sim_age_curve: Simulate the Aging Curve of a Focus Player
In guytuori/simScores: Similarity Scores for Baseball Players

Description Usage Arguments Details Value References See Also Examples

Models the aging curve for a focus player based on his performance, and the performance of his comparables. Then simulates the fitted curve so that it can be plotted by plot_age_curve.

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sim_age_curve(fp, comps, dat, ages_pred, type = c("bat", "pit"),
  wt_power = 30, ncomps = 10, nsim = 500, simplify = FALSE,
  model_ages = c(18, 49), stat = c("woba", "iso", "k", "bb", "fip", "hr"))

`fp`	name of focus player. Must be in the format "Last; First M."
`comps`	object obtained from `age_comps`.
`dat`	statistics for comps. Obtained from `sum_stats`.
`ages_pred`	numeric of length two in the form (lower, upper). The ages to simulate the focus players aging curve.
`type`	character. Whether these are batting or pitching data. Defaults to batting.
`wt_power`	A single number which specifies the weights to use when fitting the model. The weights are based off the similarity score for each player in the `comps` object. Weights are calculated as (score / 1000) ^ wt_power so setting `wt_power = 0` weights all players equally.
`ncomps`	The number of comparable players to used when modelling the focus player's aging curve. Defaults to 10. The focus player is also used in the model, so the total number of unique players included in the model is `ncomps` + 1.
`nsim`	The number of simulations to run. Defaults to 500.
`simplify`	boolean. Whether to use a simpler model where only the intercept varies by player (TRUE) or a more complex model where the all terms vary by player (FALSE). Defaults to FALSE.
`model_ages`	numeric of length two. The range of ages to use when fitting the model (inclusive). For example, it may not make sense to use information from Albert Pujols's age 20 season because he is currently 34. Defaults to 18-49 (so basically everything is included.
`stat`	character of length one. The statistic for which the focus player's aging curve should be simulated. If `type = "bat"`, must be one of `woba, iso, k, bb`. If `type = "pit"`, must be one of `k, bb, fip, hr`. Formulas for wOBA and FIP are obtained from the Fangraphs Library. The formula for FIP has been modified for simplicity. Instead of calculating the constant, the value of 3.2 is used.

This function calculates the statistic of interest (wOBA, ISO, ...) for the focus player and the top ncomps comparables (ranked by similarity score) for each age specified by model_ages. It then decomposes the ages for each observation into orthogonal polynomials of degree 2 using the poly function.

It then fits a multilevel model where age is used to explain the specified statistics. Because age has been decomposed into an orthogonal polynomial of degree 2, this is a quadratic model for aging. This model was inspired by a paper by Jim Albert; see the References section for details. If simplify = FALSE, then the intercept, linear, and quadratic terms are modeled as varying by player. If simplify = TRUE, then only the intercept varies by player. For more details on this model, see the "Calculating Aging Curves" vignette by typing vignette("aging-curve") in R.

Finally, simulations of the fixed effects part of the model are drawn using the sim function from the arm package.

A list of length four. The first three elements are the data for the focus player, the estimated aging trend, and the simulated aging trends. These are used in plot_age_curve. The fourth element, warnings, is boolean telling whether the lmer function threw any warnings when fitting the model. If warnings is TRUE, the model should be refit before plotting.

For FIP formula: FIP. FanGraphs Glossary. Fangraphs. http://www.fangraphs.com/library/pitching/fip/. Accessed 11/24/2014.

For wOBA formula: wOBA. FanGraphs Glossary. Fangraphs. http://www.fangraphs.com/library/offense/woba/. Accessed 11/24/2014.

For aging curve model: Albert, Jim. "Smoothing career trajectories of baseball hitters." Manuscript, Bowling Green State University (2002).

For multilevel models and simulating coefficients: Andrew Gelman and Yu-Sung Su (2014). arm: Data Analysis Using Regression and Multilevel/Hierarchical Models. R package version 1.7-07. http://CRAN.R-project.org/package=arm

lme4 for the function used to fit multilevel models, sim for simulating regression coeffeicients from a fitted model.

load("H:/simScoresApp/b-comparison-app/bat_simscore_data.RData")
wts <- c(position = .05, pa = .9, bb.perc = .66, k.perc = .84, iso = .84, babip = .23, obp = .92)
f <- age_comps("Brown; Domonic L.", age_grp, wts)
x <- sim_age_curve("Brown; Domonic L.", f, age_grp, c(21:30),
                   type = "bat", stat = "woba")
## records if lmer throws a warning
x$warnings # suggests a problem
x1 <- sim_age_curve("Brown; Domonic L.", f, age_grp, c(21:30),
                    type = "bat", stat = "woba", wt_power = 500)
x1$warnings # so no serious problems
## simplifying
x2 <- sim_age_curve("Brown; Domonic L.", f, age_grp, c(21:30),
                   type = "bat", stat = "woba", simplify = T)
x2$warnings # may be a better approach

## pitchers
load("H:/simScoresApp/p-comparison-app/pit_simscore_data.RData")
wts2 <- c(throws = .01, ip = .62, k.9 = .83, bb.9 = .83, hr.9 = .91, babip = .55, fip = .35)
m <- age_comps("Buchanan; David A.", age_grp, wts2, type = "pit")
b <- sim_age_curve("Buchanan; David A.", m, age_grp, c(23, 28),
                   type = "pit", stat = "fip")
b$warnings #Hooray!