -16% 3 v 5 SIXER seized 15% -19% 2 v 5 RpK flamie 4% -11% 2 v 4 s1mple RpK 8% 4% 2 v 3 s1mple xms 24% 16% 2 v 2 s1mple SIXER 50% 26% 2 v 1 s1mple ScreaM 87% 37% Win s1mple Happy 100% 13%

s1mple PRI Calculation: 4% + 16% + 26% + 37% + 13% = 96% or 96 PRI

Given that it is a pistol round, neither side have an initial advantage. Meaning, not only does Na`Vi enter the round at worse odds than Liquid did in EliGE's ace round, but their odds continue to decrease until s1mple and Zeus are left in a 2-vs-5 situation. s1mple brings Na`Vi back from a 4% win probability by eliminating all of the EnVyUs players and netting himself 96 PRI for the round. That is almost nine times the PRI value of EliGE’s ace. Now, where does nitr0's ace fit in?

Team Liquid vs. Virtus.pro, Nuke, Full-buy Round Event Attacker Victim Liquid Win Probability Win Probability Change Start 57% 5 v 4 nitr0 NEO 72% 15% 5 v 3 nitr0 byali 86% 14% 5 v 2 nitr0 pashaBiceps 96% 10% 5 v 1 nitr0 TaZ >99% 4% Win nitr0 Snax 100% 0%

nitr0 PRI Calculation: 15% + 14% + 10% + 4% + 0% = 43% or 43 PRI

Even though both teams are on a full buy, Team Liquid have a slight advantage entering the round because they are on the CT side of the notoriously CT-sided Nuke. Since nitr0 never loses a teammate, there is not as much win probability to make up for compared to s1mple. Therefore, nitr0's PRI of 43 places his round somewhere between EliGE's and s1mple's.

Exploring More Examples

Let's also look at rounds with more commonly seen kill and death totals. Focusing on tarik, EliGE, and olofmeister, respectively, each player in the following examples finish their round with two kills and one death.

Cloud9 vs. FaZe Clan, Mirage, Full-buy Round Event Attacker Victim Cloud9 Win Probability Win Probability Change Start 46% 5 v 4 tarik karrigan 68% 22% 4 v 4 olofmeister Skadoodle 51% -17% 3 v 4 GuardiaN Stewie2K 28% -23% 3 v 3 tarik NiKo 53% 25% 3 v 2 RUSH GuardiaN 81% 28% 2 v 2 rain tarik 54% -27% 1 v 2 olofmeister RUSH 17% -37% 1 v 1 > autimatic olofmeister 55% 38% Loss rain autimatic 0% -55%

tarik PRI Calculation: 22% + 25% - 27% = 19% or 19 PRI

tarik opens up this back-and-forth round, later gets another kill to bring it to a 3-vs-3 situation, and ultimately dies to bring it back even at 2-vs-2. This is a great example of a round where every kill and death a player took part in had a significant impact. If every round were like that, there would not be significant differences between PRI, Rating 2.0, and KDR. But that is not usually the case, as we can see in the next two examples.

Team Liquid vs. FaZe Clan, Inferno, Full-buy Round Event Attacker Victim Liquid Win Probability Win Probability Change Start 49% 5 v 4 EliGE olofmeister 72% 23% 4 v 4 GuardiaN stanislaw 56% -16% 3 v 4 rain nitr0 34% -22% 2 v 4 karrigan Twistzz 13% -21% 1 v 4 karrigan jdm64 1% -12% 1 v 3 EliGE rain 6% 5% Loss NiKo EliGE 0% -6%

EliGE PRI Calculation: 23% + 5% - 6% = 22% or 22 PRI

EliGE opens the round with an impactful kill but eventually finds himself in a 1-vs-3 situation. He manages one more kill but ultimately dies, losing the round and cancelling out the impact of his second kill.

FaZe Clan vs. Team Liquid, Inferno, Eco Round Event Attacker Victim FaZe Win Probability Win Probability Change Start 15% 4 v 5 stanislaw NiKo 8% -7% 3 v 5 Twistzz karrigan 3% -5% 2 v 5 Twistzz rain <1% -3% 1 v 5 Twistzz GuardiaN <1% -<1% 1 v 4 olofmeister nitr0 <1% <1% 1 v 3 olofmeister EliGE 1% 1% Loss Twistzz olofmeister 0% -1%

olofmeister PRI Calculation: 0% + 1% - 1% = 0% or 0 PRI

olofmeister is not involved any kills before he finds himself in a nearly impossible 1-vs-5 situation, so the only way for him to have any impact on the outcome of the round is to pull off the ace clutch. Therefore, since he does not, his two kills and one death are worth virtually 0 PRI.

Aggregation of PRI

PRI for a map, match, or an entire event is calculated by taking the average of the player’s impact on their team’s win probability over that span. Below is a table listing EliGE's stats from every round of the map on which he got the aforementioned ace against Astralis.

Team Liquid vs. Astralis, Mirage, EliGE PRI Round Round Type Liquid Side Kills Deaths PRI 1 Pistol T 1 1 -5 2 Anti-eco T 2 1 -10 3 Anti-eco T 1 1 -2 4 Full-buy T 0 0 0 5 Full-buy T 1 1 -3 6 Force T 0 1 -11 7 Eco T 0 1 -12 8 Full-buy T 0 1 -16 9 Eco T 0 1 -1 10 Full-buy T 1 1 -2 11 Full-buy T 0 1 -17 12 Eco T 0 1 -4 13 Full-buy T 0 0 0 14 Full-buy T 1 0 0 15 Full-buy T 0 1 -19 16 Pistol CT 0 0 0 17 Anti-eco CT 1 0 2 18 Full-buy CT 2 0 29 19 Anti-eco CT 0 0 0 20 Full-buy CT 0 1 -30 21 Full-buy CT 2 1 35 22 Anti-eco CT 2 0 8 23 Anti-eco CT 5 0 11 24 Full-buy CT 0 1 -22 25 Full-buy CT 3 0 27 26 Anti-force CT 0 1 -19 27 Anti-force CT 1 1 3 28 Full-buy CT 1 0 16

Map PRI

The following table of aggregated player statistics showcases the differences between PRI and the other metrics. Looking at Twistzz’s numbers, we can see a case where Rating 2.0 is able to differentiate from KDR. However, both metrics still struggle to properly weight EliGE's ace. EliGE goes from being the top performer in Rating 2.0 to the fifth-best in PRI.

Team Liquid vs. Astralis, Mirage Player Kills Deaths KDR Rating 2.0 PRI EliGE 24 17 1.41 1.37 -1.46 dupreeh 24 17 1.41 1.32 6.37 jdm64 22 16 1.38 1.26 4.61 Twistzz 22 15 1.47 1.23 3.20 Xyp9x 16 18 0.89 0.93 1.62 device 15 19 0.79 0.92 -1.78 gla1ve 15 20 0.75 0.89 -0.49 nitr0 12 17 0.71 0.79 -2.16 Kjaerbye 14 18 0.78 0.75 -3.18 stanislaw 12 19 0.63 0.75 -6.15

Event PRI

PRI can also identify over and underrated performances at a tournament level. Future blog posts will likely dive into why some of these PRI values vary so greatly from the other metrics, but for now we'll just post the overall numbers for ESL One New York 2017, sorting by Rating 2.0:

ESL One New York 2017 Player Team Rounds Kills Deaths KDR Rating 2.0 PRI NiKo FaZe 151 150 62 2.42 1.70 6.58 rain FaZe 151 145 83 1.75 1.61 4.00 coldzera SK 125 134 76 1.76 1.47 5.32 s1mple Na`Vi 133 126 92 1.37 1.35 3.81 fer SK 125 101 88 1.15 1.34 -0.31 GuardiaN FaZe 151 122 75 1.63 1.32 0.98 FalleN SK 125 102 75 1.36 1.29 2.07 olofmeister FaZe 151 118 78 1.51 1.27 1.41 karrigan FaZe 151 90 72 1.25 1.20 0.67 Twistzz Liquid 337 236 202 1.17 1.16 2.12 device Astralis 145 103 93 1.11 1.14 3.10 ScreaM EnVyUs 79 60 60 1.00 1.09 -1.71 dupreeh Astralis 145 104 98 1.06 1.08 -0.90 RUSH Cloud9 142 110 100 1.10 1.06 2.99 EliGE Liquid 337 224 226 0.99 1.05 0.69 pashaBiceps Virtus.pro 90 38 48 0.79 1.05 1.76 flamie Na`Vi 133 86 94 0.91 1.05 -0.90 Stewie2K Cloud9 142 92 106 0.87 1.01 -1.82 gla1ve Astralis 145 94 100 0.94 0.99 -1.19 RpK EnVyUs 79 57 67 0.85 0.99 -1.93 Happy EnVyUs 79 59 61 0.97 0.97 2.79 autimatic Cloud9 142 101 109 0.93 0.97 0.48 Xyp9x Astralis 145 87 93 0.94 0.95 0.45 jdm64 Liquid 337 192 210 0.91 0.95 -0.11 byali Virtus.pro 90 34 47 0.72 0.94 -2.22 TACO SK 125 74 76 0.97 0.92 -1.23 tarik Cloud9 142 76 103 0.74 0.89 -1.42 felps SK 125 69 88 0.78 0.89 -3.64 Zeus Na`Vi 133 72 103 0.70 0.88 -3.49 Edward Na`Vi 133 76 90 0.84 0.87 -0.84 nitr0 Liquid 337 168 222 0.76 0.86 -0.81 Kjaerbye Astralis 145 76 99 0.80 0.85 -3.58 xms EnVyUs 79 41 61 0.67 0.83 -3.23 Snax Virtus.pro 90 37 41 0.90 0.82 -2.68 TaZ Virtus.pro 90 34 45 0.76 0.81 0.31 stanislaw Liquid 337 141 233 0.61 0.80 -3.22 Skadoodle Cloud9 142 69 103 0.67 0.78 -1.59 SIXER EnVyUs 79 52 55 0.95 0.77 -0.02 NEO Virtus.pro 90 32 50 0.64 0.68 -4.74

PRI Issues and Future Development

Our initial win probability model is rudimentary and does not yet incorporate basic, important factors such as time remaining in the round, bomb factors, damage, and changes in equipped weaponry throughout a round. It also does not account for more complex factors like map control or the skill level of players and teams involved. All of these factors are on our radar and development to incorporate some of them is already underway.

However, even with these known gaps, we are still excited to release this initial version of PRI because it offers the community a unique perspective on player performance. Feel free to share any questions, comments, or suggestions you have with us in our reddit post.