What Does Pythagoras Say?

Monday, October 03 2005 @ 09:30 AM EDT

Contributed by: Magpie

There is a fairly predictable relationship between runs scored and allowed, and games won and lost. It does stand to reason, no?

Well, way back in the dawn of pre-history (I believe it was in the 1980 Baseball Abstract, to be precise), Bill James developed a very simple formula to derive a team's expected winning percentage, based on how many runs they scored and allowed.

This formula has been passed down to us through the years. It is known as The Pythagorean Method, and there is a pithy explication of it over at The Hardball Times:

     A formula for converting a teamís Run Differential into a projected Won/Loss 
     record. The formula is RS^2/(RS^2+RA^2). Teamsí actual won/loss records tend 
     to mirror their Pythagorean records, and variances can usually be attributed
     to luck.

Variances can usually be attributed to luck - because as a rule a team that wins more (or less) games than their run differential suggests does not make a habit of it. A team that is five games over one year is just as likely to be five games under the next year. There's nothing that suggests that it's a tangible ability, or the product of a style of play... it's mainly just random luck.

So what should the 2005 standings have looked like?

	        Expected                      Actual	    Difference
EAST	        W   L  PCT  GB   RS   RA      W   L  PCT	
Boston	       91  71 .561   -  910  805     95  67 .586    +4
NY Yankees     90  72 .558   1  886  789     95  67 .586    +5
Toronto	       89  73 .547   2  775  705     80  82 .494    -9
Baltimore      73  89 .454  18  729  800     74  88 .457    +1
Tampa Bay      63  99 .391  28  750  936     67  95 .414    +4
											
CENTRAL	       
Cleveland      97  65 .602   -  790  643     93  69 .574    -4
Chicago Sox    92  70 .569   5  741  645     99  63 .611    +7
Minnesota      84  78 .519  13  688  662     83  79 .512    -1
Detroit	       74  88 .458  23  723  787     71  91 .438    -3
Kansas City    58 104 .360  39  702  935     56 106 .346    -2
											
WEST		
LA Angels      95  67 .583   -  761  643     95  67  .586    0
Oakland	       94  68 .579   1  772  658     88  74  .543   -6
Texas	       82  80 .504  13  865  858     79  83  .488   -3
Seattle	       75  87 .464  20  699  751     69  93  .426   -6
											
2005 National League Standings														
EAST		
Atlanta	       92  70 .566   -  769  674     90  72  .556   -2
NY Mets	       90  72 .554   2  722  648     83  79  .512   -7
Philadelphia   90  72 .553   2  807  726     88  74  .543   -2
Florida	       79  83 .490  13  717  732     83  79  .512   +4
Washington     77  85 .474  15  639  673     81  81  .500   +4
											
CENTRAL		
St. Louis     100  62 .617   -  805  634    100  62  .617    0
Houston	       91  71 .564   9  693  609     89  73  .549   -2
Milwaukee      84  78 .520  16  726  697     81  81  .500   -3
Chicago Cubs   80  82 .492  20  703  714     79  83  .488   -1
Cincinnati     74  88 .460  26  820  889     73  89  .451   -1
Pittsburgh     71  91 .439  29  680  769     67  95  .414   -4
											
WEST	
San Diego      76  86 .470   -  684  726     82  80  .506   +6
LA Dodgers     73  89 .452   3  685  755     71  91  .438   -2
San Francisco  70  92 .431   6  649  745     75  87  .463   +5
Colorado       69  93 .424   7  740  862     67  95  .414   -2
Arizona	       64  98 .398  12  696  856     77  85  .475  +13
Yep, while the four NL post-season teams would be unchanged, the Yankees and White Sox would have missed the post-season, replaced by Cleveland and Oakland. (Note: the "winning percentage" given above is actually an expression of the relationship between runs scored and allowed. That figure is then multipled by 162 to produce the expected wins and losses, which are of course rounded off. And this is why the three 90-72 teams all have slightly different winning percentages. In case you were wondering!)

I think this is one of the two best reasons out there for Toronto fans to be waiting impatiently for 2006. (The other, of course, is the thought of Roy Halladay starting 33 games instead of 19. The Blue Jays had the best pitching in the divison by far even though Halladay missed the entire second half.)

Why did the Blue Jays miss their expected Won-Loss record by the largest margin of any team in the major leagues?

Well, no one really knows for sure. But we do know this. The Blue Jays went 16-31 in games decided by one run this past season. No team in baseball had a worse winning percentage in one-run games. If they had just broken even, if they had gone 24-23... we're looking at an 88-74 record.

A team's record in one-run games is also mainly a matter of random chance - it's not something that repeats year after year.

I promise to explore this specific subject at a later date. But for now, let's just take note of this. It is not the case that a team with, say, a superior bullpen does better in one-run games. The Cleveland Indians had arguably the best bullpen in the AL this past year, and they went 22-36 in one run games. That was the most losses by a single run in all of the majors, and an excellent reason to make them the pre-season favourite in the AL Central next year.

It is also not necessarily the case that a small-ball team - a team in the habit of playing for one run at a time - can be counted on to have a superior record in close games. It is indeed true that the team with the best record in one-run games this past season (35-19, .648) were the Chicago White Sox. The White Sox did lead the AL in sac hits, but they also hit more home runs than the Boston Red Sox. The Red Sox, who scored more runs than any team in the universe, had a record in close games (27-15, .643) almost as good as Chicago's. The best team in the NL (28-18, .609) in one-run games was the Arizona Diamondbacks, a team whose offense is built almost entirely around drawing walks and hitting home runs.

It might be a coincidence - but I doubt it. The two teams that won the most games over and above what their runs scored and allowed led us to expect were the Chicago White Sox and the Arizona Diamondbacks. Do not expect this pattern to be repeated next year.

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