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Bauxite rabbit has penned an article projecting the Jays performance. Let him know what you think in the comments.

With no shortage of opinion on the Jays’ direction this off-season, is it possible to develop a common view of the team and potential roster decisions? To further the conversation, I simulated the 2018 season using a model that accounts for variable player performance. Simulate next season 100 times and you get team win probabilities. I won’t oversell the results, but I think this type of tool helps evaluate where we stand and the key choices ahead. Here’s a simple explanation of what I did and what it means.

From 2015 to 2017, Toronto was great (93 wins), good (89 wins), then bad (76 wins). Did they underperform last year or are the current Jays just bad? To examine this, I built an excel spreadsheet to predict team wins based on individual player performance. Using our current roster, I projected playing time and production for each player (at bats & OPS for hitters, innings pitched and ERA for pitchers). The resulting team OPS and ERA numbers were translated into runs for/against using simple formulae, and wins/losses calculated with the pythagorean formula. My ‘best guess”, or base case, predicts 80 wins. To understand the model’s sensitivity, I created two other scenarios. Here are the results, along with the past 3 years for comparison:

base:           80 wins	  (706 OR, 723 DR, .729 OPS, 4.13 ERA)
optimistic:    102 wins   (806 OR, 617 DR, .776 OPS, 3,53 ERA)
pessimistic:    57 wins   (603 OR, 815 DR, .628 OPS, 4.66 ERA)

2017:         76 wins    (693 OR, 784 DR, .724 OPS, 4.42 ERA)
2016:         89 wins    (759 OR, 676 DR, .755 OPS, 3.79 ERA)
2015:         93 wins    (891 OR, 670 DR, .797 OPS, 3.81 ERA)

It’s interesting that the optimistic and pessimistic cases produce such widely different results when both are driven by quite reasonable assumptions (Smoak repeats, Estrada bounces back, Sanchez/Tulo/Travis are healthy VS Smoak reverts, old players get old/injured, …). This highlights how fans often see what they want and why static projections have limited value: it’s unlikely that key players all simultaneously outperform, under-perform, or meet expectations. Like calling “heads” on a coin flip 10 times in a row (1 in 1000 odds), it’s not going to happen. Instead, each player will fall somewhere within their own upper and lower bounds of performance, creating a mix of individual outcomes across the team. It follows that team predictions incorporating this player variability would better assess potential.

Because of this, I expanded the model to individually simulate each player’s performance, randomly selecting optimistic, base, or pessimistic outcomes using related probabilities. This way, each simulated “season” incorporates a different mix of players performing above or below expectations … just like it happens in a real season. Simulating a large number of games then produces something really useful: a range of probabilities for specific win levels. Over a 100 season simulation, the model predicted the Jays would win 85 or more games exactly 4 times (4%) and 88 or more games just once (1%). Matching these win probabilities to Wild Card cut-off levels shows the current roster has about a 1% chance of making the playoffs in 2018.

The calculations are simplistic (OPS & ERA instead of WAR) and the player projections are mine alone, but the model is revealing - too many things have to go right for the team to succeed - and helps us see the team for what it is. More importantly, this is just the start of what can be examined. With the current roster lacking, what trades and free agent signings are needed to reach a 50% playoff probability, and how would the associated cost in payroll and prospect talent impact 2019 and 2020? More generally, how do different asset management strategies compare, especially when assessed across multiple seasons, where the costs of “win now” versus “win later” can be properly evaluated? With baseball run more and more by MBA bean-counters, and talent increasingly valued in similar ways, I’m sure many teams have tools to quantify these exact types of trade-offs.

Thanks rabbit for the post. If anyone else wants to write an article for the site, just email roster at batters box dot ca.

Guest Post: Projecting The Jays | 23 comments | Create New Account
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lexomatic - Thursday, January 04 2018 @ 09:43 AM EST (#352073) #
Interesting, but I think the optimistic and pessimistic projections are misnamed. They seem to be many standard deviations from the base, and more like best case and worst case.
Maybe Rabbit can comment a bit?
I used to do lots of BROCK2 projections, which was fun, but not super accurate.  I also stopped in 2013, so I'd have to start from scratch and that's a pain.

bpoz - Thursday, January 04 2018 @ 10:11 AM EST (#352076) #
Thank you rabbit for your effort.

Too many unknowns in baseball. None of the 3 years were reasonable or predictable in reality.

2015 had a great offense which produced many laughers in our favor. But it had cold spells. This team was 2 games over .500 on July 31. Then went on a .700-.800 winning percent. Overly lucky IMO. That was the year Stroman was injured in ST. So we would have been comfortably better on July 31.
Let me make this long story even longer. I believe the closer was to be Sanchez but the Stroman injury made Osuna the closer. I cannot remember why Sanchez made only 11 starts of 41 appearances.

2016 rotation was injury free.

You have covered all the possibilities for 2018. I expect a record between 57-102 wins. The "how" it will achieved should be interesting. Especially if it is at the pessimistic or optimistic level.

2017 the only good thing to happen was the overall performance of the pen.
GabrielSyme - Thursday, January 04 2018 @ 11:41 AM EST (#352079) #
One thing projection systems don't do well is express the reasonable range of outcomes, so I'm not sure what rabbit's likelihoods are for the pessimistic and optimistic scenarios.

Another idea I had is back-projecting seasons. Given what we know about all the players 2017 performance, this would give a good idea of whether the team was lucky with injuries and over- or under-performance. Basically, it would be a 2018 projection for the 2017 roster but minus the aging curve.
lexomatic - Thursday, January 04 2018 @ 12:03 PM EST (#352082) #
I'm home sick, so I decided to do some Brock2 to supplement this. No pitching, just hitting.
This is a test to see if I can get a table going using tableizer. Edit it doesn't work. Can we actually get a how to for tables on this site? I know it's been asked for before, but it's frustrating that I can't do things here that I can elsewhere.

bpoz - Thursday, January 04 2018 @ 02:20 PM EST (#352085) #
That is a good thought GabrielSyme.

For 2017 numbers.Smoak and Bautista stayed healthy. But Smoak rose to the challenge and Bautista could not. I don't have much of a problem with Morales. Donaldson produced very well but missed 150-200 ABs. Also when he came back Gibbons nursed him back with frequent off days. Martin, Tulo, Travis and Sanchez missed enough for the team to head towards the pessimistic record. The bullpen really rose to the optimistic level. Liriano underperformed, Biagini I don't know. Latos etc ... gave their best but those results were reasonably expected.

I thought Goins did really well for a bench player pressed into a full time role. Maile should be a prospect. He was rushed and needs AAA ABs.
John Northey - Thursday, January 04 2018 @ 05:28 PM EST (#352088) #
1% shot at 88 wins sounds pessimistic to me but I'm always the optimist here. I can see why it is so hard as you need good health from one of Travis or Tulo at least and right there the odds are low. If one goes down you can hope the new kid, Aledmys Diaz, does the job he did 2 years ago and not last years mess.

I'd say the keys are pitching (Sanchez/Stroman/Happ/Estrada being healthy and effective), and kids (Diaz in infield, Alford in OF who I figure will win one of LF/RF in spring).
BlueJayWay - Thursday, January 04 2018 @ 05:58 PM EST (#352089) #
1% chance for 88 wins can't be right. Maybe that's supposed to be 98 wins?
Michael - Thursday, January 04 2018 @ 07:23 PM EST (#352091) #
This is inaccurate because it is using Pythagoras to go to win totals. To show why, consider the Jays true talent was .500 with a 50/50 chance of winning any game. If this were true, the Jays would still have better than 15% chance of 88+ wins (binomial distribution). The luck or variance in baseball is enough that 1% playoff chance is way too low for any but the absolutely most hopeless teams (and even those might well have 1% or better chance).
Richard S.S. - Thursday, January 04 2018 @ 08:49 PM EST (#352092) #
Marcus Stroman, J.A. Happ and Marco Estrada should win 35-45 games next year without a disaster looming, but factoring in ability and luck. Defense should be much better. Bullpen always average 20-35 wins factoring in ability and luck.

Two things can increase these numbers:
1) Which Aaron Sanchez shows up, the healthy one or the blister issue? Healthy he could easily win15-20 games.
2) Who is the 5th Starter? The caliber of that choice could win the A.L. East or finish out of the Playoffs again.

How could could the Jays be in 2018? Projections are fine when you are working with a finished project. The farther you are from the “finish”, the less accurate the numbers can be. Winning the A.L. East means beating New York and Boston, and that could be done with as few as 92-93 games. Just getting in could be as little as 83-88 games depending on the field. Until something happens, it’s hard to say what to expect.
Richard S.S. - Thursday, January 04 2018 @ 10:22 PM EST (#352094) #
Possible additions to the Baseball Hall of Fame are:
Chipper Jones at a tentative 98.9%;
Jim Thome at a tentative 94.5 %;
Vladimir Guerrero at a tentative 93.9%;

Edgar Martinez at a tentative 81.2%;

Trevor Hoffman at a tentative 78.2 %;
Mike Mussina at a tentative 73.9%.
rabbit - Saturday, January 06 2018 @ 12:08 PM EST (#352114) #
Thanks to Gerry for posting my note and to everyone’s comments. I’m a long-time baseball fan and have enjoyed this site for many years before deciding to join the conversation. Here are some notes in response to people’s questions/comments:

Per lexomatic, I agree the projections are misnamed as they truly are best and worst cases and several SD from the norm. In my excitement over the idea and creating the tool, I was thinking upper and lower bounds without labeling them as such.

Per gabrielsyme, I used simple probabilities for each player (20% optim, 60% base, 20% pessim). A more refined version should have a range of of possibilities for each player as well as specific probabilities for each player’s outcomes.

Per bluejayway, the model does indeed show that 88 or more wins has only a 1% probability. More on that below.

Per michael, your observation is insightful and something I hadn’t thought of. It’s true that a team with a 50/50 chance to win each game would have a 1% chance to win 88 or more games. Playing with the binomial distribution shows that teams with a 1% chance at 88+ wins are bad but not quite horrific (73 wins or worse, equivalent to 45% chance per game).

Anyway, this really made me think - what causes the huge difference between 1% (my model) and 15% (binomial)? I checked the model calcs, ran another 100 games / achieved the same general results, checked the random number generator to make sure it was working, then broke down the model to look at sensitivities. This is where I figured out the difference. The binomial formula assumes the same performance each trial and runs multiple trials, but baseball works the other way: individual performance (which varies) produces runs which generate wins. In effect, the team performance level determines win probabilities (the model), not the other way round (binomial).

Here’s another way to look at it. The binomial formula assumes you flip a coin 162 times - how many times do you get 88 or more heads? 15%. My model, in contrast, has 24 players that are effectively 3-sided coins (optim, base, pessim) - to hit 88 wins you need about 8 more “optim” players than “pessim” (players having good seasons vs players having bad seasons). I played with the model to see this and it makes sense at a broader level (same number of pessim & optim players cancel in terms of impact above the base, each optim greater than pessim generally adds 10 runs over base projections, need about 10 runs for each extra win). Returning to our 3-sided coins and looking at the odds of hitting 8 more “optim” players than “pessim” (using the binomial formula!), we get probabilities in the 1 or 2% range (if 12 coins are base then 12 remaining coins, if 10 or more of these are optim -> gives prob of 2%; if 14 coins are base then 10 remaining coins, if 9 or more of these are optim gives prob of .5%). And this is the range of model predictions.

So, a simple way to look at the Jays is to compare how many players exceed expectations vs fall short. The model is simple and could be improved lots of ways, but I think this approach captures the reality of how teams do well (or badly) based on good (or bad) seasons from multiple players. It’s easy to be optimistic (Sanchez healthy, Stroman is the man, Biagini is decent, …), but I think it’s fair to say that given past injuries and aging players, the odds of enough things going right (and not wrong) to make the playoffs are low. Like in the 1% range.
lexomatic - Saturday, January 06 2018 @ 04:18 PM EST (#352120) #
Like I said, I've been super sick.
I have done a TON of projects using the old Brock2 system (it should still be freely downloadable if anyone wants to search... or look for an old copy of Bill James' 84 annual which has the explanation in the back. I gave mine away to value village).
Anyway. I'm uploading the files as PDF if anyone wants they can grab them and I'll post the link here.
PDF1 2018 Jays current roster, some possible minor league call-ups
PDF2 2018 FA projections for OF and IF types.
I didn't bother including multi-year projections for the big free agents, you can do stuff on your own... it's not hard.

lexomatic - Sunday, January 07 2018 @ 01:51 PM EST (#352185) #
So I thought I'd rescue this from the Solarte trade thread.
Here's a PDF printout of a few FAs (some no longer relevant with the Solarte trade) and then the current roster and a few prospects.
FYI Urena, Guerrero Jr and Bichette don't have enough experience for Brock 2 to work. Gurriel doesn't really either.
I took the lazy way out for established players with split seasons (e.g I didn't include Barney's AAA numbers) and didn't include minors numbers.
Minor leaguers get heavily discounted.
I need to update the spreadsheet for a few things.
Here's the link for the flie
lexomatic - Sunday, January 07 2018 @ 02:16 PM EST (#352186) #
Hold off a bit, I noticed I forgot 1 field that changes stuff. I'll have to redo stuff.
bpoz - Sunday, January 07 2018 @ 07:56 PM EST (#352195) #
Thanks rabbit and lexomatic for all your work.

I really appreciate the work and effort of all the Bauxites. Great bonding.
christaylor - Sunday, January 07 2018 @ 10:39 PM EST (#352197) #
Oh. That's what the Brock2 system is (see my comment in the other thread) -- yikes. Abacuses are fun, but people ought to put away their abacuses for a reason.

Thanks for the clear article rabbit, I look forward to reading more in the future.
lexomatic - Tuesday, January 09 2018 @ 04:26 PM EST (#352260) #
Hey Chris,
Brock2 has it's moments (like predicting 59 HR for Stanton this year based on previous years and partial stats this year. That was a surprise (so are the 322 HR's Brock2 projects for the next 10 seasons). It's definitely not an abacus.
It's mostly fun for having multi-year projections when other systems don't share those... like when considering free agent acquisition or retention, or trade targets.

Anyway. I updated stuff (I forgot to input a "floor" value, sort of a positional adjustment which determines playing time. You must be "this" good to start at position X).
That's why Morales' playing time projection is halved, and Martin's in two thirds.
I took the time to add ROUGH wOBA wRAA and wRC wRC+ . I say rough because wOBA calculation requires HBP, IBB, SF which Brock2 doesn't track or generate.
I also scaled everything to the 2017 season instead of updating each season individually, because that would be more work with individual formulas for maybe 15 seasons. I'm not getting paid, so screw that.
Here's the updated link This one has a January date, so if I update things closer to the start of the season after any additions, you can tell.
If anyone wants the spreadsheet, I'll post it too.
I didn't check the order of the printouts I combined, so it starts with Free agents and 2018 projections, multi-year projections for a few players in discussion (not just for the Jays), minor league player projections - these aren't the greatest, because they're massively regressed below AAA), then the Jays as of this week.

Michael - Tuesday, January 09 2018 @ 11:02 PM EST (#352268) #
Rabbit, no disrespect intended because it is very nice to discuss research articles especially when news is slow, but your method is still wrong and will have drastically too small tails (too much near the average/median). Would you really want to lay 100-1 against the Jays winning 88 or more games? That is really not a good bet for you.

You are right that the iid (independent identically distributed) assumption is not accurate for lots of reasons (home away, opponents, different starting pitching, injuries, bullpen availability, mid-season trades and promotions, etc.), but it should be close enough to show you the problem.

A different way of looking at it, is your estimate of the players individually is an attempt to model the "true talent" of the Jays, but turning that true talent into wins and loses is not a guarantee automatic Pythagoras application. You still need to apply the randomness.

Consider a different perspective, you are estimating how many runs above replacement each Jay will score or how many runs the team will allow and score over the season. But if the answer is the Jays score 650 runs and allow 680 runs you are considering it guaranteed that they end up below 500 by the Pythagoras adjustment that is supposed to tell you their most likely result (I.e., their true talent) is below 500, but there are teams that are minus run differential but plus on W-L (as well as the reverse).

Again if the Jays true talent is most likely to be 500, that is 15% 88+ wins.

Btw, baseball prospectus does the same sort of estimates that you are doing with PECOTA percentiles and estimates teams from there, but they don't calculate the record the way you do, but simulate it, and you'll see the lower teams have non-trivial chances at the start of the year, *not* 1%.

I think if you did the same calculations for every team, especially considering the 2 wild cards, you'd be putting Yankees and Red Sox in the playoffs very close to 100% in your method, much closer than they really are.
bpoz - Wednesday, January 10 2018 @ 11:26 AM EST (#352276) #
This thread has generated a very good discussion. I love the fact that so many Bauxites have good understanding of projection systems.

We know that there are unpredictable variables. The main 2 being injuries and who gets injured. If it is Donaldson, Osuna or Martin, the replacement cannot replace them successfully or so I/we believe. I am sure that Donaldson's replacement will definitely not. Martin probably not, unless Jansen is very good. A tall order. Osuna maybe, if someone comes in and gets the 3 out save he is supposed to get. In theory it sounds possible but in practice it very often does not happen for various reasons. Timlin and Fraser and others I suppose could not do it.

Performance is the other big variable. Smoak out performed his expectations last year.

Grilli lost the set up job. He was given enough opportunity to not fail. That cost us games that we had a decent chance to win. Maybe 2 or 3 extra wins. We were lucky that Tepera or J Smith had immediate success or we would have lost more in the search for Grilli's replacement.
We also know Osuna's failure rate regarding saves.

Do any of these models predict/calculate failure rates? E Gagnon for LAD. WOW!!! No way that could have been predicted.
rabbit - Friday, January 12 2018 @ 10:48 AM EST (#352334) #
Michael, no disrespect taken. Because baseball is so numbers driven, it's easy to play with things and see what happens. Everyone here is very informed, so the conversation is always substantial.

I'm sure you're right, my projections/approach are flawed. But I'm not sure I agree with your reasoning. My 1% probability for 88+ wins does seem (really) low, but when I look at the numbers and what has to go right for that to happen, I don't know what's missing. I don't believe simulating wins as 162 50/50 coins flips is right - a team does not have a certain level of performance (e.g. a ".500" team) available every game. I think the 25 3-sided (or 4 or 5-sided) coins to simulate what each player produces, with runs and wins resulting from that, is closer to reality. What I'm trying to capture is the inherent variability players have around their "base" or expected performance level. I'm positive my mechanics and calculations are crude and imprecise, but the approach feels right.

Thanks for the PECOTA reference. Had not heard of those projections before and did a quick scan to better understand it. Very cool how much data is applied and that player simulation is used. Do you know how simulation is used to produce player projections and wins? I don't understand how they use simulation to get discreet numbers for players. Does PECOTA just make discreet projections or are there probabilities assigned to possible team outcomes? This is really interesting area and would love to learn more.
Michael - Sunday, January 14 2018 @ 04:48 AM EST (#352383) #
Ok, here's another set of experiments to show that randomness is much more than you are giving credit for in the outcomes.

Consider the 2017 Blue Jays. There actual record was 76-86. The scored 693 Runs and they allowed 784 runs. First of all, note that they actually scored those runs and the Pythagorean W-L given those runs scored and allowed would actually be 72-90. This is all available to see at

If in your experiments with the Jays you had a trial run with combination of optimistic, realistic, and pessimistic estimates that figured the Jays would score 693 and they'd allow 784 what would you figure the W-L would be? Pythagorean would say 72-90, but the actual was 76-86. If you don't allow those type of changes you aren't measuring it right.

More over, in baseball the amount of runs scored and the amount of runs allowed are mostly disconnected - other than the fact the game isn't allowed to end in these numbers being the same, essentially. That is, especially in the AL, because the competition between the opposing pitcher and our hitter is mostly disconnected between our pitcher and the opposing hitters, you could take the season and simulate it, except choosing the runs scored at random from the runs scored in any of our 162 games, and similarly taking the runs allowed at random from any of the runs allowed in any of our 162 games. This sort of re-sampling allows us to take the observed Jays quality of scoring and preventing runs, but through re-sampling get some feel for how lucky the Jays were based on sequencing (I.e., did they waste runs when not needed, or did they match a shutout to a game where they only scored 1 run). In our simulation if the random runs scored are more than the random runs allowed, that is a simulated winning game. If the random runs scored are less than the random runs allowed, that is a simulated losing game. If the simulated runs scored are the same as the simulated runs allowed, we'll flip a coin and 50% of the time it will be a win and 50% of the time it will be a loss.

Now I know that this isn't 100% accurate as there are some connection between runs scored and allowed due to things like home games versus away games, good teams often being good at both hitting and pitching and bad teams likewise often bad at both, players who are all glove and no hit will decrease both while the reverse will increase both, the types of relievers or baserunning strategy will depend on the closeness of the game, etc. But it is still a pretty effective way to take the observed Jays team from 2017 as the known quality and trying to see what randomness of sequencing of team runs scored/allowed could do to the number of wins the team makes.

Again, in 2017 the actual real life numbers were a Pyth 72-90, and an actual W-L 76-86, all based on 693 RS and 784 runs allowed. Since in our earlier posts we talked about a true talent .500 team being 15+% likely to win 88 games, I also thought we should see how often the simulated Jays would win 88 games. But also, since the actual 2017 Jays were a 76 W team, not an 81 W team, check how often they win 83 games (I.e., 88 W is 7 more than 81 W; 83 W is 7 more than 76 W). But also, since the Pythagorean 2017 Jays were a 72 W team, not an 81 or even 76 W team, I'd also check how often they win 79 games (I.e., 88 W is 7 more than 81 W; 79 W is 7 more than 72 Pyth W).

So I simulated 162 games a season as described, and simulated 600 such seasons and this was the results using the 2017 actual Jays runs scored and runs allowed per game as the inputs:

average 692.19 786.4533333 76.04333333
stdev 36.13156122 46.70853563 6.57496559
min 566 636 56
10th 648.9 727.9 67
25th 669 756 72
median 693 784 76
75th 716 818 80
90th 739 850 84.1
max 798 926 98
>=79? 222 37
>=83? 101 16.8
>=88? 24 4

As you can hopefully tell from the above table, this sort of simulation - again where the true talent of the Jays stayed exactly as 2017, and the likelihood of runs scored and runs allowed as a team in a given game exactly matched the distribution observed in 2017, still had a wide range of wins and losses possible. While on average with this sampling the Jays teams still scored 692 and allowed 786 and won on average 76 wins, you can see the variety of wins and losses are very, very wide. There was one of the 600 seasons with 98 Wins, and the worst season was 76 Wins. Note, in the table for the min/med/max and percentiles the table has the number for each of R, RA, W separately. I.e., the maximum number of runs the Jays scored in any of the 600 seasons was 798. The maximum runs allowed in any of the 600 seasons was 926. The maximum wins was 98. These 3 were, obviously, not in the same simulated season! For answering the threshhold, note that 222 times there were >= 79 wins, which is 37 percent. 101 times there was greater than or equal to 83 wins, which is 16.8%. 24 times there were >= 88 wins, which is 4%. And again, this is taking a team that Pythagerous said was only worth 72-90.

Hopefully this is more than enough to show you the power of randomness is really strong. In doing this I haven't made assumptions about any player being suddenly much better or worse then they actually were, I'm using the real data from 2017 and just resampling it.

But, just to anticipate a possible objection, because I was re-sampling with replacement, it is possible that some players will look much better, just from luck, because I may have taken their best 5 games 4 times each and their worst 20 games 0 times each - just by luck - and as a result that is why there is the widely different results and you may think this explains the difference. I.e., if the Jays win much more or less it must be because they score much more or less, and if they score much more or less it must be because the hitters hit better or pitchers pitch better. First of all, this doesn't need to be the case, as sequencing inside the game (I.e., if a player goes 1/4 is it the hit with the bases loaded or bases empty - that sort of thing is largely just random luck but has a big impact on scoring). But anticipating this possible objection I tried a different 600 sample.

This time, what if we said that we would just permute the runs scored and runs allowed so that each actual game's runs scored would be used exactly once in the simulation and similarly each actual game's runs allowed would be used exactly once in the simulation. Same rules otherwise about win if RS greater than RA, loss if RS less than RA, and flip a 50/50 coin when RS equal RA. So now in the simulation because each and every game is included exactly once, each Jays player line will be *exactly* what it was in 2017. Every hit, walk, out, RBI will occur the exact same amount in each and every simulated season as it occurred in actual fact in 2017. But still there will be a fair specturm of luck in the outcomes of the season. Showing the same stats as for the other simulation we get:

average 693 784 76.43
stdev 0 0 3.844441818
min 693 784 64
10th 693 784 72
25th 693 784 74
median 693 784 76
75th 693 784 79
90th 693 784 82
max 693 784 86
>=79? 171 28.5
>=83? 35 5.8
>=88? 0 0

Unsurprisingly the runs scored and runs allowed in every season is 693 and 784 because that was a rule of how we set it up. On average we still won 76 games. The standard deviation is about half of what it was in the selection with replacement model in this selection without replacement, and now the simulated seasons go from a low of 64 wins to a high or 86 wins. But we still have 171 or 28.5% of the time above 79 wins, 35 times or 5.8% above 83 wins, but don't reach 88 wins.

But this model constrains exactly each and every hitter and pitcher on the Jays to have exactly the same line they actually had in 2017. Moreover, it constrains the Jays as a team to have exactly the same runs scored and runs allowed - and even distribution of runs scored and runs allowed as they had in 2017. In actual reality for 2018 all of these are much more random than that and a vast source of possibility for the Jays to do much better (or much worse) than this 2017 estimate. But even with all of that constraining to essentially force things to be as much like 2017 as possible, there was still a span of 22 wins difference from the best and worst simulated season from this 600 season sample. 10% of the time the Jays beat their Pythagorean win percentage by 10 games.

Basically in reality the Jays you have to do something like the following:

Simulate who ends up playing for the Jays (health, trades, promotions, signings). Some randomness here (and tied to the results of some of the other choices - players who play worse more likely to be benched or cut, players who play better more likely to win more playing time).

Simulate how good each individual player ends up being in 2018. Lots of randomness here.

Simulate the offense for each of the games, which will be a sequence of each of the players, and do we get lucky or unlucky in bunching hits or in scoring. Some randomness here.

Simulate the defense for each of the games, which will be a sequence of each of the pitchers and opponents, and do we get lucky or unlucky in the opponents bunching their hits and scoring. Some randomness here.

Simulate how the offense and defense goes together in terms of doing we get just enough to win more often and getting blown out in losses or are we unlucky and have the reverse happen. Some randomness here too. I.e., what the second simulation.

To really know you have to simulate all of the opponents here, with all this randomness for each team in the league, and what ends up being the distribution of wins and losses in the various leagues and wild cards and what not.

The second simulation is really just doing that one random choice there. And even in doing that, the spread in the 600 seasons is 22 wins from best to worst and 10% of the time the Pythagorean win total is 10 wins less than the actual observed win total!

When you put all that together, if you think the true talent / most likely result / baseline is the Jays are an 80 win team (I.e., very close to .500), the this would be an even better team than that which was simulated here (which again was a Pythagorean 72 win team). So that team should do significantly better (some 4-8 wins better depending on if you compare the 80 win baseline to the 76 observed wins or the 72 deserved wins based on the 2017 numbers). When you add back in all the randomness from all the different sources this isn't that likely to make the average move much, but it is likely to make the standard deviation increase and make the tails (in both direction) more likely. So that 1% chance of 88+ wins is still way, way too small.
bpoz - Sunday, January 14 2018 @ 09:07 AM EST (#352386) #
Thanks Michael for all your work and theorizing. I could never do this kind of computer work myself. So I really rely on all the Bauxites.

Some very good points:

1) Bunching of hits.

2) Cito knew that a single was only equal to a walk with nobody on base. A walk at 1B followed by a single is an advancement based on the speed at 1st and the arm and location of the OF.

3) Runner in scoring position requires a hit more than a walk. The double play still lurks. Pitch carefully or use a walk to fill 1B and set up the DP.

4) All laughers influence Pythagoras more than the record.
rabbit - Wednesday, January 17 2018 @ 10:42 AM EST (#352550) #
Michael, very good analysis and I now understand. The Pythagorean formula gives a decent approximation of wins but cannot capture the randomness of how runs are bunched and the related impact on wins. This randomness must be incorporated into any projection of win probabilities. As you show, my 88+ win probability should be closer to 10%, not 1%. Version 2.0 is under development - thanks for your input.
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