How To Graph Pennant Races

January 04, 2006

The pennant race graphs I created display each team's performance in terms of games above or below .500 (wins minus losses), not winning percentage, as is more often done. Graphing a pennant race by showing winning percentage is a terrible idea--don't do it!

Improper Emphasis

In particular, graphs of winning percentage:

  1. overemphasize movement early in the season and underemphasize movement late in the season
  2. overemphasize movement towards .500 and underemphasize movement away from .500

Both of these effects can be observed by looking at any full-season graph of winning percentage. The overemphasis of early season movement is seen in the wild fluctuation at the left-hand side which happens for every team that doesn't start the season with a long winning or losing streak. Underemphasis is visible in the way all teams level off as the season progresses. Over- and underemphasis of movement towards and away from .500 is also visible in the "italic" look of the lines.

In more precise terms, given a team that is above .500, the slope of the line representing a win will be greater in magnitude than the slope of a line representing a loss, (until the team falls below .500 where wins are "steeper" than losses). In other words, for a team that is above .500 a loss counts more than a win. Say the team has won 60 out of 100 games for a winning percentage of .600. A win would make them 61 out of 101 or .604, a gain of .004. A loss would make them 60 out of 101 or .594, a loss of .006. So at .600 a loss loses significantly (50%) more than a win wins.

1990 AL West, Winning Percentage
Note the fluctuation at left followed by leveling off.

1990 AL West, Games From .500
No crazy fluctuations, equal emphasis of wins and losses at all times.

Streak Distortion

A winning percentage graph distorts winning and losing streaks. For example, a team at .750 will have to maintain an impressive winning streak (3 of every 4 games) to stay there, and yet their performance will appear on the graph as a straight line. While it is true that their performance has "leveled off" relative to their prior performance, if we are interested in studying streaks this is probably not the graph we want to see. Also, any streak where a team plays exactly .500 ball will be horizontal only if they started at .500. More useful is a graph which shows any .500 streak as a horizontal line.

2001 AL West, Winning Percentage
Seattle's record-tying season (116 wins) appears to trail off...a great start and then kind of ho-hum.

2001 AL West, Games From .500
Here Seattle's feat looks more like it was: strong and steady (lost just 5 series, swept only once).

Aesthetic Concerns

Because of the great fluctuation at the start of the season (necessarily -1 to +1) the range of the winning percentage graph must be much wider than we would like. For this reason authors often cut off the first few games (with the widest fluctuation) so the graph does not need to be so tall. This fixes the problem but is hardly ideal. One shouldn't sacrifice data for looks, and the type of plot chosen should show the data efficiently.

Secondly, William Cleveland has stated that plots are easiest to compare when the absolute values of their slopes are close to 45 degrees. This makes good sense intuitively (avoiding "stretched" graphs) and while neither type of graph will ever be perfect in this regard, the winning percentage graph cannot even be close because by its nature the slopes at the left-hand side approach infinity and the slopes at the right-hand side approach zero. The games from .500 graph should be nearer this ideal, given a reasonable choice of scaling.

Case Study: 1951 NL

The 1951 National League pennant race is one of baseball's most often-examined. The winning percentage plots for the New York Giants and the Brooklyn Dodgers look like this:

1951 National League pennant race by winning percentage.

Here we see the typical fluctuation at the start and leveling off as the season progresses. New York's April-May winning streak (17 of 25, .680) appears more significant than the better August-September streak (37 of 44, .841). From this graph one could easily get the impression that while New York got off to a bad start, they quickly recovered by mid-May and kept pace with the Dodgers until mid-August when they gradually started to catch up. But this is far from what actually happened, and my preferred graph tells a very different story:

1951 National League pennant race by games from .500.

Here we see the Giants' various streaks in better relation to each other as well as some Dodger streaks we didn't notice before. The Giants' late Spring streak is clearly inferior in both length and magnitude to what they started three months later. We also see that they were significantly farther behind the Dodgers in mid-August (13 games) than they had been May 23 (4.5 games), the teams' trajectories being nowhere near parallel in July and early August as the first graph suggests. (If the teams were parallel at any time it was May and June.) Brooklyn's plot here reveals a significant winning streak starting June 30 (31 of 42, .738) and ending just after New York's streak begins. (In fact it ends precisely when they are swept by New York in a three-game series August 14-16.)

In any case, the point here is not to analyze the 1951 pennant race but to show that the games from .500 graph should be the preferred tool for those wishing to do so. The winning percentage graph hides the streaks and generally distorts the data and I submit that it is the incorrect graph to use for this purpose.