*(First, if you haven't had the chance to read the preceding post, you may consider doing that. The following post assumes knowledge of the preceding post.)*

**Introduction**

First, I just want to say thanks again for everyone who has read and commented about the previous post. It represents weeks of personal data analysis, and for all the people who have sent me messages offering to help, I'd just like to extend a hand of gratitude (or arms, if you're a hug guy like me).

Truthbetold, my only reason for doing this in the first place was because I couldn't get myself to consciously ladder without satisfying the curiosity of knowing where I stood relative to everyone else. I am a very competitive person and I tend to get compulsively addicted to anything I do. As such, being unable to rate myself with other players, I then became set on and consumed by figuring out this system enough to satisfy myself.

I feel that I've accomplished that, and as such am losing interest in pursuit of the final pieces of the puzzle--partly because I'm content, but mostly because the promotion aspect hopefully won't apply to me once I can sit down, improve, and just play more games.

The goal of this addendum will be to address some of the prevalent questions, criticisms and comments about the post. I'll try to be clearer about things I wasn't as clear about before, in hopes that it will better enable other data-curious individuals to continue this work, should they choose to (and I hope you do, because I'm still very curious!).

**A Modeling Primer and the Promotion Prediction Equation**

First and foremost, I feel the extended focus on the Promotion Prediction Equation to be a bit unfortunate. This was one of the very last things I created before posting that, and I didn't properly address the limitations of that equation.

W = Win %

Pp = Rank Point Differential

M = Magic Number

A = Average Win (bonus pool adjusted)*

B = Average Loss

G = Games required for promotion. (This is what we're calculating.)

**Bonus Pool matches your earned points from a win. Subtract out these gained points from each win.***G = 5 + [M - Pp] / [W*A + (W-1)*B]**

As with any model, it is only as accurate as the most current information available. Even with every unknown solved, access to the real function(s) used in calculating MMR and promotion, and working at Blizzard, it is not possible to determine exactly when you will be promoted beyond one game.

You must actually play the games, and with every new piece of data you create, the model may become less and less accurate, as it forecasts future data, which you yourself must determine.

However, for players who are far away from promotion, this equation creates a simple static-slope line that approximates how many games you need to play for your Rank Point Differential to equal or eclipse your corresponding Magic Number. 5 games are then added to get your Simple Moving Average over 10 games to also equal or eclipse that Magic Number.

In other words, because the slope is a constant, it assumes a static linear increase in your MMR (usually between 1-2 points). For an average win of 13 and loss of 11 at 50% win rate, this equation assumes that you alternate wins and losses every game such that your MMR jumps up 1 point per game until you reach your M-value.

This equation makes assumptions based on an already-simplified equation, such that you can very quickly get a rough estimate if you are far away from promotion.

If you have a win rate less than 50%, you may get a negative number, because you may never get promoted with such a win rate. Also, if M - Pp < 0, you're going to get a negative number as well, because your Rank Point Differential has already eclipsed the Magic Number.

At this point, the equation has limited if any predictive value because you're very close to promotion, and this equation is optimized for players who are not close.

Therefore, if you decide to make use of this equation, you should keep in mind that it's only useful as a generalized estimator of the number of games you would need to play, at your current skill level, and current win rate, to be promoted. Those values change with every game you play (albeit slightly in most cases), and so after every game you play, the equation's original prediction may become less and less accurate unless you can continue to update it.

**The MMR Equation and Working Backwards**

For completeness, consider again the Matchmaking Rating Equation in its unsimplified form:

P = Rank Points

U = Unspent Bonus Pool

B = Total Bonus Pool

W = Win Percentage

M = Magic Number

Pp = Rank Point Differential

C = League Conversion Constant

K = Division Modifier

**MMR = P + U*W*2 - B + K + C**

I spent too much time in ms paint. |

**The Bonus Pool**

*(this works in the latest version of Google Chrome; no idea if it works in other browsers or those few of you who were brave enough to actually try and read this blog on a mobile device.)*

**Win Percentage as an Estimator**

**Calculating Your Displayed Matchmaking Rating**

**dMMR = P + U - B + C + K**

**Other Questions and Concerns**

**Closing Comments**