Winning at Match Play vs. Stroke Play

[reidsou]

19 minutes ago, iacas said:

It did in later posts.

Plus one can still feel “easier” even if the math is similar.

The question dates back to Hagen’s PGAs.

I think I'm right about the literal answer to the question asked.

In the specific case of Walter Hagen or similar player the size of field still matters. Though I would think statistically that better players would be more likely to win when aggregating 4 rounds.  Tiger won 7 tournaments In a row one year. Byron Nelson won 11. 

Edited June 28, 2022 by reidsou
Correct the numbers of tournaments In a row

[iacas]

2 minutes ago, reidsou said:

I think I'm right about the literal answer to the question asked.

Cool? I wasn't talking about the question asked, and you were responding to a comment down-thread after discussions were had about it.

3 minutes ago, reidsou said:

In the specific case of Walter Hagen or similar player the size of field still matters.

Sure, but winning at match play when you're one of the better players is not a matter of "1/128." It changes.

4 minutes ago, reidsou said:

I remember Tiger won 6? tournaments In a row one year. Byron Nelson won 13?

There's a LOT more that goes into that than just field size.

[billchao]

Having not read anyone’s responses, I’m voting stroke play is tougher in both polls. You have to put up the best total score over four days out of the whole field.

In match play you only have to beat your opponent for the day. It doesn’t even necessarily take a great round to do it. Strategy can change if your opponent puts one OB, for example, then you can kind of play it safe and still win the hole.

[Golfingdad]

23 hours ago, boogielicious said:

I voted stroke play for both. In match play, you only have to beat one player at a time and for each hole, only best that player regardless of number of strokes. You both have the same conditions, wind, etc and you have the advantage of changing how your play based on what they do. If they hit it OB, you can play conservatively.

In stroke play, you are against the whole field. Some may have better conditions than you have at your time of play. The PGA this year was a good example where weather was a factor for roughly one half the field due to morning/afternoon differences. Also, you must try and score the lowest on each hole regardless of what your playing partners do. 

 

22 hours ago, GolfLug said:

Haven't three players won just about everything of importance in men's tennis in the last 20 years? Match play reduces luck factor as someone pointed out in a prior post. Stroke play is a simultaneous match play with everyone in the field... i.e. much harder to standout. 

 

I followed the directions of the OP and answered before reading anything ... and I went with match play being easier.  After reading the whole thread to this point, I would actually change my vote to them being equally hard with the same size field.  Everybody's answer is based on the perspective they chose.  A couple of examples that stood out are above:

In @boogielicious case in the bold above, you are choosing the perspective of the player who gets the bad weather.  But there is also an equal chance that some may have worse conditions than you.

And in @GolfLug's example, he is choosing the perspective of Federer, Nadal and Djokovic ... and yes, it's clearly been "easier" for those 3.  But what about the rest of the tennis pros out there?

From a logic/math perspective, this was a fun read.  Lot's of good points all around.

 

 

[iacas]

28 minutes ago, Golfingdad said:

I followed the directions of the OP and answered before reading anything ... and I went with match play being easier.  After reading the whole thread to this point, I would actually change my vote to them being equally hard with the same size field.

If you read all the posts, you'd know the question is really about the better player's chances of winning… which is tougher in stroke play.

IMO. 🙂 And perhaps mathematically.

Also, there are almost never 128-player match play events. 🙂

[mdl]

19 hours ago, Big C said:

Again - might be easier for some. Which means it must be harder for others. Saying it is universally easier is not mathematically possible.

Fair. The probabilities of each player winning better sum to one in both cases 😆

I think what I mean is to me it feels "easier" to win at match play because you aren't required to sustain as much constant excellence, both round to round and hole to hole.

I think what I'm saying is finishes should be better calibrated to skill in match play? Like, you don't have to go on a 72 hole heater to win. You just have to be able to win more holes than each opponent. That feels to me like it slightly reduces the element of luck in winning?

So to your point, I'm arguing win probs go up for the top half of the field and down for the bottom half. Winning for the bottom half of the field is always a crazy long shot. So fiddling with the order of magnitude on infinitesimal chances feels not super material, hence my saying match play is easier to win.

[GolfLug]

2 hours ago, Golfingdad said:

And in @GolfLug's example, he is choosing the perspective of Federer, Nadal and Djokovic ... and yes, it's clearly been "easier" for those 3.  But what about the rest of the tennis pros out there?

It's easy for the rest of them too. Easier for them to lose, that is... 😜

[iacas]

6 hours ago, mdl said:

I think what I'm saying is finishes should be better calibrated to skill in match play? Like, you don't have to go on a 72 hole heater to win. You just have to be able to win more holes than each opponent.

No, the opposite. Could I win a one-hole match against Rory McIlroy? Yes. Could I win over 72 holes? No. The shorter the time, the more luck plays a role.

[mdl]

19 hours ago, iacas said:

No, the opposite. Could I win a one-hole match against Rory McIlroy? Yes. Could I win over 72 holes? No. The shorter the time, the more luck plays a role.

I meant more what you were talking about in terms of the memorylessness of match play. Even a top player doesn't have zero chance of a blowup hole. Have too many of those (2? 3?) in a tournament and you're pretty much out of it. That's what I meant by you have to go on a 72 hole heater to win stroke play tourneys.

In match play each hole is a mini competition with no carry over. So you can think of a match as the mean outcome of 18 competitions. If you did stroke play tournaments also bracket style but just did 1 on 1 stroke play, then I'm less certain about which outcome would better reflect true player quality ranking. But stroke play tournaments are 72 hole sums. Sure the best players average better. But a few bad scores screws you. The difference in double bogey rate isn't that big between, say, 25th and 75th percentile. My contention is that the randomness of whether you have one too many blowup holes in a stroke play tournament means there's more luck involved in winning than there is in averaging per hole win probability over 18 draws 7 times (or however many rounds there is in match play).

[iacas]

2 hours ago, mdl said:

I meant more what you were talking about in terms of the memorylessness of match play. Even a top player doesn't have zero chance of a blowup hole. Have too many of those (2? 3?) in a tournament and you're pretty much out of it. That's what I meant by you have to go on a 72 hole heater to win stroke play tourneys.

In match play each hole is a mini competition with no carry over. So you can think of a match as the mean outcome of 18 competitions. If you did stroke play tournaments also bracket style but just did 1 on 1 stroke play, then I'm less certain about which outcome would better reflect true player quality ranking. But stroke play tournaments are 72 hole sums. Sure the best players average better. But a few bad scores screws you. The difference in double bogey rate isn't that big between, say, 25th and 75th percentile. My contention is that the randomness of whether you have one too many blowup holes in a stroke play tournament means there's more luck involved in winning than there is in averaging per hole win probability over 18 draws 7 times (or however many rounds there is in match play).

It's still backward, though. Luck plays a larger role in match play because the sample size is smaller.

[mdl]

17 hours ago, iacas said:

It's still backward, though. Luck plays a larger role in match play because the sample size is smaller.

I wish there were more than the Accenture so there were big enough samples for average world rank of winners in match versus stroke play tournaments. I see what you're saying in terms of 72 holes tightening the distribution of total/average score around a player's true average. But I'd contend that it's not clear that means stroke play tournament results are more correlated to total player ranking.

One way to think about is that to undo the damage from a double bogey in stroke play you need two good holes (birdies). In match play you only need one good hole. To me that makes it unclear whether the central limit theorem reduction in variance around a player's true average with a 72 hole sample is actually stronger in shrinking likely tournament rank towards real player rank than the 50% reduced penalty in a blowup hole but the increased variance of averaging only over 18 holes at a time.

[iacas]

6 minutes ago, mdl said:

One way to think about is that to undo the damage from a double bogey in stroke play you need two good holes (birdies). In match play you only need one good hole. To me that makes it unclear whether the central limit theorem reduction in variance around a player's true average with a 72 hole sample is actually stronger in shrinking likely tournament rank towards real player rank than the 50% reduced penalty in a blowup hole but the increased variance of averaging only over 18 holes at a time.

You're just making up scenarios. I could make up contrary ones. What if you make an eagle? It's just winning one hole, and it takes two bogeys to give that back, too. It's the same thing.

The sample size is smaller in match play (you win or lose daily, sometimes only over 14 holes), so over 72 holes there's a greater chance it evens out more. Over 14 holes, less chance it's close to even.

[jmanbooyaa]

Match play is more fun in my opinion.  Which adds nothing. Moving along.