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A Brief History of Run Estimation: Although all of these formulas are intuitive in that they are based on a model of how the game is played, one of the differences between RC and both BR and its variant ERP is that RC is a non-linear formula. In other words, RC essentially says that the whole is greater than the sum of the parts in reference to offensive events while BR and ERP use a linear approach that assign weights to the various offensive events.

In this installment of the series I'll look at another intuitive but non-linear run estimation formula called Base Runs BsR.

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History Base Runs BsR was developed by David Smyth in the early s and since then much discussion of it has occurred on the Strategy and Sabermetrics forum. Like RC and BR this formula is based on team scoring, which is then applied to individuals. The basic formula for BsR is: To many, this is the strength of BsR in that it capture a more intuitive and accurate model of how runs are created.

Like RC the formula is then further broken down into components like so: So you can see that the ScoreRate is defined as the advancement value divided by the advancement plus the outs consumed. I've seen several versions of the B factor including: Although this seems intuitively wrong, this is because homeruns are a special case considered in the D factor.

This value is historically around. This is used in the same way as the varying value for outs in the Batting Runs formula to gauge it for a league. The full formula using the first B factor above is then: Team A hits 97 homeruns and makes three outs while team B draws walks and makes no outs.

In the case of Team A common sense says the team will score 97 runs. In the case of team B common sense says they'll score 97 runs and leave the bases loaded. But of course major league baseball is not played at the extremes.

This is why all three formulas can be relied upon to approximate the nearly straight line relationship of offensive events to runs in the frequency ranges for events in major league baseball. All three however, were in the range of A challenge for BsR is that, like RC, BsR is in essence a run estimator for teams and so when applied to the statistics of an individual the formula automatically forces interaction of the offensive events with themselves.

However, a player never creates runs in the context of a team of clones and so the result is that BsR over estimate runs for players with high slugging and on base percentages.

However, it doesn't do so as much as RC since homeruns are isolated. In order to negate this effect the RC formula now includes contextualizing a player's individual statistics with eight mythical average players see my article on RC for the details.

The same approach can be used with BsR as Heipp shows in this article. A second challenge for BsR is to more accurately approximate the ScoreRate. Of course, one way of coming up with empirical weights for the offensive events is to calculate the ScoreRate for entire leagues using the known number of baserunners, outs, and runs and then run a regression on the offensive events.

That may in fact be what Smyth did although I don't know.Search the world's most comprehensive index of full-text books. My library. Epic has released a bunch of free content for Unreal already. There's some cool stuff in the Learn tab of the launcher you can download.

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