Saturday, January 24, 2015

Pythagoras and the HarbourCats' playoff chances

Many years ago, Bill James created the Pythagorean Theorem of Baseball in an attempt to calculate a team’s expected winning percentage based on the number of runs scored and allowed during the season. He used the term Pythagorean Theorem because of its resemblance to the famous mathematical equation created by Pythagoras:
This equation has a variety of uses, although my favourite is to use the expected winning percentage in the middle of an MLB season to anticipate a jump (or drop) in the standings for a team that is winning fewer (or more) games than it really should. Teams may deviate from their expected winning percentage for a variety of reasons, although random chance is the most likely cause. Over a 162-game season, the average difference between actual and expected wins for a major league team is roughly three games.

After further study, statisticians found that the difference between expected and actual winning percentage could be further reduced by using an exponent of 1.83 (or 1.81) in the equation instead of two. However, many baseball web sites, including ESPN, still use James’ original equation. Using the improved version of baseball’s Pythagorean Theorem gives us the following numbers for the 2014 West Coast League regular season (teams sorted by actual wins):

                             Run        Exp. Win
Team           G   RS   RA   Diff. Wins Wins Diff.
Bellingham     54  276  195   81    37   35    2
Yakima Valley  54  326  236   90    35   35    0
Corvallis      54  319  230   89    35   35    0
Bend           54  316  274   42    31   31    0
Wenatchee      54  324  298   26    30   29    1
Walla Walla    54  350  357   -7    28   27    1
Medford        54  301  272   29    26   29   -3
Victoria       54  296  296    0    25   27   -2
Cowlitz        54  237  234    3    24   27   -3
Kitsap         53  266  319  -53    23   22    1
Klamath Falls  54  280  457 -177    15   16   -1
Kelowna        53  239  362 -123    14   17   -3

Baseball didn't exist in his time, but we're pretty
sure Pythagoras would have been a fan if it did.
As you can see from the last column in the table above, Bellingham had some luck on their side in compiling a 37-17 record, especially since their run differential trailed both Yakima Valley and Corvallis. The unluckiest teams in the league were Medford, Cowlitz and Kelowna, as all three teams won three fewer games than expected mathematically. Victoria scored exactly the same number of runs as they allowed, so their 25-29 record came in at two games below their expected mark.

The magic number of wins to get into the WCL playoffs is generally believed to be 32. So by how much do the HarbourCats have to improve in 2015 to become a playoff team? Yes, wise guy, seven wins is the obvious answer, but the Pythagorean Theorem of Baseball gives us a more granular look at the level of improvement required to get into the post-season.

Before we do that, it’s worth noting that the easiest way for the HarbourCats to get into the playoffs is to improve their pitching. Although the team finished seventh in the league in both runs scored and runs allowed in 2014, they were second in team batting average and tallied only 30 runs less than the second-best offense in the league (Yakima Valley). The Victoria pitching staff, on the other hand, gave up a whopping 101 runs more than the league leaders (Bellingham) and 60 more runs than the fourth-best pitching staff.

New head coach Graig Merritt won't accept 
another losing season in Victoria.
Let’s first assume that the HarbourCats offense scores the exact same number of runs this season as they did last summer (296). By how many runs does the pitching staff have to improve in order to notch 32 wins and (very likely) get into the playoffs? The answer is 50. That’s right folks, the team has to allow almost a run per game less this summer to make the post-season provided the offense scores the same number of runs. New pitching coach Alec Adame has his work cut out for him, but I wouldn’t be shocked if he can turn the trick.

Of course, there are many other combinations of runs scored and runs allowed that will get the team to the magical 32-win mark. For instance, they could score 20 more runs and allow 34 fewer, or tally 27 more and surrender 28 fewer. No matter how you slice it, the team needs to take a big step forward this season to even earn the wild card spot.

The HarbourCats have publicly expressed that their goal is to win 35 games in 2015. How much does the team have to improve in order to reach that lofty level? Just over half of their roster has been announced so far, but one of the more likely scenarios sees them scoring 27 more runs and allowing 60 fewer. In a short 54-game season, that’s certainly easier said than done. While I’m skeptical that the HarbourCats can go 35-19 this summer, I applaud the fact that they are setting their goals so high. We’ll get a better idea of the team’s playoff chances once we get closer to opening day, but right now their prospects have never looked better.

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