A Likelihood Score Primer
Placing probabilities on possibilities
An important statistic used by the v30 Club is the Likelihood Score. The number rates the possibility of a player meeting a home run related criteria and is presented on a 0-100 scale. Let’s dive in on the math.
Four Components
Likelihood Score relies on four easily collectible stats. To find a player’s score you need to know:
Number of plate appearances over a period. Not at bats, at least in our version.
Number of home runs over the same period. When we say period it could be any span of games - a season to date, the last seven days, or the last three years.
The number of team games in the period. This is not the same as the number of games the player appeared in. Consider a platoon player. Over the course of thirty games they might start in twelve games. In those twelve games they have 48 plate appearances which calculates to 4.0 plate appearances per game played. However, spread those 48 PA across the thirty team games and they would average 1.6/game. The latter frequency is much more accurate in terms of how often the player might play/homer in the future.
The number of games remaining against each opponent, or the number of game opportunities to consider.
The Initial Math
We then combine the first three components to get two ratios.
Plate Appearances per Team Game (PATG). As described above we need to know how many plate appearances a player may get (on average) in a single game.
Plate Appearances per Home Run (PAHR). We then take the total plate appearances and divide by the home run count. This gives us an idea of how often a player is hitting a home run when they play.
The Probability Math
Now we put these ratios together with the fourth component. This becomes a standard probability formula. In our example, let’s say a player has 100 PA and 5 HR in 25 team games. The player also has four games remaining against the Giants.
PATG = 100÷25 = 4.0 PA/team game
PAHR = 100÷5 = 20 PA/home run
Projected PA Opportunities against opponent (PAOAO) = 4 games * 4 PATG = 16 plate appearances
Probability of hitting a home run in any plate appearance (PROB) = 1 ÷ PAHR = 1 in 20 PA = .05
Probability of hitting at least one home run in the four game series = 1-((1-PROB) raised to the PAOAO) = 1-((1-.05)^16) = 1-(.95^16) = 1-.44 = .56 or 56%
Multiply that by 100 to get a Likelihood Score of 56 for that player against the Giants.
Now Against Everyone
We can calculate a player’s probability of joining the v30 Club by taking their Likelihood Scores against each team they need and multiplying them all together. Same player as above also has all 13 divisional games against the Brewers to go.
1-((1-.05)^(4 PATG*13 games)) = 93% probability to hit one against the Brewers this season.
.93 * .56 = .52 = A probability of 52% to join the v30 Club (assuming these are the only two teams the player needs)
When a player fails to hit a home run against a team and is no longer scheduled to play more, their Likelihood Score drops to zero because you’re multiplying by zero.
Pump up the Score
We generally see the higher Likelihood Scores from players that have more games per team remaining. It certainly helps to be an every day player who hits home runs with regularity, but each game where a player doesn’t hit a home run will more drastically reduce their chances over getting a bit colder with the home runs or suffering a short-term injury.
In the Club
You mainly see Likelihood Score around the v30 Club in Ledger Watch where the top ten players most likely to hit a home run in the upcoming series are listed. These are scores based on a three game series regardless of if the actually series is two, three, or four games. It pops up other places too.
Change it Up
While the v30 Club numbers generally focus on in-season and whole-season production, you could pick any time frame for a player to calculate their score. For example, based on the last two weeks of games, how likely is a player to hit one in the coming series. Or longer term, we can use something like Bill James’s Favorite Toy to predict production levels before a season even starts.
Likelihood Score is a handy tool to compare and contrast players. Now when you see the numbers, you know how we got them.