FA Premier League 2019/20. The season was affected by the COVID-19 Pandemic while each team had a so-called quarter of their schedule left. ("quarter" ? Since each team has 4/9 or 5/9 number of away games and 4/19<1/4<5/19 mathematically, just don't mind about it.) Here is proposal to shut down the league by using my acceptance as follows:
- Better teams are better at it.
- If the difference between home points that home team averaged and away points that away team averaged over $\mathtt{magic}\,\mathtt{number}= .2$ then three points are awarded to better team. Otherwise, each team receives one point.
Final standings of that season (FA preml.ge)
Let me explain things one by one:
Magic number (sports,wiki): is a number used to indicate how close a front-running team is to clinching a division title and/or a playoff spot. It represents the total of additional wins by the front-running team or additional losses (or any combination thereof) by the rival teams after which it is mathematically impossible for the rival teams to capture the title in the remaining number of games (assuming some highly unlikely occurrence such as disqualification or expulsion from the competition or retroactive forfeiture of games does not occur). I've derived Magic number variant of football even without bothering about the ties as scenario above
$\mathtt{magic}\,\mathtt{number}= .2$
Based on Theory of "Banking a draw meaning a new kind of loss": We have witnessed best engaging two of five last seasons with the gap of one point between City and Liverpool. Although City have had more losses than Liverpool both time, but always won Premierships at the end of seasons. Observe the number of draws/losses in these two seasons:
- 2018/19: City (2/4), Liverpool (7/1)
- 2021/22: City (6/3), Liverpool (8/2)
Nash equilibrium (based on theory of "about a quarter of its matches end in draws"):
If A defeat B and B draw C, the trend is A defeat C (C still has self-determination, however, a draw again is a bad draw).
If A defeated by B and B draw C, the trend is A draw C (A is passive, C have chances from a draw to a win).
Comment: C still has self-determination. But that's not enough to decide whether C "may draw" or "may not draw". So the gap is of two points between a draw and a win $\mathtt{magic}\,\mathtt{number}= 2.\!$ To seek delicate relationship between home average & away average. I divided it into cases and realized:
For tournament of four teams
$0/1< 1/2< 1/1\Rightarrow\mathtt{magic}\,\mathtt{number}= 4/4.\!$ So on.
For tournament of twenty teams
$4/9< 1/2< 5/9\Rightarrow\mathtt{magic}\,\mathtt{number}= 4/20= .2$
My formula to calculate the performances of teams (as description above):
$$\left | \overline{{\rm Home}}_{i}- \overline{{\rm Away}}_{j} \right |\left\{\begin{matrix}
\geq .2, {\rm three}\,{\rm points}\,{\rm awarded}\,{\rm to}\,{\rm the}\,{\rm better}\\
< .2, {\rm each}\,{\rm point}\,{\rm to}\,{\rm each}\,{\rm team}\,{\rm of}\,i,\,{\rm and}\,j
\end{matrix}\right.$$
Up to my method: MUFC stand 6th, Villa relegated.
In fact: MUFC stand 4th. (LCFC have been in top 4 through round 1 to round 37, what bad luck they stand 5th at the end of the season.) Villa qualified the following season (goal-line technology doesn't award Sheffield the goal against Villa, if not, Villa had been back to Championship). Sincerely, this modeling is totally wrong. Liverpool and City both over-estimated, get a maximum of 27/27 points scoring for Liverpool (including against City). Should it be possible to decrease the effort and motivation of an elite sample like that ? I think it says something about human nature that we still exert a bit more effort when we’re slightly behind, and Liverpool were way too far behind. I need much more concentration to improve formulas to stand in their way like: $$\left | \frac{h(\overline{{\rm Home}}_{i}, \overline{{\rm Away}}_{j})- g(\overline{{\rm Home}}_{i}, \overline{{\rm Away}}_{j})}{f(\overline{{\rm Home}}_{i}, \overline{{\rm Away}}_{j})} \right |\left\{\begin{matrix} \geq e, {\rm new}\,{\rm standard}\,1\\ < e, {\rm new}\,{\rm standard}\,2 \end{matrix}\right.$$ We still miss the scenario of a quarter of its matches end in draws. I need your help to seek $e, f, g, h\!$ for my variant in order to avoid linear equivalence. Thanks a real lot !