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Benefit Plans - Narrative (Details) | 12 Months Ended
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Oct. 03, 2020 USD ($) installment shares | Sep. 28, 2019 USD ($) shares | Sep. 29, 2018 USD ($) shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based compensation expense | $ 24,300,000 | $ 21,300,000 | $ 18,000,000.0
Deferred tax benefits recognized related to equity awards | $ 8,200,000 | 9,200,000 | 8,200,000
Employer matching contribution, percent of eligible earnings (up to) | 4.00% |  |
Amount of contributions | $ 9,800,000 | 9,300,000 | 8,100,000
SERP |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Deferred compensation liability | 12,600,000 | 12,100,000 |
Total value of assets held by trust | 12,600,000 | 12,100,000 |
Amount of contributions made to participants' SERP accounts | $ 700,000 | 600,000 | 1,000,000.0
Other Postretirement Benefit Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Term of deferred compensation agreements | 15 years |  |
Deferred compensation liability | $ 100,000 | 200,000 |
Total value of assets held by trust | 10,800,000 | 10,400,000 |
Amount of payments made to participants | 100,000 | $ 100,000 | $ 100,000
RSUs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Unrecognized compensation expense | $ 17,000,000.0 |  |
Unrecognized compensation expense, weighted average period of recognition | 1 year 3 months 18 days |  |
PSUs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Performance period | 3 years |  |
Payout, percent of shares granted | 100.00% |  |
Unrecognized compensation expense | $ 8,800,000 |  |
Unrecognized compensation expense, weighted average period of recognition | 1 year 9 months 18 days |  |
Vested (in shares) | shares | 100,000 |  |
Granted (in shares) | shares | 100,000 | 100,000 | 100,000
PSUs | Minimum |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting percentage | 0.00% |  |
Number of shares that may be issued (in shares) | shares | 0 |  |
PSUs | Maximum |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting percentage | 200.00% |  |
Number of shares that may be issued (in shares) | shares | 500,000 |  |
PSUs | Vest Based on Market Condition - Relative TSR of Common Stock Compared to Companies in Russell 3000 Index |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Payout, percent of shares granted | 148.40% |  |
Payout at target, TSR threshold percent of companies in Russell 3000 Index during performance period | 50.00% |  |
PSUs | Vest Based on Performance Condition - Three-Point Annual Average of Absolute Economic Return |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Payout at target, average economic return threshold percentage over performance period | 2.50% |  |
Options and SARs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Options and SARS granted in period | shares | 0 | 0 | 0
Fair value vested | $ 0 | $ 300,000 | $ 1,300,000
Total intrinsic value exercised | $ 10,900,000 | $ 2,400,000 | $ 10,900,000
2016 Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Maximum number of shares authorized under the plan (in shares) | shares | 3,200,000 |  |
2016 Plan | Cash Incentive Awards |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Long-term cash awards per employee that may be granted annually | $ 4,000,000.0 |  |
2016 Plan | Stock Options |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Number of annual vesting installments | installment | 2 |  |
Term | 10 years |  |
2016 Plan | SARs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Number of annual vesting installments | installment | 2 |  |
Term | 7 years |  |
2016 Plan | RSUs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Performance period | 3 years |  |
2016 Plan | PSUs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Performance period | 3 years |  |
2016 Plan | PSUs | Vest Based on Market Condition - Relative TSR of Common Stock Compared to Companies in Russell 3000 Index |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting percentage | 50.00% |  |
2016 Plan | PSUs | Vest Based on Performance Condition - Three-Point Annual Average of Absolute Economic Return |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting percentage | 50.00% |  |

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