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# DISC+: Quantifying the game's most disciplined hitters

By quantifying discipline -- using a new metric called DISC+ -- we look at the most patient hitters since the inception of plate discipline stats in 2002. Meanwhile, we look at the historically great and horrendous DISC+ seasons of Marco Scutaro and Josh Hamilton.

Have you ever found yourself lost looking at a FanGraphs discipline tab -- you know the one with all the cool stats like: O-Contact%, Z-Contact%, O-Swing%, Z-Swing%? Sometimes, when looking at these metrics, I need context to further my understanding of their meaning in relation to the league averages.

So what if we could condense these metrics and manipulate them to create a metric that cohesively describes plate discipline? That way, we could have one easy and understandable metric to represent the player's patience at the plate.

To do that, we'd need to first define our definition of plate discipline so that we can express it through our use of these metrics:

Note: FanGraphs offers a nice tutorial page with the league averages and definitions here. If you're not already familiar with these stats, it can't hurt to look this over before reading on.

1. A player who does not swing at many pitches outside the zone -- but when he does, he makes contact at an above league average rate.
2. A player who makes lots of contact with pitches inside the zone -- at an above-league average contact to swing ratio.
3. A player who does not swing and miss at balls outside the strike zone.
4. A player who does not constantly fall behind in the count by swinging at the first pitch.
5. A player that endures long at bats -- fighting off pitches, no matter the count or situation.
With focus on these basic ideas, we can use the discipline metrics to yield just what we like.

For item #1 , we can cook up a contact per swing ratio -- outside the strike zone:

The proportion yielded is a product of the equation O-Contact% / O-Swing%.

Next, we want to do the same exact method for deriving item #2:

This yields something similar, which is contact ratio from swings on pitches inside the zone -- O-Contact% / O-Swing%.

For item #3, we want to measure the amount a player swings and misses at pitches outside the zone. This is measured by SwStr%*(1-Zone%).

And for principle item #4, we wish to find the amount a player falls behind after swinging on the first pitch. First pitch agression can be a precursor or a signal of a player being overly-aggressive at the plate. Aggression does not mean lesser results, but for the sake of quantifying discipline, we probably should include first pitch swinging. This is calculated by FStrike% * SwStr% .

Lastly, item #5 exemplifies patience. Pitches / PA as a measure of discipline -- because those who wait for their pitch are (typically) rewarded.

So here's the list of items that correlate to the various ideas outlined above:

• (O-CONTACT% / O-SWING%)
• (Z-CONTACT%/Z-SWING%)
• ((1-Zone%)*(SwStr%))
• (FStrike%*SwStr%)
• (Pitches/PA)
• ### DISC+ Formula

With all of the information above, we have our DISC+ formula ready to go:

((Z-Contact%/Z-Swing%) / (Z-Contact%(lg) / Z-Swing%(lg))*100+((O-Contact % / O-Swing%) / ( O-Contact%(lg) / O-Swing%(lg)) * 100 + ((SwStr(lg)*(1-Zone %(lg))/( SwStr*(1-Zone%) *50 + (SwStr(lg) * FStrike(lg)) / (SwStr * FStrike) * 50 + (Pitches/PA)/(Pitches(lg)/PA(lg))*100 = DISC score

Disc Score /4 = Disc+

Each metric is adjusted by the league average from the player's season. "(lg)" represents league average. Much like ERA+, any metric in which high results are considered bad are instead dividing the league average rather than being divided itself. Also, both metrics that included SwStr are weighted by half because they capture nearly the same thing.

All of this is added up and divided by 4 to yield DISC+. Much like wRC+, 100 is league average.

### Findings

Let's take all qualified hitter seasons since 2002 -- the beginning in which discipline stats where recorded. This gives us a population of 1684 individual player seasons. Using DISC+ we can capture who the mastered the art of discipline and patience at the plate. (Note: the mean DISC+ for this data-set was 108)

From 2002-2012 the best DISC+ seasons:

Num Season Player Team DISC+
1 2007 Luis Castillo - - - 254.37
2 2009 Luis Castillo Mets 244.46
3 2005 Luis Castillo Marlins 242.91
4 2012 Marco Scutaro - - - 236.84
5 2009 Marco Scutaro Blue Jays 228.04
6 2010 Marco Scutaro Red Sox 227.60
7 2006 Luis Castillo Twins 219.74
8 2005 David Eckstein Cardinals 213.26
9 2010 Juan Pierre White Sox 208.91
10 2005 Brian Giles Padres 205.65
11 2006 Brian Giles Padres 203.09
12 2011 Juan Pierre White Sox 201.32
13 2003 Luis Castillo Marlins 195.68
14 2006 Juan Pierre Cubs 193.37
15 2004 D'Angelo Jimenez Reds 191.57
16 2010 Brett Gardner Yankees 191.54
17 2004 Luis Castillo Marlins 191.47
18 2006 Scott Hatteberg Reds 190.82
19 2004 Juan Pierre Marlins 189.98
20 2011 Jamey Carroll Dodgers 189.63
21 2010 Jeff Keppinger Astros 187.88
22 2004 Jason Kendall Pirates 187.70
23 2003 Brian Roberts Orioles 187.13
24 2004 Brian Giles Padres 185.15
25 2007 Brian Giles Padres 184.94

Well, who would have thought Luis Castillo was the most disciplined guy on the face of the earth in 2007, at 254% better than league average. Then, Marco Scutaro's miraculous 2012 season appears at No. 4. This guy last year was locked in at the plate -- after coming to the Giants his Contact% was 96.9% and a SwStr% of 1.1%, and that is scary good. But as you can see Scutaro is accustomed to being patient at the plate, holding the No. 4, No. 5, and No. 6 spots -- so his discipline last season was no fluke but a real repeatable skill. Meanwhile, Scott Hatterberg checks in at No. 18. We find that Beane's OBP poster boy is backed up by DISC+ -- and he also did it for the Reds in 2006. Then we have other players we'd expect to find on a plate discipline leaderboard -- players like David Eckstein, Jamey Carroll, Jason Kendall, Brian Roberts, and the better Giles brother.

The bottom 25 brought no surprises, except the new \$125 million man:

Num Season Name Team DISC+
1 2012 Josh Hamilton Rangers 64.69
2 2011 Miguel Olivo Mariners 66.50
3 2007 Delmon Young Devil Rays 67.81
4 2006 Jeff Francoeur Braves 69.97
5 2004 Craig Wilson Pirates 70.17
6 2003 Jacque Jones Twins 71.11
7 2004 Jacque Jones Twins 72.04
8 2009 Mark Reynolds Diamondbacks 72.25
9 2007 Jeff Francoeur Braves 72.37
10 2002 Jacque Jones Twins 72.78
11 2002 Alfonso Soriano Yankees 72.95
12 2007 Alfonso Soriano Cubs 73.05
13 2012 Delmon Young Tigers 73.27
14 2003 Andruw Jones Braves 73.40
15 2003 Vinny Castilla Braves 73.67
16 2008 Delmon Young Twins 73.69
17 2003 Geoff Jenkins Brewers 73.79
18 2011 Josh Hamilton Rangers 73.93
19 2004 Corey Patterson Cubs 74.09
20 2009 Russell Branyan Mariners 74.42
21 2008 Josh Hamilton Rangers 74.55
22 2010 Vladimir Guerrero Rangers 74.56
23 2004 Torii Hunter Twins 74.60
24 2002 Vinny Castilla Braves 74.77
25 2005 Jacque Jones Twins 74.94

One thing is certain: Josh Hamilton is not one you would call disciplined. His aggressive approach is his trademark to success and -- while discipline does not necessarily mean good results -- Hamilton remains the poster boy for aggressive but successful.

We have Vladdy and Delmon Young here as well -- guys who love(d) to swing at everything. But for Hamilton this does not look like the group a player would like to find himself associated with. None of these guys aged well at all besides Torii Hunter and Vladimir Guerrero. Guys with "old-player skills" tend to age poorly and fall off a sudden cliff when their skills are no longer able to mask their horrendous approaches at the plate. So the question is: Can Hamilton continue his aggressive ways as he ages and losses bat-speed, or will he fall off a cliff like the rest of these guys have already? Certainly, Hamilton will have to make some disciplinary adjustments if he wants to age well and make Angel fans happy.

Maybe he should call up Luis Castillo for some pointers.