## Statistical proof that Tiger Woods of 2013 is the same as Tiger of 2000

USA TODAY Sports

In case you haven't noticed, Tiger Woods is having a historically significant 2013 on the PGA Tour. SB Nation golf writer Adam Fonseca crunches some numbers to prove this significance.

Every so often, I get this hankering to put on my Statistics Cap -- which looks a lot like a baseball cap, but with more decimals -- and play around with golf data. Admittedly, I am a huge golf nerd that should be doing more with his time, like fighting crime or saving the world. But that's not any fun, at least not to me.

Over the weekend, I found myself locked in (yet) another conversation about whether Tiger Woods is "back," whatever the hell that means. My opinions on the matter have been well documented in this space, so I'll leave those articles to speak for themselves. Still, one question that came up during the course of conversation struck a chord with me:

"I bet that if you compare Tiger from 2000 to Tiger of 2013, you'll see he was a better player back then. Right?"

This question touches on something statisticians call the null hypothesis, which assumes there is no statistically significant difference between Tiger of 2000 and Tiger of 2013. The person above believes there is a difference, which means he subscribes to the alternative hypothesis (i.e., there is a difference).

If you choose to answer the above question from a high level, thus remembering that Tiger won an astounding nine tournaments in 2000, you'll probably agree with the statement that there is a difference between Tiger of 2000 and Tiger now. After all, people recall information from the past in clusters. It's just more intellectually efficient to group past events together for easier recollection instead of remembering, "Hey, Tiger's average score was blah blah blah that year ...".

However, when you compare Tiger's individual performance in the four tournaments he's won before June in both years, something interesting happens. Allow me to explain.

First and foremost, the best statistical analysis of Tiger Woods I have probably ever seen came from Grantland's Bill Barnwell in 2012. In his work, Barnwell used something called the Z-Score to show exactly how dominant Woods has been throughout his career in comparison to the other players in each tournament field. Woods was not only statistically better than his peers, he was significantly and historically better. I highly recommend reading Barnwell's analysis. It's downright fantastic.

The only element of the above study's work that left me uneasy, however, was that Z-Scores rely heavily on the performance or value of other variables in a sample population (i.e., Tiger's Z-Score is influenced by the performance of other golfers in the same tournament). The Z-Score doesn't speak to how Tiger compared to himself in past years, specifically. That brings me back to the aforementioned question of Tiger 2000 vs. Tiger 2013.

For the sake of simplicity, I went back and gathered individual round data (his scores from each round) from each of Tiger's first four victories in 2000 (Scores A in the chart below) and 2013 (Scores B). That gave me 16 data points from each year for a total of 32 individual values. I decided to omit any data related to driving accuracy, birdies made or anything other than strokes related to par. After all, the only stat that matters at the end of the day is how many strokes it took you to finish a golf hole, right? Right.

Using a statistical tool called a 2-Sample t-Test, which measures two different samples to see if there is a statistical difference between their averages, I was able to calculate another fancy statistical term called the P-Value. This value is defined as the probability that the observed results could occur when the null hypothesis is true (i.e., if there was no difference between Tiger then and now, his average tournament scores would be statistically similar). If the P-Value is greater than 0.05, then there is no statistical difference between the two samples. I also drew up a few graphs for the sake of a visual representation.

What I discovered was a P-Value of 0.739, which is significantly higher than the 0.05 threshold. This means that not only is there no difference between Tiger's individual performances in tournament victories between 2000 and 2013, they are close to identical.

I would be remiss to not admit there are a few biases in the above comparison. First, I only compared Tiger's individual performances during actual victories in 2000 and 2013 and not all tournaments. That was done purposely to point out that when Tiger is winning, he truly is the same player now as he was some 13 year ago.

But, just for funsies, I decided to run the data on all of Tiger's scores up until May of both 2000 and 2013.

As you can see, there was still no statistical difference between Tiger's total tournament scores from 2000 when compared to those from 2013. Not only is he the same player when he is winning, he's also statistically the same player when he loses.

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