# When Ten Runs isn't a Win

January 8, 2009 2 Comments

*This is my first post at StatSpeak, though I’ve been a frequent commenter here for around two years. I’m a freshman business major at Cornell University, and a die-hard Yankees fan. Around thanksgiving, I started Poor Man’s Analyst, which is a stats-oriented Yankees blog. I’m looking forward to writing here…*

As hard as it may be to believe, Sandy Koufax and Roy Halladay have the same career ERA+. Koufax allowed 713 earned runs in his career, and a league average pitcher over the same time span in the same conditions would have allowed 935 runs. That’s 222 runs better than average for Koufax. Halladay has allowed 706 runs, versus a league average of 925 runs. That’s 219 runs. These feats were accomplished in a different amount of innings, but you’ll see in a minute that that’s not important.

The general rule of thumb analysts use today is that 10 runs equals one win. This works pretty well in today’s game, because the 10-to-1 conversion is tailored to the current run environment. So what this means is that when a player is said to be 30 runs above average, he is 3 wins above average as well. By this principle, ignoring everything else, Koufax would be +22 wins and Halladay also +22. It’s simple, it’s easy, it works.

But baseball wasn’t always played the way it is now. Runs were few and far between in the mid ’60s, when Koufax played much of his career, with teams scoring around four runs per game. Roy Halladay, on the other hand, has had to pitch in a much more “offensive” run environment, with the average AL team scoring around five runs per game. In low scoring games, each individual run takes on a greater role in the outcome of a game. In other words, one run scored (or saved) in a pitchers duel has a bigger impact on the outcome than it does in a slugfest. The graph below shows the pythagorean winning percentage for teams that score exactly 10 runs more than they allow, over a wide range of run environments. The x-axis represents the runs scored and runs allowed in a particular run environment, and the plotted points represent the expected winning percentage of a team which scores and allows that number of runs.

What this shows is that a difference of ten runs when runs are scarce is more valuable than ten runs when runs are plentiful. Just how much more valuable? In today’s 5 runs per game per team environment (10 total because, as you may know, two teams play in each game). The conversion of 10 runs per win works well. At a higher run environment, there is a higher conversion rate (it’s somewhat of a coincidence that 10 total runs per game is the same as the runs to wins converter). Below is a graph of the runs to wins conversions in a variety of run environments, with the runs per game per team in parenthesis:

As you can see, the conversion rate changes as the run environment changes. How does this affect the career numbers of Sandy Koufax and Roy Halladay? Above, we said that the two were worth about 22 wins above average for their respective careers in today’s run environment. Koufax was at +222 runs and Halladay at +219. Using the approximate runs to wins conversions shown in the second graph, we can recalculate the wins above average. Koufax is now 222 / 8.3 = 27 wins above average, and Halladay remains at 22 wins. So with two pitchers who save the same amount of runs, the pitcher in the lower run environment will provide more wins than the other.

When comparing players across different eras, it is extremely important to consider the run environment in which they played. In the end, we shouldn’t care about runs as much as we care about wins, and this only reinforces that.

Now that comments are working…

I used an exponent of 1.85 in the first graph for anyone wondering, not that it really matters.

Yankees fan? You’re fired!