Tuesday, January 10, 2012

Digging Deeper Into Effective Shooting

By Dan Shirley

A little while ago Mike introduced my effective shooting percentage metric which prompted me to finally take the initiative to crunch the numbers from last season. Well, it wasn't really crunching the numbers as much as copy and pasting the numbers from the NLL website into Excel and dragging formulas all around. While doing this I realized something that was pretty cool (I promise, it's interesting).

I know that baseball is not a favorable word around lacrosse blogs so I'll apologize up front for using it but that's what this post relates to. Most of you probably know what batting average is (hits divided by at bats) but not many of you might know what the Mendoza Line is. The Mendoza Line originated from teammates of a player named Mario Mendoza teasing other players about their batting average. Mendoza played for the Seattle Mariners, Pittsburgh Pirates, and Texas Rangers and was known for having a low batting average (0.215 over nine seasons). A player whose BA drops below 0.200 is said to be hitting below the Mendoza Line which means that their offensive production is so poor that their defensive skills, no matter how good, can not compensate for the lack of hits and they are not worth keeping in the lineup.


Now that we all know what the Mendoza line is, let's get visual (and a lot mathematical). The following graph is a normal probability plot. If data is completely in a straight line then the data is considered to be "normal" (fitting a bell curve where most data points are near the mean). The values on the X-axis is what we are measuring while the values on the Y-axis are the assumed probability of each point. In the following graph for batting averages we have 178 data points. The way that we set up the plot is by first ordering the data from smallest to largest. Each batting average data point becomes our x-value (independent) and our y-value (dependent) is measured off of the spot in the list (the formula is # divided by (1+ the number of points). For example, the lowest point's y-value is 1/(1+178) and the second lowest would be 2/(1+178) and so on up to the highest which is 178/(1+178)). The reasoning for this is that if the plot was perfectly normal, the median of the data values would have a 0.500 probability (the median is in between 89 and 90 because we have an even number of points. 89/(1+178)=0.497 and 90/(1+178)=0.503). Wow, sorry for getting all mathy on you there, I guess I just got off on a tangent. See what I did there? Anyways, your graphs:

As you can see, the data at the top of the chart is to the right of the line which means that batting averages are left skewed. Left, or "negative" skew is shown on the left picture below and represents there being very few low points.
Insert joke about a skewed sense of humor
The red zone to the left of the graph is representative of the batting averages below the Mendoza Line. The only player with 450+ at bats that hit below 0.200 was Adam Dunn of the Chicago White Sox who hit 0.159.

Enough baseball, this is a lacrosse blog after all, isn't it? Plotting the eS% of all players with a minimum of 50 total shots yielded the following results.


Pretty normal, eh? Most players are shooting around the mean (0.261) with very few efficiency deficient players. Here are the top ten and bottom ten from last year:

Top Ten Shooters
Player
eS%
Kasey Beirnes0.396
Jordan Hall0.378
Jarrett Davis0.373
Joel Dalgarno0.359
Ryan Benesch0.348
Jamie Rooney0.348
Scott Ranger0.339
Chad Culp0.323
Curtis Dickson       0.323
Jeff Shattler0.316

Bottom Ten Shooters
Player
eS%
Bill McGlone0.080
Gavin Prout0.147
Alexander-Kedoh Hill     0.172
Brendan Mundorf0.177
Brett Bucktooth0.183
Cliff Smith0.191
Sean Pollock0.192
Ryan Boyle0.198
Paul Rabil0.200
Brian Langtry0.203

Now that we have covered the basics of who the best and the worst shooters were in the league last year, we can bring this article full circle and discuss the Mendoza Line of the NLL. As you can see in the Effective Shooting Percentage graph above, the red area is now representative of the players who shoot below the Henderson Line. The Henderson Line is named after Tony Henderson who played for the Syracuse Smash, Philadelphia Wings, Arizona Sting, Minnesota Swarm, and the Buffalo Bandits.
What a fun loving guy
According to the website Swarm It Up, Henderson's highest shooting percentage was 0.248 and he had three seasons with a 0.000 shooting percentage (I would calculate eS% for you guys but shots on goal were not tracked back then). These miserable shooting performances led to Henderson being remembered solely for his (lack of) shooting prowess. 

If an offensive player falls below the Henderson Line they should start receiving less playing time until they can get out of their slump. This is because the team would be leaving valuable goals on the floor that they could have scored had an average player been playing instead. 

Hopefully through reading this article you have learned a little more about statistics and the value of a good shooter. It is my understanding that you will be seeing more of the eS% here on the NLL Blog and hopefully it will spread to other sites as well. 

For more lacrosse and general sports related banter, feel free to follow me on twitter (@danshirley) or catch my writing on either of the two blogs I write for (SportsMinds and InLaxWeTrust).

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