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Now that we have all the parts and pieces we can combine these data points, percentages, minutes, and seconds to come to a more informed conclusion, that which one would, with human perception.
Distributed Points Algorithm:
To recap, lets list the considerations and then approximate the percentage of success based on the algorithm available from online stat sites, quick napkin math, and potentially some fandom approximations.
- There is 4 minutes left in the game
- I need four (4) points
- Twenty Eight (28) percent of the time Josh Allen passes to Stefon Diggs
- Seventy (70) percent of the time Stefon Diggs catches the ball thrown to him by Josh Allen
- On average Stefon Diggs receives for twelve (12) yards or two point two (2.2) points a catch
- Each team has the ball for one (1) minute and forty-eight (48) seconds
With four minutes left in the game, we can divide the 4 minutes by the possession time of 1.48 minutes which gives us 2.7 possessions left in the game.
If there are 2.7 possessions left in the game that means that we can multiply them by the amount of downs or plays left in those possessions which is 4, so 2.7 multiplied by 4 is 10.8 plays left in the game.
If there are 10.8 plays left in the game that means that the odds of Josh Allen passing to Stefon Diggs is 10.8 multiplied by .28 or 28%, which is 3.02 passes to Diggs.
If there are 3.0 passes to Diggs left in the game that means that there is a .7 or 70% chance of him catching them so we multiply the 3.0 passes to Diggs by .7 which gives use 2.11 caught passes.
If Stefon Diggs catches 2.11 passes that means that we can multiply the 2.11 by 2.2 to get 4.66 points.
We take the naive algorithm approach, assuming that these are not end of the game touchdowns, but quick progression passes. Assuming that all percent of plays that are not passes to Diggs are passes or rushes from other players. Assuming that all of these passes are over ten yards so that we can carry the average points to each pass. All else equal it seems that the odds of winning are far greater, almost undeniably greater, unless the situation falls to uncommon circumstances.
We can assume the equation would be something like (((((Time Remaining / Avg. Time Of Possession) * Avg. Plays Per Possession) * Avg. Passes To Diggs) * Avg. Catches By Diggs) * Avg. Points Per Catch)
*Algorithm still under peer review
This algorithm gives us a forecast of the points we should earn based on the time remaining but to understand an approximate percentage of that points attainment occurring we need another naive algorithm.
Naive Percentage Algorithm:
If there is a 28% chance of Josh Allen passing to Stefon Diggs and 70% chance of Stefon Diggs catching that pass, then we multiply .28 by .70 and get .196 which we then multiply by 100 which gives us a 19.6% chance of winning.
- 19.6% Chance Of Points Occurring On One Pass
The 19.6% is based on the probability of one pass, though in this instance with the time remaining we have three passes left in the game with this percentage of outcome, which should leave us with a naive assumption of a 20% chance of winning.
- 20% Chance Of Points Occurring On Three Passes
Taking these assumptions and the isolated factors for a path to a win, with the exception of only being reliant on the outcome of Stefon Diggs, we can build a win algorithm of all these contributions together.
(((((Percent Avg. Passes To Diggs / 100) * (Percent Avg. Catches By Diggs / 100)) * 100) * Passes To Diggs Left In The Game) / (Passes To Diggs Left In The Game * 100))
*Algorithm still under peer review
The overall naive algorithm from this simple model would predict that if all goes as expected, my actual percentage of win would 20% instead of the 1% that the progress bar showed me.
This whole thesis is accepting that at the end of the game Josh Allen threw to Diggs as he did on average, maybe not even more to increase the odds, or less to reduce them. Potentially not of more yards to increase the points, or less to reduce them. Even accepting that what could occur, but would probably not based on the human experience of loss would lead us to believe, that one of these passes was for a touchdown, increase the points by a larger factor. I believe a predictive model would perform on these statistics as well, the game time, and the odds of these considerations for making an estimate of my approximate win.
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