## Pages

### RPScore Ratings RPScore
• This is my best guess of each team's "true" record, or the record one would expect a team to post if it played an infinite number of games against a .500 team on a neutral field.
• Because the breadth of the distributions of its two components, Elo Win and Xº Win', RPScore is an average of the two components weighted by the other component's standard distribution.
• This ensures that neither component "outweighs" the other solely due to the breadth of their distribution.
• Since Elo Avg is seeded with projected team Wins Above Replacement, this has the effect of regressing early season ratings heavily towards preseason expectations.
• RPScore = ((Elo Avg * Elo WeightXº Win) / (Elo Weight + 1)) + Adjustment
• Elo Weight is the amount that Elo Avg is weighted against Xº Win to determine RPScore
• Elo Weight is based on the relative standard deviations of Elo Avg and Xº Win as well as how many regular season games have transpired.
• Elo Weight = (SD of all Xº Win' scores / SD of all Elo Avg scores)^((162 - regular season games played) / 162 + 1)
• Adjustment is the value that ensures that the average of RPScores equals .500.
• If the mean of all team RPScores deviates from .500, the difference between the initial mean and .500 is added to each final score to ensure that the mean of all RPScores.
Elo Avg
• Based on the Elo rating system most commonly used in chess, RP's version of Elo differs in several ways.
• First, my system uses Brandon Heipp's (cached) version (the second of his three) of David Smyth's Base Runs formula to predict the expected run differential for each game, calculates the Pythagenpat estimated win-loss record for that game, and then assigns a fraction of a win or loss to each team based on their Pythagenpat score. For instance, if the Nationals beat the Yankees 2-1,  would assign a full win to Washington and a full loss to New York. Instead, RP's system assigns them a fraction of a win based on their expected run differential if the two teams had played each other an infinite number of times.
• Second, my system adjusts for home field advantage (based on Matt Swartz's work) when calculating the expectation that either team will win the contest. The home team is awarded ~23 points for divisional match-ups, ~29 points for intraleague and ~35 points for interleague match-ups.
• Third, instead of starting each team out at 1000 at the beginning of the season, it adjusts their initial Elo to match a WAR depth chart where each team's expected total WAR is projected using Tom Tango's WARcel method.
• Starting Elo = ((Projected Team WAR + 52.8) / 162) * 700 + 650
• RP's Elo system assumes a K-factor of 8. This was arrived at by determining which K-factor produces estimations of next-game outcomes with the lowest Brier Score.
• The Elo Avg metric converts the Elo rating to a rate.
• Elo Avg = 1 / (1 + 10^((1000 - Elo Rating) / 400))
Xº Win
• This is the simple average of 0º Win, 1º Win, 2º Win and 3º Win. It is inspired by Baseball Prospectus' Hit List Factor.
• Xº Win = (0º Win + 1º Win + 2º Win + 3º Win) / 4
0º Win
• This is simple win percentage.
• 0º Win = W / (W + L)
1º Win
• Pythagenpat, developed by Dave Smyth and Patriot, is a method for estimating true record using runs scored and allowed.
• 1º Win = Scored^X / (Scored^X + Allowed^X) where X = ((Scored + Allowed) / Games)^.287
2º Win
• This is Pythagenpat estimated win percentage but with the run differential replaced with Base Runs differential. It is inspired by Baseball Prospectus' 2nd Order Win Percentage.
• Furthermore each of the component stats of Base Runs is multiplied by a decay factor, which intentionally underweights older totals at a rate of .998^day.
• For instance, a team's most recent one-game hit total (H0) would be H * .998^d = H * .998^0 = H * 1 = H.
• A team's hit total from 10 days ago would count for H * .998^10 = .980 * H = H10.
• A team's hit total from 100 days ago would count for H * .998^100 = .819 * H = H100.
• A team's hit total from n days ago would count for H * .998^n = Hn.
• The sum of a team's decayed hits over a season of duration n would be H0 + H1 ... H(n-1). We can express this as ΣH(0...n-1) or, more simply, Hd.
• As per David Smyth and Brandon Heipp, Base Runs = A *  B / (B + C) + D where, when using decayed stats:
• A = Hd + BBd - HRd - CSd
• B = 0.76*1Bd + 2.28*2Bd + 3.8*3Bd + 2.28*HRd + 0.038*BBd + 1.14*SBd
• C = ABd - Hd
• D = HRd
SOS
• This is the 2º Win of a team's opponents, weighted for frequency, discounting stats logged against the team in question, and adjusted for park effects on H, 2B, 3B, HR and BB.
3º Win
• This is 2º Win adjusted for strength of schedule (and, by extension, park effects). It is inspired by Baseball Prospectus' 3rd Order Win Percentage.
• 3º Win is adjusted for strength of schedule by multiplying the odds ratio of a team's 2º Win by the odds ratio of its strength of schedule.
• 3º Win = (2º Win / 1 - 2º Win) * (SOS / 1 - SOS) / (1 + (2º Win / 1 - 2º Win) * (SOS / 1 - SOS))
L7/L30
• Change in RPScore over the past seven or 30 days multiplied by 1,000.
• L7 = (RPScore0 - RPScore7) * 1,000
• L30 = (RPScore0 - RPScore30) * 1,000
• RPScore0 = RPScore at present; RPScoren = RPScore as of n days previous.
Luck
• This estimates how much better each team has performed relative to their RPScore.
• Essentially, I subtract each team's standardized 0º Win rate from its standardized RPScore and multiply that value by 100.
• Luck = (zt,W0 - zt,RP) * 100 where:
• zt,W0 is any team's 0º Win rate minus the mean 0º Win, multiplied by the standard deviation of all 0º Win rates.
• zt,RP is any team's RPScore minus the mean RPScore, multiplied by the standard deviation of RPScores.

Those who are interested in access to my data may request it via email. I download all of the data I use to calculate ratings via Zach Panzarino's excellent mlbgame package for Python. I encourage anyone with questions, comments or criticisms to share them in the comments below.