357 Missing Scores
In short, you can trade a small increased chance that you won't win any squares for a much larger chance that you'll win two, three, or even although rare four squares in a single game. Using the professional football game box scores regular season , over one billion computer simulations have been run where squares are picked, a game is chosen, and rows and columns assigned random digits.
It turns out there are 60 unique configurations you can select up to five squares given the digits for rows and columns are random. Over a billion simulations are needed because there are 4,,,,,, total possibilities 10! At the extreme ends, there are two strategies that emerge. If you pick squares such that each square selected has a unique row and column, you will maximize your chance at winning something most often only a single square and minimize your chance, relative to other strategies, that you'll win two or more squares in a single game.
The other extreme is to select a strategy that maximizes your chance of winning two or more squares. You can try to go home the BIG winner I like this strategy! Consider selecting four squares in the two extreme strategies Expanded, the probability table looks like this: The expected squares are calculated by multiplying the number of wins with the associated probability and summing it all up.
Notice, that essentially your strategy - how you select your squares - allows you to trade off a small probability for winning something for a much larger probability for winning two or more squares. All possible ways to select up to 5 squares Below is a final tabulation of all possible ways to select squares along with the probability of winning 2 or more squares and the probability of winning something.
Reading top to bottom and then left to right, the configurations are ordered to maximize your probability of winning two or more squares. The column direction reflects the underdog team and the row direction reflects the favorite. What about 4 points during a game? Kyle Harrington had to ruin everything by getting another safety making the score completely forgettable.
They ended up losing in overtime anyway, so I hope he learned his lesson. You could've been part of history Kyle. You could've been a contender. Also worth noting, the first ever college football game in between Rutgers and Princeton ended in a Rutgers victory. Obviously scoring was vastly different in those days, as were attitudes about the game. One professor was seen waving an umbrella during the contest, yelling "you will come to no Christian end!
Yes, it has happened 6 other times in NCAA history. Clemson 3, Duke 2 - Oct. TCU 3, Texas 2 - Nov. Iowa State 3, Kansas State 2 - Nov.
VMI 3, Kentucky 2 - Nov. This game also came very close to ending in a final score. In the 4th quarter, with Mississippi St. Inexplicably, Sylvester Croom went for it, to the shagrin of not only me but the color commentator, who lambasted him for this decision. Sure it didn't make sense football strategy wise, there was plenty of time left to force a 3 and out and get the ball back, but it also killed a relatively decent chance that the bulldogs would finish with 4 points, which also should've been taken into account.
In conclusion, fuck Sylvester Croom. Otherwise, to estimate the probability of any particular square winning we'd have to rely on historical data, and create a running tally of how each square has performed. Needless to say, this is more work. Unfortunately, it seems that this is necessary work. By looking at data from 4, preseason and regular season games from the season was the first in which the two-point conversion was instituted , I tallied the counts for each winning square in the case of both the traditional football pool and the digital root pool.
Here is the data:. Recall that for the digital root pool, the digit 0 only occurs if one team doesn't score - to even things out, I have assigned a score of 0 with a digital root of 9 I discussed reasons for this in my earlier post.
Using a standard statistical test for independence, we conclude that there is essentially no way that the digital root of one team is independent of another team, or that the last digit of one team's score is independent of another team's score. Therefore, assuming the digital roots of the away team and home team's scores were independent, the probability of winding up in the 2,2 square would be 0. In other words, if you know that the score of the home team's digital root is 2, it is suddenly much less likely that the score of the away team's digital root is also 2.
Using this larger data set, we also find that it's actually unlikely that the digital roots become equally distributed among the digits from 1 to 9. While the distribution is certainly more uniform than in the case of the second digit, we also see that certain digital roots occur significantly more frequently than others 5 occurs much less frequently than 1, for example.
Even though away team and home team 2nd digits and digital roots are not independent, one may expect that the probability of having a score with a given 2nd digit or a given digital root should be independent of whether the team is the home team or the away team. Interestingly, in the case of the 2nd digit, this is not true.
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