Tuesday, July 15, 2008

Quantifying Dominance, Part 2: Winnings

With Paula Creamer validating her place in the LPGA's Big 3 and Suzann Pettersen winning again in Europe, now is the time to continue my series on quantifying dominance. Last month, I looked at wins and other finishes; today, I propose to look at winnings. There are some very simple numbers that can help us compare and contrast players between tours, generations, even eras--and answer the usual objections against using money as a measure of dominance. I'll use the examples of Lorena Ochoa, Annika Sorenstam, Paula Creamer, and Seon Hwa Lee, who together have won 14 of the 19 LPGA events in 2008, to demonstrate the usefulness of these figures for a single season.

Winnings Percentages (actual money won divided by total purses in events started and by total purses in all events): Career money lists are interesting to track, but their totals are relevant only for players in the same rookie class or perhaps three-year generation (at best), what with inflation, irregular growth of purses, and the rise and demise of various events. But these measures allow you to track how much of the pot a player has raked their way over the course of a career relative to actual purses and so compare players across generations and across tours. Comparing the two percentages golfer by golfer can help us determine, for instance, whether the modern limited-schedule approach leads to more or less dominance than in the previous generations.

On the LPGA, the 19 events played thus far this season have a total purse of $34.3M. Using the LPGA money list, it's easy to calculate overall winnings percentages for the LPGA's Big 4:

Lorena Ochoa .059
Annika Sorenstam .043
Paula Creamer .037
Seon Hwa Lee .029

Even the winningest players on tour have won less than 17% of the total purse thus far this season.

But what about in the events they've started? Here the percentages are quite a bit higher for Ochoa and Sorenstam, who have played several fewer events than Creamer and Lee:

Ochoa .085
Sorenstam .055
Creamer .041
Lee .035

So the LPGA's Big 4 still have won less than 22% of the purses in the events they've entered. This shouldn't be all that surprising, given that the typical LPGA first-place finisher takes home 15% of the total purse for that event (Inbee Park won almost 19% of the U.S. Women's Open purse). Which leads me to my next stat.

Winnings Rates (actual money won divided by winners' prizes in events started and by winners' prizes in all events): These may be the gold standard when it comes to money rankings, because you can't win more of the purse than what's set aside for the top finisher and you can't win what you don't play for.

As the most anyone could have won this season is $5,265,000, here are the Big 4's overall winnings rates:

Ochoa .386
Sorenstam .277
Creamer .239
Lee .189

The next winnings rate measures how efficient they've been at maximizing their returns on their investments in the events they've entered:

Ochoa .599
Sorenstam .371
Creamer .275
Lee .204

So how does Lorena Ochoa compare to Tiger Woods in these measures of dominance this season (total winnings percentage, winnings percentage in events entered, total winnings rate, winnings rate in events entered)?

Ochoa .059, .085, .386, .599
Woods .033, .141, .180, .783

Because there are so many more PGA than LPGA events and PGA purses are typically 2 to 4 times larger than the LPGA's, and because Tiger's played in half the number of events that Lorena has, it stands to reason that he's taken home a smaller percentage of the pot and is further from the perfect season of winning every event played (the 1st and 3rd figures). But as his worst finish this season is a T5, it makes sense that he's much more efficient than Ochoa at maximizing his winnings in events he's entered (the last figure) and hence has taken a larger portion of the pot from them (the 2nd).

Feel free to compare Annika Sorenstam and Kenny Perry, Paula Creamer and Phil Mickelson, Inbee Park and Stewart Cink, and Seon Hwa Lee and Anthony Kim (the rest of the LPGA's and PGA's top 5 money winners this season) using these figures. Heck, bring in the top 5 on every major tour, from the JLPGA, KLPGA, LET, and Futures Tour for the women to the various men's tours around the world. Compare season-by-season results and compile career records. Using such results, you can see clearly just how close the #2 is to the #1 golfer on each tour and hence get more precise when figuring out who the most dominant players in the world are and have been.


Hound Dog said...

Veddy interesting! I especially like the percentage of money won in the events the player has entered. Ochoa taking home nearly 60% of the money available in the events she's played is a great example of her dominant play - terrific stat. And much better than raw money totals to show the difference between players - note the distance between Sorenstam and Creamer.

The Constructivist said...

Thanks, man! Looks like I'll have a lot of fun this winter playing around with these figures....

The figures also help sharpen the debate about what constitutes dominance. Is Lorena more dominant than Tiger b/c she's taken more of the total pot and winners' share than he has, or is he more dominant b/c of his greater efficiency in the few events he's entered?

courtgolf said...

"Veddy interesting...but stupid. (MAN I loved Artie Johnson's characters on Laugh In !!) :-)

Anywho - it's not a huge statistical anomaly (a word I don't get to use very often), but are both tours using the same formula to figure payouts from a purse ? Smaller purses mean paying less at the top so the bottom players can make enough money to pay their bills. If one LPGA event pays more or less to the winner than another, then figures 2nd, 3rd, 4th differently, then the numbers are skewed not only from tournament to tournament, but from Tour to Tour.

Four of Tiger's six starts this year have come in short field events, where Ochoa has played mostly full field events - more players means lower percentages.

As cool as the numbers are - is there really a need to go any further than winning percentage followed by finishing position per event ? The dollars and cents seem to confuse the issue. Since Tiger has played in only 6 tournaments, won 4 and hasn't finished lower than 5th in any of them, and no lower than 2nd in a major - that kind of locks down the "dominance" issue (which leads into the ol' "what the heck is wrong with the rest of the guys on the PGA Tour ? Can't anybody stand up to this guy ?).

Ochoa, on the other hand, has won half of her 12 starts, won a major, and finished 3rd and T31st in the next two, with an 8th, 12th, and 6th in regular events.

NOW the question comes up - "would Tiger have the same percentages if HE had played 12 events in the same period of time ?" A question that can't be answered because of how they choose their schedules. (personally, I think Tiger is capable of keeping those stats up, but history says it isn't - nobody wins 2/3's of their starts - even Tiger Woods) Ochoa has to play more events to make the big bucks, plus she understands her importance to building the LPGA Tour - Tiger is playing for 2-4 times as much money everytime he tees it up, so he doesn't have to put himself out there as often to make the money - and his endorsements far outweigh his tournament winnings.

Am I picking nits ?

Hound Dog said...

You know, I've never looked at how the purses get divvied up. I know that the number of players who make the cut will change the lower end payout, but the champion's cut at equal-purse events seem to match.

I don't think you're picking nits (although I would rather you leave Tiger out of it - his numbers skew everything, and why does he ALWAYS have to be the definition of "dominant"?). I think we do need to quantify stuff instead of just relying on winning % and stating the number of Top 10s. That's the whole point of my rating system: to bring together several important stats, weigh them appropriately and let the result give us a composite picture of a player's talents without any other subjective influence.

courtgolf said...

Makes sense - but how can you write a definition of "dominant" and start anywhere other than with Tiger ?

Sounds like you checked the percentage of the purse that the winner gets from week to week. I guess it's just the spots below 1st that vary.

sag said...

One element your system seems to want to discern is which players tend do better at higher-purse events. I'm skeptical of that notion. Performance is more apt to vary based on how a player's skill set matches the particular course, or where the event falls in her performance cycle, etc.

If you're willing to agree with me that performance is generally independent of the purse, I'll offer a much simpler system for comparing the top players that should correlate well with what you're doing and also enable historical comparisons.

5 pts for each win, 3 pts for 2nd, 2 pts for 3rd (I chose those point values to be roughly proportional to the payouts for those finishes). Total that up and divide by the number of events started.

2008 year-to-date:

Ochoa 32/12=2.67
Sorenstam 23/13=1.77
Creamer 20/16=1.25

As you can see, the ratios between each player are similar to your numbers. Sorenstam is about 40% higher than Creamer, and Ochoa is a bit more than double Creamer.

No need to do all that research on the purse of each tournament. All the data points you need for previous years are in the grid at the bottom of each player's bio page on LPGA.com.

The Constructivist said...

cg and sag, I covered finishes in part 1 of this series--feel free to comment there. (next up is scoring.) I agree that both top 3s and average finishes matter, but since someone's already thought hard about money per finish, winnings can be a proxy for them (but definitely not a substitute). I haven't thought much about how to put together the 3 measures just yet, so thanks for your comments.

one thing I learned researching this post was that except for the US Women's Open so far, the winner's share of the purse on the LPGA is always 15%. don't know if that's standard across the tours.... this leads me to one correction to hd's 1st comment: Ochoa has taken home nearly 60% of the winner's share in the events she's entered this season. she's "only" taken home 8.5% of the available money--which makes Tiger's comparable stat even more impressive, given the max is somewhere around 15%....