What does the Offense Ratio Diagram tell you

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What does the Offense Ratio Diagram tell you?

P. Adel, July, 1998

The power average that is used on the Offense Ratio Diagram is different from slugging average. Slugging average is total bases (TB) divided by at-bats (AB). Total bases is the sum of each hit times the number of bases collected, i.e., TB = (singles x 1) + (doubles x 2) + (triples x 3) + (homeruns x 4). The power average is the sum of total bases and walks (TB+BB) divided by hits (H). The batting average is of course hits divided by at-bats.

Most baseball enthusiasts are accustomed to looking at batting statistics in terms of at-bats (batting average, slugging average), and pitching statistics in terms of games (earned run average is the average number of runs that a pitcher would allow in a 9 inning game). However, the use of the term average can be applied to any ratio of one number to another. Hence the power average is the average number of bases (total bases plus walks) a batter collects per hit.

People always ask why walks are included in the power average. There are two reasons:

It makes the equations work out on the diagram.
Offense Ratio calculated this way has a strong correlation to runs per game, which implies that it is correct (or at least it is defensible).

When I started looking at baseball statistics carefully, I decided that what I really wanted to know about a batter is how many runs does he produce with his bat. Runs win games. Therefore I want to reduce the statistics to the point that I can estimate run production on the basis of one batter swinging at one pitch.

Imagine for a moment that the bases are loaded every time a player comes to bat. One run scores every time the batter draws a walk. If the batter hits a single, at least one run scores, maybe two, rarely three runs score. If the batter hits a double, at least two runs score, maybe three. If the batter hits a triple, three runs score. If he hits a home run (a grand slam because we assumed the bases are loaded every time), four runs score.

From this we find that the number of runs produced by a hit is proportional to the number of bases collected with the hit, with a maximum of four runs for a home run, and at a minimum, every walk produces exactly one run.

Power is the term given to how many bases are collected per hit. Someone that hits a lot of homeruns is said to have a lot of power. Someone that hits a lot of singles and few home runs is not considered to be a power hitter. It is a recognized phenomenon however, that a batter who gets a lot of home runs, or a lot of singles compared to other batters, also gets more walks. The long ball hitter will be intentionally walked more frequently. The frequent hitter may also get more intentional walks, but also tends to be able to discern good pitches from bad ones, avoid swinging at bad pitches, and in ignoring bad pitches will walk more frequently.

Getting back to our bases loaded scenario, consider further that sometimes our batter strikes out. Or he may foul out, fly out, or ground out. He may also be hit by a pitch but we are going to ignore this because it doesn’t happen often enough to have an effect on the statistical estimation of runs. The number of runs scored under our assumed bases loaded scenario will vary somewhat depending on the type of out. No runs score on a strikeout (unless the catcher loses the ball on the third strike and a run scores on an error, which again occurs rarely enough not to effect the statistical estimation runs). No runs score on a foul out unless a runner steals home. One and sometimes more than one run may score on a fly out or a ground out. However, the point I am driving at in a roundabout way is that regardless of how many bases per hit our batter averages, if he does not often get a hit, in the long run he wont drive in as many runs as someone who gets the same average number of bases per hit but hits more frequently. A batter who has a home run with every hit won’t produce a lot of runs if he gets a hit once in a blue moon.

Now assuming the bases are always empty, what has been described above still applies. The ability to reach base frequently, translates into scoring more frequently. Getting more doubles and triples puts the batter in a better position to score a run on a hit by a subsequent batter. A home run with the bases empty still scores one run every time.

Now we can see that power (total bases plus walks per hit) is a measure of run production, and by itself, power alone does not equate to runs. It quickly becomes clear that the player who will have the greatest run production is the player who hits with power, getting the most bases (total bases plus walks) per hit, and gets a hit more frequently and an out less frequently. To say it another way:

RUN PRODUCTION IS PROPORTIONAL TO THE RATIO OF
BASES PER OUT

Here is why the equations work out on the diagram. Offense Ratio (OR) is calculated with only four batting statistics: hits, walks, at-bats and total bases. The SIMPLE equation for Offense Ratio is:

Offense Ratio (OR) = (TB + BB) / (AB - H)

Recall that all at-bats result in either a hit or an out (strikeout, foul-out, fly-out, and ground out). That means subtracting hits from at-bats leaves outs. Using this relationship, we arrive at an even MORE SIMPLE equation:

Offense Ratio (OR) = BASES / OUTS

This equation is the numerical equivalent of the statement in the box above. As it turns out, it is possible to express this equation in terms of our two averages, batting and power. By making the appropriate substitutions and reorganizing the equation, we arrive at the complex form of the equation for the Offense Ratio Diagram:

Offense Ratio = (Power Average x Batting Average) / (1 - Batting Average) Offense Ratio can also be expressed exactly in terms of batting average, slugging average and on-base average. Click here to see the form of the equation.

The significance of this equation is that the Offense Ratio, which is proportional to run production, can now be presented on a graph with batting average as one axis and power average as the other axis. This means that we don’t have to mess around with equations and calculators anymore.

The Offense Ratio Diagram shows the batter’s hitting frequency (batting average), hitting power (power average), and potential for run production (offense ratio or bases per out). This allows for rapid visual comparisons of one batter with another, and is particularly valuable for comparing batters with different styles (great power vs. great average) in terms of their potential for run production.

It is now possible to address the question of whom you would choose for your dream team, Mickey Mantle or Joe DiMaggio. I can sense the blood pressure rising in the average red-blooded American baseball enthusiast as he reads this. It has long been considered either foolishness or sacrilege to choose between Mantle and DiMaggio, particularly on the basis of SIMPLE batting statistics. Without taking into consideration fielding ability, base stealing ability, or intangible factors such as leadership qualities, I will select Mickey Mantle over Joe DiMaggio for my dream team batting lineup because:

Mantle's career Offense Ratio is 1.098 bases per out (.298 BA,.557 SLG,1733 BB,1710 SO)

DiMaggio's career Offense Ratio is 1.028 bases per out (.325 BA,.579 SLG,790 BB,369 SO)

To accept this conclusion, one has to accept that Mantle’s greater number of walks are worth more in runs produced than DiMaggio’s higher batting average and slugging average. Rather than getting caught up in the details of that debate, I will show in the next section that the Offense Ratio correlates well enough with runs per game on a whole-league basis that the question of the relative value of walks can be left to a later discussion (Or, click here to skip straight to the discussion of walk value).

NEXT Accuracy of OR

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