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