Converting Runs to Wins

Wins and losses are the currency of baseball. They’re the only things that count in the standings, so we want to develop statistics and metrics that align with that reality. Teams are trying to win. That’s a rather obvious statement, but you have to build your framework for evaluating players from the ground up. You win games by scoring more runs than your opponent, meaning that run scoring and prevention are the building blocks of wins and losses. So when we say we care about winning and losing, we really care about scoring and preventing runs and the things players do toward those ends.

As you’ve likely seen in our other Library entries, most of own individual statistics are based on runs. For example, we derived wOBA based on the relative run scoring value of different offensive events. As a result, that means we can take a player’s wOBA and their PA to determine their batting runs (after park and league adjustments). We also have base running runs, fielding runs, positional runs, replacement runs, and league adjustment runs. In other words, we have lots of player stats based on runs.

But thinking in terms of wins and losses is often conceptually easier for most people. Adding +3 wins to a team’s total is a little easier to grasp than adding 28 runs, for example. There’s nothing inherently better about using Wins Above Replacement (WAR) rather than Runs Above Replacement (RAR), but WAR seems to be more popular. For that reason, we need a way to convert RAR into WAR. In other words, we need something that converts runs to wins.

Runs per win (RPW) is the value that allows us to convert runs to wins. It is based on the run environment and is usually between 9 and 10. You’ve probably heard the rule of thumb that 10 runs equals one win, but the actual ratio depends on run scoring in the league that year. The process reflects the average number of runs a team needs to score in order to add one win to their total. For example, if an 81-81 team has a run differential of zero, what would you expect the run differential to be for a team that is 82-80? That’s runs per win.

Calculation:

There are a variety of ways to arrive at RPW. The most famous is likely Patriot’s Pythagpat, which is is win estimator we use elsewhere on the site. However, for our RPW number we use a simplified version developed by Tom Tango that winds up matching Pythagpat give or take about .02 runs per win in any given year. Our formula looks like this:

RPW = 9*(MLB Runs Scored / MLB Innings Pitched)*1.5 + 3

In other words, this is the league’s runs scored per nine innings times 1.5, plus three. You will wind up with essentially an identical number as if you use the Pythagpat formula and matches the real life runs per win relationship just as well. You can find the values for each year here.

Keep in mind, this is a league wide value that we use for our position player WAR. Pitchers influence their run environment more directly, so they have their own individual calculations based on a variety of factors. Better pitchers will have lower RPW values because if you allow fewer runs in your starts, it’s easier for your team to win. Individual hitters don’t have the same ability to alter their environment, so we use the same value for all of them.