Based off of that 61% win rate I then created a monte carlo simulation. Assuming everything else is equal how many wins do you expect to get per run if you win rate is 61%? Here's the correct answer:
Your expected number of wins is 4.6. But how accurate is my model? After all I only included one parameter. Well here is what our winstogram looks like:
Looks pretty good to me! Please ignore the binning offset. Let's take a look at the features. First of all we see more 12 wins than 10 or 11, and that is just what the model predicts. It makes sense since all the 12's are really >12s because the run could have kept going. The next feature is our complete lack of 0s. I think that comes from the matchmaking nature of the Arena. A better model would track win rate as a function of record and use that function as the MC seed. Outside of that everything looks to be within the noise to me.
So now that we trust our model lets take her for a spin and figure out what kind of win percentage we need to get an average of more than 7 wins. We would also like to know what win percentage we need to go infinite but the rewards are pretty variable. So instead we will just find a win percentage that guarantees over 7 wins. So we turn the mc crank for a while and here's a plot of expected number of wins versus win percentage.
So it looks like to expect 7 wins we need to hit a win percentage of about 72%. That is a redonkulous improvement in play from where we are at. Assuming a baseline of 50% we have gone up 11% and need to go up another 11% to hit the goal. But presumably the first 11% is easier than the next. We are going to need to level up hard.
But how satisfying is a 72% win rate? Here is the winstogram.
And just for good measure here it is for 85%.
We've got a long way to go. Peace.
i can share my game log if you like, from which win rate can be extrapolated by previous record
ReplyDeletetempting. also stache has been wanting to keep an obsessive level of statistics. maybe it's time. at a minimum I would love to see the log. also it may be time for us to make a bigger spread sheet for a tab for each player and a summary tab for when we wan't to see everyone's results. i figured you have put a pile of time into a sweet log.
ReplyDeleteok apparently i am super into this idea. let's make it happen.