The Hidden Game of Baseball: Capitulo 4

Linear Weights assigns run values to the various offensive events.

It’s back to back basics, foundation is the same underlying the Rickey formula and most of the new statistics since: that wins and losses are what game is about; that wins and losses are proportional in some way to runs scored and runs allowed; and that runs in turn are proportional to the events which go into their making.

With Linear Weights, these events are expressed not in the familiar yet deceptive ratios( base hits to at bats, wins to decisions, etc ) but in runs themselves, the runs contributed( batting, stealing ) or saved ( pitching, fielding). Normalizing factors(to league average) built into the formulas for all but base stealing, where league average is not a shaping force, allow us to compute the number of runs provided last year in excess of those an average hitter might have produced in an equivalent number of plate appearances. And, by adjusting for home park influences, the Linear Weights comparison may be extended to how many runs accounted for beyond what an average player might have produced in the same number of at bats had he too played half his games in a specific stadium.

Having determined the number of runs required to transform a loss to a win in the final standings we can convert a player’s Linear Weights record, expressed in runs, to the number of wins above average he alone contributed. Last, by reviewing the contributions of all the team’s batters, pitchers, fielders, and base stealers, we may establish a solid assessment of that team’s strengths and weaknesses for the upcoming season whether, for example, it figures to be a pennant contender without any personnel changes, or whether it will have to import some new bodies just to stand in place.

We should recognize that a substantial part of the run value of any non-out is that it brings another man to the plate. This additional batter also has a chance of reaching base and thus bringing another man to the plate, as do the batters to follow. The indirect run potential of these batters cannot be ignored.

The values of Linear weights are denominated in terms of the number of runs and RBI’s each event produced. The run values in Linear Weights in the Linear Weights identify the batters real contribution. 

Stolen Bases and Caught Stealing are not part of the Linear Weights formula because of their situation-dependent, elective nature: Attempts are apt to occur more frequently in close games, where they would be worth more than if they were distributed randomly the way an event like a single or a home run would be.

The Formula

Just as these run values change marginally with changing conditions of play, they differ slightly up and down the batting order ( a home run is not worth as much to the leadoff hitter as it is to the fifth-place batter; a walk is worth more for the man batting second than for the batting eighth); however, these differences have been averaged out in the figures above. 

The events not included in the formula that you might have thought to see are sacrifices, sacrifice hits, grounded into double plays, and reached on error. The sacrifice has essentially canceling values. trading an out for an advanced base which, often as not, leaves the team in a situation with poorer run potential than it had before the sacrifice (more on this in Chapter 8). 

The sacrifice fly has dubious run value because it is entirely dependent upon a situation not under the batter’s control: While a single or a walk always has a potential run value, a long fly does not unless a man happens to be poised at third base (Whether it is achieved by accident or design is open to question, as well; but that is beside the question getting hit by a pitch is not a product of intent, either).

Last, the grounded into double play is to a tar greater extent a function of one’s place in the batting order than it is of poor speed or failure in the clutch, and thus it does not find a home in a formula applicable to all batters.

The Linear Weights formula can be condensed by eliminating the components for steals, caught stealing and outs on base.

The Linear Weights formula for batters may be long, even in its condensed form, but it calls for only addition, subtraction, and multiplication and thus is as simple as in slugging percentage, whose incorrect weights (1. 2, 3, and 4) it revises and expands upon.  

Each event has a value and a frequency, just as in sIugging percentage, yet as in no batting statistic you have ever seen,| outs are treated as offensive events with a run value of their own (albeit a negative one), a truth so obvious it somehow escaped notice, Just as the run potential for a team in a given half inning is boosted by a man reaching base, it is diminished by a man being retired; not only has he failed to change the situation on the bases but he has deprived his team of the services of a man further down the order who might have come up in this half inning, either with men on base and/or with scores already in.

What Linear Weights does is to take every offensive event and treat it in terms of its impáct upon the team-an average team, so that a man does not benefit in his individual record. The relationship of individual performance to team play is stated poorly or not at all in conventional baseball statistics, in Linear Weights it is crystal clear: The linear progression, the sum of the various offensive events, when weighted by their accurately predicted run values, will total the runs contributed by that batter.

Linear Weights has a “shadow stat”: OPS. While OPS is not expressed in runs and thus lacks the philosophical appeal of Linear Weights, it consists of two measures, OBP and SLG, which are somewhat better than batting average. OBP as previously noted brings the BB and HBP in from the statistical cold but treats all bases alike. SLG weights the hits according to the bases gained, but it does not take into account any base gained without a hit. These two one-legged men, when joined together, make for a very sturdy tandem. The weaknesses of the one are almost exactly compensated by the strengths of the other.

However, as an average or ratio, OPS measures the rate of batting success(efficiency), while Lineare Weights measures the amount of success. Clearly, longevity, or amount of production, is no less important than the rate of production. Linear Weights, which has a built-in normalizing factor in its variably weighed out.

Runs and Wins

Because OPS is not expressed in runs, it less versatile than Linear Weights. For just as runs are proportional to the events which form them, so are they proportional to wins and losses. Bill James, in the Baseball Abstract, developed winning percentage equal as R^2 / ( R^2 / RA^2 ).

What does Wins have to do with Linear Weights? Remembering that Linear Weights is expressed is runs, the conversion from a batter’s Linear Weights to his wins is a snap.

Just as Linear Weights can show an above-average hitter to have contributed beyond average runs and thus wins to his team, it will also show below-average hitters to have negative run marks, which result whenever the runs loss through outs exceeded the runs gained through times reached base.

Base Stealing Runs

It takes a fabulous stealing performance to produce as much as one extra win for the team. The fact is that while the gain from the stolen base is entirely visible ( an extra base which may be followed by a hit that would otherwise not have produced a run) the cost of the caught stealing is entirely invisible, or conjectural, except with the aid of statistics.

What Linear Weights indicates is that, on balance, not on a specific-case basis, the stolen base is at best a dubious method of increasing a team’s run production.

Linear Weights in Practice

Having formulas for pitching, fielding, baserunning, and batting we can assess the run scoring contribution of every individual who has ever played the game, and thus the number of wins he has contributed in a given season or over his career. 

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