Conditional Linear Weights

[bedir than average]

DETECT-O-VISION » Preview of Conditional Linear Weights and Super DNRA

Before we can start to understand how player statistics reflect real world value, we need to come up with a system for evaluating the events that make up a baseball game that comes as close as possible to crediting the players for the part of the event over which they have direct control. Let’s begin by discussing how best to define an event type.

When a ball is struck (by the batter), there are infinitely many possible shapes the flight path can take depending on weather conditions, the angle of impulse (the force of the bat propelling the ball), the initial contact velocity, and any spin on the ball. Statisticians have classified the trajectory types four ways. You’ve got grounders (the initial velocity of the ball is not directed upward to any degree and the ball touches the ground before leaving the infield), pop ups (the ball does not leave the sphere of influence of the infielders and spends a long time in the air), line drives (the ball does not reach very high into the air and does not touch the ground before leaving the infield) and flyballs (the ball is contacted upward and outward, leaving the infield). Two additional classes have been added to the above four by our previous database optimization, those being bunts (the batter intentionally uses his bat to deaden the ball, no swing is made) and foul flies (different from pop-ups and flyballs because they have zero chance of resulting in the batter reaching base and are not restricted to the infield or outfield).

and

DETECT-O-VISION » Open Question: Is Team Defense Worth More?

When BillJames created wn shares, one of the kludgy things he did to try to force the ratings to look "right" to him was to make team defense 52% of the picture and team offense 48%. Logically, it doesn't seem to fit. If you score as many as you allow, you're a .500 team, not a .490-whatever team. Offense and defense are essentially independent halves of the game, so why did James choose to make that correction?

He probably didn't know it, but he was most likely sensing two facts that can't be ignored.

I like his ideas, what I'm wondering is are they new? Who else is working on this kind of thing?

[nanwynnfan]

Rather than double-post, I responded on/to blog link.

[dlb]

If you score as many as you allow, you're a .500 team, not a .490-whatever team.

I don't think this is true. To win, you have to score at least one more than you allow for every game won. Therefore, this is only correct if every win and loss is by an equal number of runs.

That almost never happens. So, I'd imagine that the better defensive team has a better chance of winning more often, because they don't have to score as many runs to win.

[nanwynnfan]

The work I've done on defense covers the period 1901 through 2006 and attempts to evaluate the runs saved [or lost] each season, by individual position. Each position is covered, except pitchers; and that omission is only because I started out that way; and after 107 roster searches and spreadsheets, I wasn't inclined to go back an include pitchers.

As I originally set it up, my comps were against a Player X at each position, a journeyman at each position whose performance was input by me based on performance expectations during the season among players with considerable if not "full" playing time. The Player X concept appealed to me in that I did not have to get too specific, dealing with seasonal changes in averages, medians and means. The bottom line was to cover "generations" of play, realizing that quite often, one position [catcher] may undergo more generational changes than others.

Between 1990 and the present, setting Player X aside and referring to approximate average ratings, by position, I come up with:

C: .935
1B: .950
2B: .950
3B: .945
SS: .950
LF: .935
CF: .950
RF: .945

NOTE: Each position has its own inputs and weightings, so the above figures do not suggest similarity of positional demands on a player.

Arriving at individual player ratings against the above position "averages," I attempt to determine +/- defense runs. Over 107 seasons, a solid, above average [not outstanding] defender might save runs over a full schedule as follows:

C: 6.14
1B: 3.41
2B: 6.95
3B: 3.56
SS: 7.48
LF: 3.78
CF: 7.56
RF: 5.67

Team: 44.55 defense runs saved, solid defenders at each position.

Since the up-front presumption was full-time play, in actual practice the above level would be modified by players sharing play [and performance] at each position, which would knock the number down by almost 40% in actuality, so a solid defensive team would save a pitching staff 26.73 runs im a season.

A truly average team would come out at very nearly 0.00.

Looking at it to maximize defense, each season I looked at teams of all-stars at each position; and the cream of the crop results are volatile, with some bumper crop years adding up to 120-160 runs, most coming in around 30-80 runs saved.

Defensive play is the 500 pound gorilla sitting in the corner without whom games would never end as players ran the bases like ponies on a carousel. This, for me, argues the case that pitching must fairly be considered a subset of defense, merely because 75% of outs recorded continue to be on batted-balls-in play.

What shares of defense-side-of-the-ledger should be allocated to position players and pitching elements I don't pretend to know with any clarity; but I'd suggest that the 75% must be considered in the equation.

[nanwynnfan]

This topic of linear weights and balanced total player values, which factors in offensive or hitting contribution and defensive contribution, has been studied and debated for years.

However, for those inclined to be satisfied with simplicity rather than complexity, I offer the following, which is the result of noodling around with one ransom team from 2007, the Philadelphia Phillies.

The most simplistic of formulas I've seen for batting runs created is:

Total Bases * On-Base Percentage = Runs Created

It is not consistently exact; but it comes very close to much more complicated and involved formulas; and I present the key Philly players first, then the team totals as an example.

Taking the 9 Phils with playing time > 100 AB's and multiplying their individual TB * OB%, I arrived at batting runs created through June 12.

Player........RC

Rowand......41.65
Utley.........56.99
Rollins........46.98
Victorino....32.54
Howard......33.07
Dobbs........19.70
Burrell........28.95
Nunez........13.00
Helms........15.61

I then jumped directly to total bases by the entire Phils roster and multiplied that by the team OB%:

977 TB * .345 OB% = 337.

Actual Phil team runs = 334.

I'd suggest a total player value be taken as a two-step process, in which the formula above for hitting RC is applied, then divided by AB. [IF one is inclined to add BB into the Total Bases mix, one would have to go with plate appearances. I'd argue that OB% largely factors in RC credit to guys who draw a lot of BBs, without exaggerating the RC.

1. Go with either net RC, adjusted for playing time;

2. Add or subtract player defense runs, similarly net for playing time.

It's similar to the approach used by Baseball Encyclopedia; but the inputs of my calculations are arrived at differently and so vary somewhat with theirs.

Added to original post:

If we apply the above to the Phil major players, now adding Carlos Ruiz for catching:

1. The batting runs created (RC) are absolute, the product of TB * OB% is ongoing thru the total season; and any sanpshot thru X number of games = productio of RC;

2. The defense runs have to be related to total playing time at position (shared) so I reviewed the numbers as add adjusted defense runs to the offensive RC above to get a net player worth (in runs) to date:

Player........Batting RC........Adj. Def. Runs........YTD Runs Value

Rowand........ 41.65............ -2.68 ................... +38.97
Utley............56.99............ -1.61.................... +55.38
Rollins...........46.98............ -3.41.................... +43.57
Victorino.......32.54............ +13.63................... +46.17
Howard.........33.07............ -1.15................... +31.92
*Dobbs...........19.70............ ****.................... +19.70
Burrell...........28.95............ -10.52.................... +18.43
Nunez...........13.00............ 7.30.................... +20.30
Helms............15.61........... 1.00.................... +16.61
Ruiz..............18.59............ 8.54................... +27.13

It's a thought as to a reasonable approach at total position player value, which weighs in playing time and defense along with the headline grabbing long ball star contributions.

*Dobbs has played 1B, 2B, 3B, LF and RF as back-up, so I took the lazy way out instead of calculating each defensive position ... he appears to be defense neutral, weakest at 3B, pretty dependent otherwise. Just being a jack-of-all trades holds a value of versatility, all its own.

[bedir than average]

nan, can I put in a request for the same exercise with the Mariners?

[nanwynnfan]

bedir asked for a like study of the Seattle Mariners.

I just did this, taking data from the SI (Sports Illustrated) website, where up-to-date stats are posted for batting, pitching and fielding.

So others who may want to figure out a similar study for their own team[s] of interest, I'll explain each step as taken, with explanation, where such seems to be in order.

Because I've just posted player ratings on defense through this week, and it can be a time consuming exercise to update, I've taken the liberty of using my YTD defense numbers, as posted for the defense side of the ledger.

For those who may be new, Total Bases = singles *1 + doubles*2 + triples*3 + HR *4 ..... then multiply sum by OB%

Mariners, key players, by position:

Player........Position.....TB.......OB%....B~R.... %Pos. Inn..Adj.DR.....R~Value

Sexson..........1B.........84..... .294.....24.70... .851............1.15....25.85
Lopez............2B........92..... .332.....30.54.. .938............3.21....36.96
Beltre............3B.......100.... .310.....31.00.. .838............1.95....32.95
Betancourt.....SS........92.... .325.....29.90.. .956...........-0.67....29.23
Ibanez...........LF........97..... .340....32.98... .875...........-5.67...27.31
Suzuki...........CF.......121.... .394.....47.67.. .958...........21.57...69.54
Guillen...........RF........96.... .336.....32.26.. .876...........-9.29...22.97
Johima............C........99.... .355.....35.15.. .795........... 1.22...36.37

Team......................938.... .338....317.04; Actual Runs = 323

Note: The defense runs here vary from the defense runs on the YTD spreadsheets, because the runs are multiplied by the % of playing time at the position for each player under %PosInn colum above, as a three-place decimal.

As I said, I use the team stats on SI, up to date and comprehensive.