One way to determine a hitters patience is to look at the average number of pitches they see per plate appearance (PA). I wondered if this stat would remain consistent year over year, or at least to what degree would it.
The first thing to do is grab the data showing hitter PA and # of pitches seen.
Fangraphs data from 2010-now
Second simply graph the data and note the trend / Rsq
You can see from this dataset that this statistic is in fact fairly predictive of future performance.
So the next question on your mind is likely:
"How does this rate translate into production?"
Well lets try to do that too. Easy enough, we'll just graph the data again. But not year over year this time, instead let's compare P/PA as the independent variable to a dependent WRC+ (this should give a good general idea of how effective a hitter is)
Using that same dataset (removing data points where 200 pitches were not seen that year) we get:
So this suggests that there is a slight correlation between these variables; however, that in reality it's not all too suggestive at all.
This should be sort of intuitive. The idea that different hitters have entirely different approaches and that those different approaches can work. So not everybody needs to be aggressive to succeed; likewise, not everybody needs to be cautious. It can work either way, but when in doubt, caution (i.e. seeing more pitches per PA) does correlate slightly to increased production.
While single season P/PA to WRC+ values seemed to not correlate extremely well, what about player averages over periods of time. So instead of just looking at Robbie Cano's 2013 year, what if we look at Robbie Cano's career and compare that to other players.
So i again took that dataset and filtered it down one way, excluding players who never had a season from 2010-now where they saw greater than 200 pitches. This largely excluded pitchers, and a few extreme role players or single season call ups who never made it. So with those players excluded, i setup a table
This table ends up showing something dramatically different. There is a very clear correlation over time for players who have a higher P/PA stat to their WRC+.
Conclusion:
This appears to show that while there may be players out there who can succeed with an aggressive plate approach, it likely still benefits players to be patient. Since the year to year stat is fairly predictive (46% rsq) it's a reasonable thing to evaluate early on and see how players stack up.
