Steamer Projections, Pythagorean Expectation and the AL Central

Most projection systems are out and some can be seen at FanGraphs, including Steamer, ZiPS, Oliver and even Fan predictions. I'm choosing Steamer because they seem to take playing time into consideration. Oliver gives every batter 600 PA regardless if they are a bench player or minor leaguer and ZiPS also over-projects playing time for bench/minor leaguers (for example, they project Steven Moya at 399 PA and Francisco Martinez at 479 PA).

Pythagorean Expectation is a formula developed by Bill James to show how many games "should" have been won based on how many runs a team has scored and allowed. The formula is:

Runs Scored^2/(Runs Scored^2 + Runs Allowed^2)

As can be seen, the similarity to the Pythagorean Theorem is the reason for its name. However, a more accurate formula is to use 1.83 as the exponent instead of 2. This is what Baseball Reference uses, so that's what I'm going to use for this experiment.

First, Steamer's projection for runs scored:

Miguel Cabrera 105
Ian Kinsler 92
Austin Jackson 88
Torii Hunter 80
Victor Martinez 69
Nick Castellanos 60
Jose Iglesias 58
Andy Dirks 52
Alex Avila 49
Rajai Davis 38
Don Kelly 26
Steve Lombardozzi 22
Bryan Holaday 18
Francisco Martinez 7
Jordan Lennerton 4
Ramon Cabrera 3
Hernan Perez 3
Total 774

Runs allowed is a little tricky, because they only show earned runs allowed:

Rick Porcello 77
Justin Verlander 76
Anibal Sanchez 75
Max Scherzer 70
Drew Smyly 55
Jose Alvarez 38
Bruce Rondon 25
Joba Chamberlain 24
Joe Nathan 22
Jose Ortega 22
Al Alburquerque 21
Evan Reed 18
Phil Coke 15
Luke Putkonen 13
Ian Krol 11
Casey Crosby 5
Kyle Lobstein 1
Justin Miller 1
Jose Valdez 1
Melvin Mercedes 1
Total 571

We need to convert this to all runs allowed. The standard is about 90% of all runs are earned, but the number has actually been higher over the last few years:

Year Runs Earned Runs ER/Runs
2013 20255 18750 92.6%
2012 21017 19341 92.0%
2011 20808 19067 91.6%
2010 21308 19629 92.1%
2009 22419 20779 92.7%
Total 105807 97566 92.2%

I'm going to use the five year average of 92.2%. 571/.922 = 619.

774 runs scored and 619 runs allowed gives a .601 winning percentage using the Pythagorean Expectation, for a win/loss record of 97-65. I've done the same thing for the rest of the AL Central:

Team Runs Runs Allowed W% Wins Losses
Tigers 774 619 0.601 97 65
Royals 721 639 0.555 90 72
Indians 672 622 0.535 87 75
White Sox 701 701 0.500 81 81
Twins 602 717 0.421 68 94

I could've ended it right there, but I wanted to see how much playing time was taken into effect. I added up the projected PA and IP and compared them to last year's totals:

2014 Projected PA 2013 PA Difference
Tigers 6247 6388 -141
Royals 6091 6093 -2
Indians 5711 6165 -454
White Sox 6038 6077 -39
Twins 5461 6212 -751

2014 Projected IP 2013 IP Difference
Tigers 1387 1462 2/3 -75 2/3
Royals 1282 1448 1/3 -166 1/3
Indians 1338 1441 1/3 -103 1/3
White Sox 1293 1455 -162
Twins 1382 1450 1/3 -68 1/3

As can be seen, they underestimated all around, although the Royals and White Sox' PA were pretty darn close. So how do we account for the lost playing time? To take the easy way out, I will assume a league average rate of run production. Basically, I took the same five-year league runs scored and divided it by league PA and IP to determine a league average rate:

2013 20255 0.109562 0.463997
2012 21017 0.114112 0.484762
2011 20808 0.112327 0.478044
2010 21308 0.114835 0.492041
2009 22419 0.119837 0.518095
Total 105807 0.114148 0.487335

So for the Tigers, I took the 0.114148 R/PA and multiplied it by the 141 difference to get an additional 16 runs scored (790 total) and the 0.487335 RA/IP and multiplied it by 75.66667 to get an additional 37 runs allowed (656 total). 790 runs and 656 runs allowed gives a new record of 95-67 using the Pythagorean Expectation. I did the same thing for the other teams in the AL Central:

Runs Runs Allowed W% Wins Losses
Tigers 790 656 0.584 95 67
Indians 724 672 0.534 87 75
Royals 721 720 0.501 81 81
Twins 688 750 0.461 75 87
White Sox 705 780 0.454 74 88

The biggest difference here is that the Indians are now in 2nd place instead of the Royals and the White Sox are now last instead of the Twins.

Of course, the Pythagorean Expectation doesn't always equal the real win/loss records. Take a look at last year's records:

Team Real W/L Pythagorean W/L Difference
Tigers 93-69 99-63 -6
Indians 92-70 90-72 2
Royals 86-76 87-75 -1
Twins 66-96 63-99 3
White Sox 63-99 67-95 -4

Going by Pythagorean W/L, the White Sox "should" have been ahead of the Twins by 4 games instead of behind them by 3 games.

Anyway, I just thought this would be a fun experiment.

This is a FanPost and does not necessarily reflect the views of the <em>Bless You Boys</em> writing staff.

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