I’ve added a star rating to each game. It measures the “enjoyability” of a game based on a few different factors. There are many elements to a game that can make it enjoyable to the unbiased fan. I’ve tried to include the most important of these.
The rating system ranges from 0 stars to 5 stars and goes in increments of .25 stars. The average game will be around 2.5 stars.
Leverage Index (aLI)
The first and most important element is leverage index, which measures the importance of each situation in the game. The more crucial a moment in a game is to the outcome, the higher the leverage index will be. A leverage index of “1” is average. A leverage index of “3” is equal to three times as important as the average play. FanGraphs has a primer on LI for those interested.
In the game rating formula, I use average leverage index over the course of the entire game. I could have chosen to just go with the top X plays in a game, or the number of plays over a certain threshold, but I felt the average over the course of the game is best suited to gauge the intensity of the entire game.
Win Expectancy Change (WE+/-)
Next is change in win expectancy per play. Suppose an RBI single increases a team’s win expectancy from 55% to 65%. That would obviously be an increase of 10 percentage points. I calculate the average absolute value of WE change over the course of the entire game and use that number for my rating formula.
The average play in the average game will have a win expectancy change of about 3.3 percentage points. Bigger and more exciting plays will increase this number, while plays in blowout games will do the opposite.
Leverage index and win expectancy change very likely have a high correlation, which would cause these elements to be “double counted”. I have taken that into consideration and am fine with it since they are the most important factors in gauging a game’s intensity.
Championship Leverage Index (CLI)
Championship leverage index is similar to in-game leverage index (above), in that it gauges the importance of a single game as opposed to a single play. The game importance is measured in how much a team’s probability of winning the World Series changes in a win versus a loss.
The average game will have a CLI of 1 and is equal to the average game on opening day. In the 2nd Wild Card era (2012-present), the average game on opening day can change a team’s chances of winning the World Series by 0.59 percentage points.
The CLI used in this ratings formula is the average of the two team’s CLI for this game.
Examples: A team that is already eliminated has a 0% chance of winning the World Series. A win will not increase their chances, so their CLI will be 0. The same goes for a team that has already clinched their division. A division title ensures that a team is 1 of the 8 teams in the postseason tournament, meaning they have a 12.5% chance of winning the World Series. A win or a loss after clinching the division will not change this number. But a one-game playoff for the division (game 163) is a “win or go home” scenario and will have a CLI of around 21, since it is 21 times more important than the average game on opening day.
The final element is comeback, which is defined as the highest win expectancy the losing team reached during the game. A comeback can range anywhere from 50 percentage points to 100 percentage points. A comeback of 100 percentage points means that the losing team had a 100% chance of winning, but still managed to lose the game. A comeback of 50 percentage points means the losing team was never able to increase their win expectancy above the 50% level at the beginning of the game and likely means the game was never much in doubt.
Formula and Weights
Each of the four elements (LI, WE+/-, CLI, CB) are individually compared to a large sample of games ranked in a percentile. These percentiles are then weighted and combined to create the star rating. The weights are:
aLI = 1.5
WE+/- = 1.5
CLI = 1
CB = 1
Example: A game has an average leverage index of 1.25, an average win expectancy change of 4.5 percentage points, a championship leverage index of 1.55, and a 85% comeback. Their percentiles and weights are:
aLI = 70 * 1.5
WE+/- = 82 * 1.5
CLI = 92 * 1
CB = 90 * 1
Their sum is 410. This number is divided by 25 and rounded to the nearest whole number. It is finally divided by 4 to give you the star rating. This game would be a 4 star game (410 / 25 = 16.4 = 16 / 4 = 4).
Elements of a game not currently included in star rating system
Individual game performances and milestones. A player hitting 4 HR in a game is exciting and uncommon and makes each of the at bats more important. A pitcher taking a no-hitter or perfect game late into the game has the same effect. These types of elements are currently not included, but are “on the table” for future versions.
One could argue that the more superstar players in a game could make it more enjoyable. This rating system does not take the players superstar status or skill level into account.
While Derek Jeter’s final home game was exciting in its own right, I would argue that it was even more enjoyable since it was his final game at Yankee Stadium. This rating system doesn’t take these rare situations into account.
The Home Crowd’s Enjoyment
As mentioned above, this star rating measures the enjoyment for the unbiased fan. The home crowd may have a different definition of an enjoyable game based on whether their team wins, but this system makes no such distinction.