# How to determine the proper sets or subsets of outcomes when autocorrelating frequency of each from year to year

I am trying to determine whether a baseball player has the ability to influence the outcome of an "at bat" by calculating the correlation coefficient between the percentage of at bats which result in a given outcome from one year to the next, for each player-year in the sample.

For example, suppose that an at bat can result in one of the following outcomes:

• The player strikes out (SO)
• The player puts the ball "in play" by hitting a ground ball, a line drive, or some other type of batted ball (BIP)

Let's further suppose that the correlation coefficient between strikeouts per at bat (SO%) from one year to the next is found to be 0.85. Based on this, we can conclude that a player's ability to put the ball in play and avoid striking out is a "skill", of which different players have varying degrees.

### My question is, how can I take it a step further and determine whether players have the ability to influence which type of batted ball they put in play?

For example, suppose instead of starting with a set of two possible outcomes (strikeout or ball-in-play), we started with four:

• The player strikes out (SO)
• The player hits a ground ball (GB)
• The player hits a line drive (LD)
• The player hits a fly ball (FB)

The difficulty arises when we try to calculate the correlation coefficient between line drives per at bat (LD%). Since a LD is a subset of BIP, and BIP% is well correlated from year to year (recall we found r = 0.85), LD% will also be well correlated from year to year (although possibly to a lesser degree). In fact, we would expect to see some correlation even if the number of line drives is a totally "static" percentage of the number of balls in play and has nothing to do with a player's skill or propensity to bat "frozen ropes" around the ball park.

The only solution I can think of is to calculate r for LD per BIP instead of per at bat. However, the question now becomes: how do we know whether to treat line drives as a percentage of all balls in play? What if line drives are a random occurrence of "air" balls, any number of which can end up a fly ball or a line drive? Or what if we find that the correlation for LD per at bat is higher than that of SO%? Do we then treat LD as the independent outcome and calculate SO as a percentage of SO+GB+FB? That doesn't even make sense.

I guess what I'm trying to ask is, is there a systematic way to "tease out" which sets or subsets of outcomes are a result of player skill and, if so, how do we decide which of these sets to include in our correlation?

I'm not even sure if what I'm saying makes sense so please let me know if anyone has any questions.