By Roger Weber

 

Comparing numbers on different scales like fielding percentages and home runs is difficult using just the raw numbers. To find a way of fairly and equally comparing the two, you can use z-scores. Z-scores are measures of standard deviations above or below an average value. One standard deviation over average is a z-score of 1. One and a half standard deviations below average is a z-score of -1.25. This makes it easier to see if a player's home run total or fielding percentage is best compared to the rest of the league.

 

Often in doing comparisons statisticians use a sum of z-scores. To measure players they might find a z-score for hitting, fielding and speed. Then they add the z-scores to find a total. This method should give fairly accurate rankings of players. For teams they might add all the players' z-score totals.

 

But what if a player is an excellent hitter but has no fielding ability? Is he as valuable as a player who has a hitting z-score 15% lower but whose fielding z-score is 45% higher? (Remember that hitting is about three times as important to a team's success as fielding) Using cumulative z-scores these players are equal but a player who can't field, unless he is a designated hitter, will never be elevated to the major leagues. The point is that a player with a good five value in each of baseball's tools is more valuable than a player that is great in one area but weak in others.

 

The same goes for teams. A batting order with one player who gets a double every time he comes up and eight players who strike out every time up is certain to produce fewer runs than another team with nine players with slugging percentages of .225, despite the fact that the z-score sums are almost equal.

 

While there is not usually a huge discrepancy, a team that is good in all elements – pitching, hitting, fielding, base-running and any other intangible elements – is usually better than a team that is remarkable in one and weak in the others. This makes it difficult to compare players, far more difficult than simply adding z-scores. With teams, you can bypass this issue by using team statistics like win percentage.