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— Where BTF's Members Investigate the Grand Old Game
Wednesday, June 04, 2003
Super Linear Weights, 2000-2002
Revised methodology with complete 3-year results.
Several years ago I introduced a new series of metrics for evaluating the complete performance of a player, called Super Linear Weights. I have once again revised some of the methodologies, most notably defensive linear weights, or Ultimate Zone Rating (UZR). For a complete discussion of UZR, see my two-part series.
Like traditional offensive linear weights (lwts), each of the categories is expressed as a number of runs above (plus) or below (minus) the league average, which is naturally defined as zero. For example, a player who had a defensive lwts of -5 was a below average fielder. In fact, he allowed 5 more theoretical runs to score than an average defender at that position. By convention, regardless of the category, minus is always bad and plus is always good. Because each category uses the same "currency" (runs above or below average), all of the categories can be summed to produce each player?s total linear weights, or Super Linear Weights (SLWTS). A player?s SLWTS tells us exactly how many runs above or below average he is "worth" to an average team under average conditions.
Super Linear Weights is only "better" than traditional lwts, BaseRuns, Runs Created, or other such offensive metrics, because it includes defense, baserunning, and a few other odds and ends. This makes it a much better metric or series of metrics for evaluating total player value. There are many players whose good or great offensive performance are mitigated or in some cases completely negated by their poor defensive and baserunning skills. As well, great defensive value can turn a good offensive player into a great overall player, poor defense can turn an otherwise marginal player into a terrible player, etc. The permutations are unlimited and are in fact critical in terms of evaluating and measuring total player value.
2000-2002 Super Linear Weights Results
Here are the Super Linear Weights categories and their brief explanations. For a more detailed explanation of each category, see the links to previous Superlwts articles below:
In order to fairly compare players across the defensive spectrum, it is important to use position-adjusted Superlwts for two reasons. One, it is assumed that a player at a more demanding defensive position has better defensive skills than a player at a less demanding defensive position, therefore less offense is "tolerated" from that player. Two, a player?s run values in all categories other than the defensive ones are relative to a league average player at all positions. A player?s run values in the defensive categories are relative to an average player at that position, so it would be adding apples and oranges to combine all categories without doing a positional adjustment.
Keep in mind that a player?s Superlwts, like any metric or stat, is only a sample of a his performance, and thus represents only the first step in estimating a player?s theoretical value to a hypothetical team (his "talent") or projecting his future performance. The other step is regression. Regression is a function of, among other things, and most importantly, the size of the performance sample, which in this case, is the number of a player?s PA?s or "games played". If one wanted to compare the theoretical value of two players using their respective Superlwts results, either both players would have to have approximately the same number of games played (or PA?s), or if not, one would have to regress one or both player?s Superlwts, and then compare them. For example, if Player A had a Superlwts value of +8 "per 162" in 900 PA and Player B had a Superlwts of +10 "per 162" in 830 PA, one could say that player B was likely "better" (of more value) than player A, all other things being equal or unknown. However, if Player B was +10 per 162 in only 300 PA, then one would have to either first regress Player B?s Superlwts to make it "equivalent to" Player A?s 900 PA sample, or regress both Player A and Player B?s Superlwts in order to make them equivalent to each other. In either case, it is now likely that Player A is the better player (Player A?s +8 in 900 PA might get regressed to +6 and player B?s +10 might get regressed to +4).
The reason for this is that in order to compare players with different numbers of games played or PA?s, in terms of deciding which one is likely "better", we might first estimate their true Superlwts (true "talent") from their sample Superlwts. In order to do this, as with any other sample stat, we must regress the sample result towards the mean. If we know nothing else about a player but his position-adjusted Superlwts results, that mean is usually going to be zero.
The charts at the links below contain the results of the 2000-2002 seasons, both separate and combined.
SLWTS 2000, part 2
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