Success Rate (in Sports)

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The success ratio is an all-in-one statistical model in sports that highlight the accumulation of total success against the mistakes made between two competing teams that are simultaneously trying to win a game. This model was created and developed by Eli Joseph.

Calculation

Let O(x), D(x) and E(x) be continuous functions as a given game progress over time, t. ($\Delta$t $\rightarrow$0)

Suppose that V is a game between two competing teams, Team A and Team B.

Assuming f(x) = Team A and g(x) = Team B:

${\begin{alignedat}{2}f(x)=\lim _{x\to \infty }\sum _{i=1}^{N}\left({\frac {O(x)_{A}+D(x)_{A}}{E(x)_{A}}}\right)_{i}\\g(x)=\lim _{x\to \infty }\sum _{i=1}^{N}\left({\frac {O(x)_{B}+D(x)_{B}}{E(x)_{B}}}\right)_{i}\end{alignedat}}$

where

• All x values are real and positive
• O(x) = Offensive Function
• D(x) = Defensive Function
• E(x) = Error Function
• N = the number of periods that are available throughout the duration of the single game

The team with a higher ratio, regardless of the score of this game, is the successful team.

Note that the calculation of this statistical model is independent to the actual result of a scoreboard in any sporting event. In other words, there are cases that a successful team did not win the game.

This model can be used in sports that has a time limit requirement. These sports include (but are not limited to): Basketball, Football, Association football, and hockey. Sports that do not have a time limit (for example: baseball) have slightly different functions within this model.

Statistical Guide

In the beginning of every game, regardless of the sport, the success rate of both teams are indeterminate.

In a basketball game, the calculations of the success ratio are:

• O(X) = Offensive Rebounds + Assists + 2*(2-Point Field Goals made) + 3_*(3-Point Field Goals Made) + Total Free Throws Made
• D(X) = Defensive Rebounds + Steals + Blocks
• E(X) = Missed field goals + Missed Free Throw Shots + Total Fouls + Total Turnovers

In his TEDx talk, Eli Joseph provides a graphical example of a Success Rate throughout the #11 Syracuse vs. #3 Duke game in the 2018 NCAA Men's Basketball Tournament

In a football game, the calculations of the success ratio for are:

• O(x) = Total Offensive Yards + 6_*(Touchdown) + 3*Successful Field Goal(s) + 2*Two Point Conversions + Point after Touchdowns + 2*First Downs + Complete pass attempts + Total Return Yards
• D(x) =  ${\textstyle {\frac {1}{4}}}$*(Total Tackles) + 2*(Safeties forced) + Block Kicks + 2*Turnovers forced
• E(x) = ­­Incomplete pass attempts + Punts + 3*Unsuccessful Field Goals +Unsuccessful Two Point Conversion Attempts + 2* Total turnovers + Blocked Kicks + Penalties

In a soccer game, the calculations of the success ratio are:

• O(x) = 2*Goals + Corner Kick(s) + 2*Successful Penalty Kick(s) + ${\textstyle {\frac {1}{2}}}$*(Shots) + Shots on Goal + Possession % with Ball (expressed as a decimal)
• D(x) = 2*(Saves)
• E(x) = Fouls + Yellow Cards + 2*Red Card(s) + 2*Goals Allowed + Possession % without Ball (expressed as a decimal)

In a hockey game, the calculations of the success ratio are:

• O(x) = 2*Goals + 2*Assists + 2*Successful Shootout Attempt
• D(x) = Blocks + Saves
• E(x) = 2* Goals allowed + Shots allowed on Goal +2*Penalties in Minutes + Unsuccessful Shootout Attempt

In a baseball game, the calculations of the success ratio are:

O(X) = 4_*(Runs) + Base Hit(s) + Base on Ball(s)

D(x) =  ${\textstyle {\frac {Assists}{3}}}$ + Putout(s)

E(X) = 1 + (Error(s) + Hits allowed + 4_*(Runs allowed) + Walks allowed)₁+...+ (Error(s) + Hits allowed + 4_*(Runs allowed) + Walks allowed)_i

with i = number of innings

Empirical Examples

The average success rate of the four major professional sport leagues can be seen in the table below.

As of April 2018

Sports League	Season	Number of Games	Unsuccessful Scoreboard Winners**	% of Success Ratio Agreement***	Average Success Rate	Average Points Scored
MLB	2017 Season	2,430	52	98%	2.52	4.65
NBA	2017-2018 Season	1,231	116	91%	2.30	106.38
NFL	2017-2018 Season*	268	38	86%	21.25	21.86
NHL	2017-2018 Season	1,271	100	92%	0.86	2.97
Total Games Played		5200	306	--	--	--

* Including Playoff games

**Unsuccessful scoreboard winners reflect a particular team that won the game with a lower success rate than the opposing team.

*** The success rate agreement reflect the percentages of games where the winning team have the higher success rate than the losing team.

Applications in economics and finance

This is a stock chart that compare the prices between IBM and the Dow Jones Industrial Average between June 2009 and September 2009.

In economics, all major forms of resources including capital, land, labor and time are extremely scarce. Therefore, market participants have to strategically find ways to allocate these resources and satisfy certain wants and needs. In game theory, market competition arises because a plethora of participants are contending to obtain resources in an efficient manner. This competition may lead to a zero-sum game where a participant's gain in resources may result in the opposing participant loss in resources. In this statistical model, the activities of the successful team will ultimately affect the opposing team's chances of winning the game.

In finance, the graphical characteristics of this statistical model relates to the principles of financial stock charts in technical analysis. Stock charts display key market trends over time. These trends can provide information regarding the market conditions. This statistical model also demonstrates certain trends throughout a game. Some scholars have even speculated a correlation between the results of a sporting event and the outcome of the financial markets.

Other applications

• Predictive modeling

• Sports betting

See also

• Game theory

• Technical analysis

• John Wooden

• Player efficiency rating

• Sabermetrics

• Sports analytics

External Links

This article "Success Rate (in Sports)" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Success Rate (in Sports). Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

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