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## Championship Win Probability Added (cWPA)

Championship Win Probability Added (cWPA) takes individual game win probability added (WPA) and increases the scope from winning a game to winning the World Series. Where a player's WPA is the number of percentage points that player increased or decreased their team's probability of winning a single game, their cWPA is the number of percentage points the player increased or decreased their team's chances of winning the World Series.

### Calculation

To calculate the cWPA of an individual play, we first need to figure out the difference in World Series win expectancy based on whether the team wins or loses the game in question.

For example, on 9/7/1978 the Yankees traveled to Boston to start a series which would later be referred to as the "Boston Massacre". Entering the game, the Yankees World Series win expectancy was 3.75%. A victory on that day would increase that number to 5.29% while a defeat would decrease it to 2.38%. Therefore, the difference between a win and a loss for the Yankees in this game is 2.91 percentage points (5.29 - 2.38).

During the first inning of this game, the Yankees took the lead with an RBI single by Reggie Jackson. The play increased their probability of winning the game from 53.32% to 64.46%. Therfore, it was worth .1114 WPA (.6446 - .5332). To find the cWPA, we multiply this number by the change in World Series win probability between a win and a loss (.1114 * .00291 = .003242 cWPA). So it can be said that the RBI single by Jackson increased the Yankees probability of winning the World Series by .3242 percentage points.

## Championship Leverage Index CLI

While Leverage Index (LI) measures the importance of a particular play to the outcome of that game, Championship Leverage Index (CLI) measures the importance of a play or game to a team's chances of winning the World Series.

Leverage Index requires a baseline as a denominator. For Leverage Index, the baseline is about .03424. This means that the average play in the average game has a win expectancy change of 3.424 percentage points. Each situation in a game based on inning/outs/runners/score yields a different leverage index.

For example, throughout baseball history, plays in the top of the ninth, with no outs, a tie score and bases empty have averaged a win expectancy change of 7.689 percentage points. If we divide this by the baseline, we get leverage index (7.689 / 3.424 = 2.246). This means that plays in the situation are 2.246 times more important to the outcome of the game than the average play. Naturally, a LI greater than 1 is of above average importance, while a LI less than 1 is of below average importance.

The baseline for Championship Leverage Index is equal to the average game on opening day in the two wild card era (2012 to present). The reason why a particular era is needed is because with the addition of teams and playoff rounds throughout baseball history, the importance of each regular season game to a team's World Series expectancy has decreased. Realistically, any number or era would work as a baseline. However, the current era is chosen due to familiarity. The average game on opening day in two wild card era impacts a team's World Series win expectancy by .5869 percentage points.

As an example, we will refer to the game above from 9/7/1978 between the Yankees and the Red Sox. The difference between a win and a loss for the Yankees was 2.91 percentage points of World Series expectancy. If we divide this by the baseline, we get a game CLI for the Yankees of 4.958 (.0291 / .005869). The LI of the situation of the first inning RBI single by Reggie Jackson was 1.977. If we multiply the LI by the game's CLI, we get the CLI of the individual play (1.977 * 4.958 = 9.802). This means that this play for the Yankees was 9.8 times more important to their World Series win expectancy than the average play on the average game on opening day in the two Wild Card era.

To further complicate matters, the game's CLI is often different for both teams in the same game. This is because teams often have different records, remaining schedules, and/or play in different divisions with different opponents. So while the game CLI for the Yankees on 9/7/1978 was 4.958, we will have to do another calculation to get the Red Sox point of view.

Going into the day, the Red Sox were ahead of the Yankees by four games with 24 games remaining. Clearly, the Red Sox were in a more favorable position with a 20.88% World Series win expectancy. A win in this game would increase this number to 22.3% while a loss would decrease to 19.2%. Therefore, the Red Sox CLI for this game was 5.28 ((.223 - .192) / .005869). So while the game was important for both teams, it was slightly more so for Boston. Additionally, the CLI for the play from Boston's perspective was 10.44 (1.977 * 5.28).

### Postseason

For postseason games, the CLI is the same for both teams, as their World Series win expectancies are direclty related.
The game CLI for the 7th game of the World Series is 170.39 (1 / .005869). Since a win for each team would mean a 100% chance of winning the World Series and a loss 0%.