The Olympics is, at least for some observers, a competition between countries for medals. Now that the Beijing Summer Games have ended, which country won that competition? It depends on how you count ∪ and there are lots of different possible ways, and winners, including the U.K., Zimbabwe and Kenya.

As noted here last week, China was well ahead in the gold-medal tally, but trailed the U.S. in total medals. That trend held, as China finished with 51 golds and 100 total medals, compared to 36 and 110, respectively, for the U.S. That marked just the fourth Summer Olympics with a different leader in each category (in the prior three the U.S. led in golds but trailed in total medals), and just the fourth time the leader in gold medals had more golds than bronze and silver combined.

Though the U.S. had been aided in those three prior anomalous Olympic medal tables by an emphasis on gold, most recently in 1964, this year U.S. Olympic Committee Chief Executive Jim Scherr offered a novel metric: 'More individual U.S. athletes will carry home gold medals around their neck than any other nation, if you want to count it that way.'

I want to count it that way, if only to see how that shuffles the leaderboard. And Mr. Scherr is right; by that measure ∪ which awards 24 gold medals to the triumphant men's and women's basketball teams, even though each of their wins counts only once in the official tables ∪ the U.S. leads all nations in gold medals by a hefty margin, with 125 to China's 74. (Russia and Germany trail with 43.)

But such a measure also produces some anomalous results. For instance, Italy won eight golds and 28 total medals, many of them in individual events. Argentina won just two golds and six medals, by conventional counts, but passes Italy in both categories, thanks to its medals in men's basketball, men's soccer and women's field hockey. Similarly, Australia leapfrogs Russia and Great Britain to rank third in total medals, thanks to its medals in women's basketball, softball, women's water polo, men's field hockey and several swimming relays.

Here are some other possible ways to rank Olympic countries:

Weighted scoring: Rather than choose between golds and total medals, why not incorporate both? In 1908, gold was worth five points, silver three and bronze one. By both that measure and an alternate system of three for gold, two for silver and one for bronze, China edges the U.S., with the rest of the top of the leaderboard mostly unchanged.

Showing improvement: Compared to its medal haul in Athens in 2004, China had the biggest absolute gain, with 19 more golds and 37 more total medals. On a percentage basis among countries with at least 10 medals this time around, China remains among the biggest gainers. Jamaica added 120% to its five medals in 2004, and Kenya doubled its prior count of seven. In golds, the most remarkable percentage gains among countries with at least five was Kenya's increase from one to five and the U.K.'s, from nine to 19.

Adjusted by population, GDP: The Bahamas earned two medals ∪ or nearly six for every one million residents. And Zimbabwe won four medals, or more than six for every $1 billion in GDP. The Wall Street Journal ranked countries by both measures, as did Simon Forsyth, a researcher in Brisbane, Australia. His GDP and population numbers are different, but he gets the same leader in each category.

Compared to expectations: Several researchers ∪ at PricewaterhouseCoopers, Dartmouth and Colorado College ∪ projected the medal count based on factors such as population, GDP and prior performance. They didn't project results for every country, but for those countries that had at least one projection, I averaged the expected totals to find which countries did better than expected.

Here, the U.K. was the winner in absolute terms, exceeding the average forecast for total medals by 18, and gold-medal forecasts by 12.5 (not everyone forecasts gold medals). China ranks second, in part because it got credit in the projections for hosting the Games, which tends to boost medal counts. In relative terms, the U.K. wins with its gold-medal haul, while Kenya exceeded expectations of two medals by 600%.

至少对一些观察人士来说，奥运会就是各国之间的奖牌争夺战。随着北京奥运会落下帷幕，赢得这场争夺战的又是哪个国家呢？这要取决于你怎么去算──可能的计算方式有很多种，由此得出的赢家也各不相同，英国、津巴布韦和肯尼亚都有问鼎可能。

正如我们上周所指出的，中国的金牌数量遥遥领先，但奖牌总数却落后于美国。这一趋势持续了下来，中国最终获得了51块金牌，奖牌总数为100枚，而美国的金牌和奖牌数分别为36和110枚。这是奥运会历史上第四次出现金牌和奖牌榜榜首不一样的情况（在前三次中，美国金牌数领先，但奖牌数落后），也是第四次出现金牌榜榜首的金牌数超过其银、铜牌数量之和。

虽然在前三次奥运奖牌与金牌榜排名不一致时，美国都是以金牌取胜（最近一次是在1964年奥运会），但今年，美国奥委会首席执行长吉姆·谢尔(Jim Scherr)提出了一个新奇的衡量标准：脖子上挂着金牌回国的美国运动员人数将超过任何其他国家，如果你愿意这样算的话。

我想这样算，只是为了看看这样会让榜单名次发生什么样的变化。谢尔说得对；按这个标准──夺冠的男、女篮球队获得了24块金牌，不过在正式的排行榜上只能各算一块──美国的金牌数量远远超过别的国家，达到125枚，中国为74枚（俄罗斯和德国各43枚）。

但这样的计算标准也产生了一些反常的结果。比如说，意大利赢得了8块金牌、28块奖牌，其中许多都是单人赛事。阿根廷以传统方法计算只赢得了两块金牌、6块奖牌，但如果按夺牌人数算，阿根廷在男篮、男足和女子曲棍球上都收获了奖牌，因此其金牌和奖牌数两项都超过了意大利。同样，由于澳大利亚在女篮、女垒、女子水球、男子曲棍球和几个游泳接力项目上夺牌，其总奖牌数也超过了俄罗斯和英国，位列第三。

以下是其他一些给奥运参赛国排名的方式：

加权打分法：与其在金牌和奖牌数之间选择，为什么不将二者合并呢？1908年奥运会上，金牌算5分，银牌3分，铜牌1分。还有一种算法是金牌3分、银牌2分、铜牌1分，以这两种方法计算，中国都领先于美国，而排名前列的其他国家位次大都没有变化。

按成绩的进步程度：与2004年雅典奥运会收获的奖牌相比，中国奖牌数的绝对增长是最高的，金牌数增加了19块，奖牌增加了37块。在本次获得10块以上奖牌的国家中，按增长的百分比算，中国也名列前茅。牙买加的奖牌总数较2004年的5块增长了120%，肯尼亚则在上一届的7块奖牌基础上翻了一番。在金牌方面，获得5块以上金牌的国家中，增长百分比最高的为肯尼亚（从1块增加到5块）和英国（9块到19块）。

以人口和国内生产总值(GDP)计算：巴哈马群岛获得了两块奖牌──折合下来相当于每一百万居民近6块奖牌。津巴布韦赢得了4块奖牌，相当于每10亿美元GDP合6块多奖牌。《华尔街日报》以这两种标准对参赛国排名，澳大利亚布里斯班的研究人员西蒙·福赛思(Simon Forsyth)也进行了同样的排名。他的GDP和人口数据有所不同，但领先的国家还是一样。

与预期比较：普华永道(PriceWaterhouseCoopers)、达特茅斯学院(Dartmouth)和科罗拉多学院(Colorado College)等一些研究机构根据人口、GDP和历史表现等因素对奖牌数作了预测。他们没有预测每个国家的成绩，但对于至少有一项预测的国家，我计算了预测的奖牌平均数，看看哪些国家的表现好于预期。

以绝对数量计算，英国是赢家，奖牌总数超过预测平均值18块，金牌数超出12.5块（并非所有机构都预测了金牌数）。中国名列第二，部分原因在于其因举办奥运会而在预测中得以加分，东道主的奖牌数量一般会有所增加。按相对增幅算，英国的金牌数领先，而肯尼亚比预测的两块奖牌超出了600%。
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