Impact: Who to Watch

This is the first article in a series I’m creating on advanced Dota statistics. Being a fan of advanced baseball statistics (SABER), I have always been disappointed with the quality of statistics available in Dota 2. The main problem is that most of the stats available and shown on broadcasts don't actually tell us much. This is because most of the numbers are what people in the stats business call ‘counting stats.’ For instance, in Dota 2 some counting stats would be K/D/A, wins as a certain hero, wins when an item is gotten before a certain time, etc. The core of advanced statistics is taking these counting statistics and dividing them by another number. In this article I’m going to dive into a new stat I've developed that I call Impact. Let’s get started.

Most good statistics, in my opinion, are based on a good question. For Impact I used one of the simplest I could think of: “Who was the best player in the game?” which I later changed to “Who had the most impact on this game?”  I also thought it would be nice if the number gave you a clue on who to watch in a replay.  An ‘entertainment value’ if you will.

To explain the method of calculation I first have to explain two fairly simple concepts: weights and positional adjustment.

Weights are simple; they are saying not everything is equal so we shouldn't treat them as such. So my first goal was to assign weights to the basic K/D/A. Here are the numbers I decided on:

Kill	1.75
Death	1.1
Assist	0.75

Using this we can get our first player ranking number like this: ((Kills*1.75)+(Assists*.75))-(Deaths*1.1). In the final formula I will call this number KDA. Now, there is a big problem with this, as I’m sure some of you will notice right away: it favors carries and semi-carries way too much. To help fix this we will use something called positional adjustments (in the final formula this will be called PA). The basic idea of positional adjustment is that some positions are harder to play than others. So, we will again use weights to give each position a number. Here I am using the traditional roles, but would like to have positional adjustments for all lane configurations eventually.

Carry	1.35
Solo Mid	1.75
Solo Offlane	1.8
Support	1.5

Are these perfect? Probably not, but I think they are a good starting point. At first I thought that would be all we would need for Impact, but I spotted a problem with the formula: carries were actually penalized too much. I realized I was missing a large part of what carries do: hurt towers. Therefore I decided to add tower damage into the formula. I did this like so: ((TowerDamage*2)/1000). Here I divide by 1000 to get a number that will be closer to the numbers in the K/D/A. In the final formula I will call this TD.

So what does all of this get us? Here is the formula:

((KDA+TD)*PA)/10

Here dividing by ten is just giving us a smaller number to work with.  All numbers from here on out will be rounded up to the nearest hundredth...unless I forget.  

So let’s get to an example!

Here are the Impact scores from the recent game Sigma - Fnatic match id: 512566540

Sigma	Impact
Sockshka	2.29
FATA	1.86
miGGel	5.41
7ckngmad	1.51
paS	2.31

Fnatic	Impact
Era	1.14
H4nn1	1.42
Trixi	0.32
N0tail	1.07
Fly	-0.08

So what can we learn from this? First, we can see the miGGel went bonkers and if we were planning on watching a replay we would keep an eye on him. Second, we can also see where things went wrong for the other team- Fly had a bad game and Trixi was abysmal. Thirdly, we can see how important supports are, with both of Sigma’s supports getting the better of their counterparts, especially in the 5 position. With paS, seeing how high miGGel’s score is, we can safely assume that he got quite a few assists, possibly while teaming up with miGGel.  Let’s have another example. Here are the scores from game 5 of the grand final of Ti3:

Na'Vi	Impact
XBOCT	2.54
Dendi	6.45
Funn1k	1.20
Puppy	1.68
KuroKy	0.63

Alliance	Impact
Loda	2.06
s4	1.73
AdmiralBulldog	4.71
EGM	2.08
Akke	0.06

From examining this we can learn a few things. First, remember that stats like these do not measure individual plays. We all know s4 had the single most impactful moment, but that doesn't show up here. Second, Dendi was awesome in the game, but I think people might be surprised at how high Bulldog’s score is. This can be explained simply; since we included tower damage the full impact of how good Bulldog’s rat dota was can be seen. Thirdly, Funn1k...oh Funn1k. Let’s try out something else using this formula.

I used www.datdota.com to see player’s stats from the 13’-14’ season, as this should show us the most impacful players on the scene right now. Also note that this will use averages for the counting stats. Here are the player rankings from just a few of the top teams (as of the 9th of February). THIS IS NOT EVERYONE:

Player	Impact	Games Played
Arteezy	3.4	43
Super	3.22	130
SingSing	2.97	93
Era	2.86	106
Loda	2.83	155
AdmiralBulldog	2.79	158
Dendi	2.76	155
H4nn1	2.76	176
Ferrari_430	2.72	125
mushi	2.71	131
s4	2.66	165
Hao	2.62	125
XBOCT	2.61	155
Sylar	2.59	87
EternalEnvy	2.58	145
BurNIng	2.56	130
Universe	2.5	133
YYF	2.33	125
bOne7	2.25	134
Funn1k	2.24	161
Trixi	2.18	76
iceiceice	2.04	131
zai	2	68
Fenrir	1.79	134
Aui_2000	1.71	154
Puppy	1.69	166
MMY	1.69	130
Faith	1.66	122
rOtk	1.61	130
Fear	1.58	133
LaNm	1.55	130
EGM	1.52	169
Akke	1.51	159
KuroKy	1.49	107
Banana	1.48	120
N0tail	1.45	166
pieliedie	1.38	147
Fly	1.37	109
ppd	1.34	81

Keep in mind that we are using only one set of positional adjustments, so this chart isn't perfect.

From this we can see that over time the carries and semi-carries are pretty much always going to be the most impactful.

This chart also brings up something important to remember when looking at any statistic: sample size. The smaller the number of games played, the less accurate the numbers are. This is why in sports such as baseball you have to have a certain number of games played, at bats, innings pitched, etc. in order to qualify for awards. Arteezy has played half the number of games as the other players on the list, which is why his number is probably inflated while ppd and Fly’s are probably a little low. Remember the more games played, the more accurate the number. This isn't a knock on any player, but just a truth of statistics.

More than anything I hope this new stat begins to start a dialogue about improving the quality of Dota 2 statistics. With all the raw numbers we have at our disposal, the number of meaningful stats we can glean from them is nearly endless.

If people are interested, I can share a template spreadsheet that people can use to calculate Impact on their own. Also keep in mind that I did all of this by hand, so there may be mistakes.

Stay tuned for the next article where we tackle another simple question: “Who is winning this game?”