title: How to weight a number by quantity?
body: <p>So I'm trying to rate the best KDA (kills, deaths, assists) for individual players. The problem is each player has played the game a different number of times.</p>
  
  <p>Player 1 has 9 kills, 2 deaths, and 1 assist OVER 1 game so their kda is (9+1)/2 = 5<br>
  Player 2 has 90 kills, 30 deaths, and 30 assists OVER 10 games so their kda is (90+30)/30 = 4<br>
  Player 3 has 16 kills, 8 deaths, and 20 assists OVER 5 games so their kda is (16+20)/8 = 4.5  </p>
  
  <p>In my mind, a KDA of <strong>4.5 over 4 games</strong> is better than a <strong>KDA of 5 over 1 game</strong>.</p>
  
  <p>I'm looking for a formula to accomplish this. Initially I tried:</p>
  
  <p><strong>games/kda+1 = SCORE</strong></p>
  
  <p>The reason I added +1 is cause people had KDA's of &lt;1 and that meant games/0.1 would boost their score instead of decrease it. With the +1 the denominator will always be >1.</p>
  
  <p>This equation yields the following scores for the above samples:</p>
  
  <p>Player 1: 0.16<br>
  Player 2: 2<br>
  Player 3: 0.909</p>
  
  <p>This equation puts a too much of an emphasis on the number of games in comparison to the KDA.</p>
  
  <p>Here's what I think the rankings should be like:<br>
  1. KDA 10 over 50 games<br>
  2. KDA 5 over 100 games<br>
  3. KDA 5.5 over 50 games<br>
  4. KDA 2.5 over 100 games  </p>
  
  <p>Any ideas?</p>
  
  <p><strong>EDIT:</strong> Based on Flight Odyssey's input I came up with two possible equations:<br>
  1. (GAMES*dampener1)+(KDA*dampener2) = score (add)<br>
  <strong>OR</strong><br>
  2. (GAMES*dampener1)*(KDA*dampener2) = score (multiply) </p>
  
  <p>Equation #2 doesn't work because that means that the score would just be adjusted by a fraction. Equation #1 means that the GAMES and KDA each have separate "adjustments" which is what I want. Then I looked at what was aiming for:  </p>
  
  <p>Here's what I think the rankings should be like:<br>
  1. KDA 10 over 50 games<br>
  2. KDA 5 over 100 games<br>
  3. KDA 5.5 over 50 games<br>
  4. KDA 2.5 over 100 games  </p>
  
  <p>I focused on scores 2 &amp; 3 and made the KDA adjustment 10, and then varied the GAME's adjustment and compared it...</p>
  
  <p>2: 50+100/x = 55+50/x then solved for X. It ended up being 10 so when the GAME'S adjuster is at 10 these two would equal each other. I adjusted that value until it "felt right" and that's what I ended up with...  </p>
  
  <p>(KDA * adj1) + (GAMES * adj2) = SCORE<br>
  adj1 = 10<br>
  adj2 = ?</p>