Two Spartans Enter…
…one Spartan leaves. But it’s a bit more complex than that when it comes to your Arena Rating. If you desperately need to know all the numerical nomenclature that goes into your ultimate Rating output for the Beta, you’ll want to dial into the description below.
Arena Rating
![[IMG]](http://www.bungie.net/images/Games/Reach/betaGuide/inlines/arena.jpg)
What is a Game Rating?
In the Arena, your Game Rating is a numeric evaluation of how well we think you performed in that game, against those opponents. A score, of sorts.
At the conclusion of a game, players will be ranked according to their rating for that game, and it is this ordering of players that is fed into the TrueSkill black box to determine which Division you belong in. The rating is also used to determine your Day Rating, but that is only used for your personal record keeping.
Surgeon General's Warning
This article is broken into two parts. Here's a handy guide for telling which part you should read:
"I want to know what makes my rating higher. And I don't like math." You! Read Part 1.
"I want to know why my number is 1325, and not 1.78. I like math." You! Read Part 2.
Part 1 - The Juicy Center
This part is concerned with the beating heart of the rating formula. For the Public Beta, it is as follows:
raw_rating = kills + assists - deaths/3 - betrayals
And that's pretty simple. It is essentially a weighted KD spread. Were you expecting calculus?
Kill and assist to increase your rating, avoid deaths that decrease your rating, and definitely avoid betrayals. If you do these things well, the Arena will rate you highly and you will move up in your Division (or across Divisions) until your Division standing accurately reflects your skill relative to your peers.
Now, it is actually a bit more nuanced than that. Here's the actual formula:
raw_rating = (kills + sa*assists) - (sd*deaths + sb*betrayals)
It's still less complicated than it looks. Let me explain each part:
kills
Simply put, the number of kills you personally were credited with. In Slayer, kills are a direct measure of your impact on the game result. These have primacy in the rating formula.
assists
The number of kills you assisted a teammate with. In Reach, an assist is defined as "doing 40% or more of the damage required to kill a target that dies to other causes before a shield recharge can occur."
This number is scaled by sa, which modifies the value of assists in the overall rating. For the Public Beta, sa is 1.0. This is important: an assist is as valuable to your rating as a kill.
One of our goals for the Arena is to reward working as a team. For some teams, this will take the form of team-shooting with DMRs. For others, calling out one-shots such that a teammate finishes off a wounded target. Regardless of the method, the Arena will reward a team who gangs up on their targets by giving their team collectively higher ratings than a team of lone wolves. If you have an off game and never land a single headshot, but you were part of every kill your team made, your rating will not suffer for it. In fact, you'll probably do quite well.
deaths
The number of times you died. This is a measure of failure in the Arena. Dying is something to be abhorred. It is giving the other team points and rating.
This number is scaled by sd, which modifies the punishment levied by deaths. For the Public Beta, sd is 1/3. This means a death reduces your rating by a third as much as a kill increases it.
We believe that this may be a bit too soft, but the Arena is ultimately about killing the other team. A player should not be so afraid to die that he forsakes all glory to cower in a corner. A strong offense should more than pay for the costs incurred. So this scalar sd is one of the numbers we'll be watching closely through the Public Beta and when Reach is released. It may go up if we feel like Arena play is too sloppy and grinding is too rewarding.
Betrayals
This part is pretty straightforward. Here, sb is set to 1.0. As such, a betrayal carries a significant cost to your rating, along with the other, Banhammer level punishments for habitual betrayals. So, blindly lobbing grenades into the room where your teammates are fighting is not recommended.
Part 2 - There Will Be Math
Part 1 wasn't so bad, was it? Still hanging in there? Good, cause now it gets hairy.
Here's what the total formula looks like:
rating = loss_penalty * (1000 + (2000/pi * atan( raw_rating * game_normalization )))
Yes, there's an atan() in there. Stick with me for the loss_penalty part, at least.
loss_penalty
If your team loses, this is a penalty applied to your rating.
But wait, you protest: "Isn't the Arena about individual performance?" It is, so our goal is that this penalty is as small as possible while still accomplishing two goals:
- Assuming equal performance, a player on the winning team should place ahead of his counterpart on the losing team.
- Playing for a personal best rating should require winning. No hanging your team out to dry to shoot for a high score.
For the Public Belta, this number is 0.96. In other words, if you lose, we shave a mere 4% off of your rating. We will be continuing to adjust this number, and we might even shift the place where this penalty is applied.
game_normalization
Ok, this part is worth reading too. This term is actually calculated as follows:
game_normalization = players_per_team / score_to_win
It simply serves to normalize the raw_rating for different games. A player in a 2v2 game to 50 would be expected to have a larger raw_rating than a player in a 2v2 game to 15, simply because there's more killing to do before the game ends. This term allows us to equalize the ratings, so that a 1350 in one game is approximately equal to a 1350 in another game.
1000 + (2000/pi * atan( … ))
Hahaha, ok. This part really only serves to beautify the result. If you only care about what you should do to make your rating higher, you can stop reading now.
Still reading? Well, ok. You asked for it.
The atan(…) is the trigonometric function arc tangent, which is the inverse of tangent. It's a handy function, but all you really need to know is that it makes a curve that looks like this:
![[IMG]](http://www.bungie.net/images/Games/Reach/betaGuide/inlines/chart.jpg)
C3CXF-H3DMJ-DPXC3-BDPMM-MDM4G
Why that curve? Because it approaches a maximum and minimum asymptotically (meaning, it reaches them only at infinity and never crosses them), and it has a finite slope at 0. This gives our scaled rating two nice properties:
- There is a maximum and minimum rating that can never be exceeded, and it takes exponentially increasing effort to approach either. This is nice because it takes more effort to beat each new high score.
- At the neutral point of 0, the rating moves fluidly but consistently, and the rate of change decelerates as you move away from that baseline.
So, we feed the rating into this function to map it onto this nice curve. The other constant numbers simply convert the output of atan(…) into the range of 0 (the lowest theoretically possible rating) to 2000 (the highest theoretically possible rating), with a neutral, baseline point at 1000.
And that's all that that part is doing.
It's worth noting that we do have a other constants in that formula that we can use to adjust things like the shape of the curve, but at least for the Public Beta, those scalars are set to 1.0 and so I've omitted them for clarity.
Caveats
If you've read this far, you must be either hungry for information, appreciative of my prose, or (more likely) looking for -blam!-s in my armor. Regardless of the reason, I offer a caveat: this formula is an evolving entity. We will be adjusting and tuning it based on how we feel the Arena is playing. Our systems will allow us to do so, just as we update our playlists. We have always and will continue to listen to player feedback to improve the experience for you guys.
Thanks for reading.
|
